The Collected Works of Tatsuo Tabata

INSTITUTE FOR DATA EVALUATION AND ANALYSIS TECHNICAL REPORT No. 22

The Collected Works of Tatsuo Tabata Volume 18 Atomic and Molecular Collision Cross Sections (3), 2002–2006

Edited with Commentary by Tatsuo Tabata December 2, 2018 Last Modified February 26, 2019

INSTITUTE FOR DATA EVALUATION AND ANALYSIS SAKAI, OSAKA, JAPAN

Institute for Data Evaluation and Analysis Technical Reports (IDEA-TR) are issued irregularly and available as PDF files only. IDEA is a virtual institute established in 1999 by Tatsuo Tabata. IDEA-TR 22 The Collected Works of Tatsuo Tabata Volume 18: Atomic and Molecular Collision Cross Sections (3), 2002–2006 / Edited with Commentary by Tatsuo Tabata. Copyright © 2018 by Tatsuo Tabata.

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ii

Papers 88. Analytic Cross Sections for Electron Collisions with Hydrocarbons: CH4 , C2 H6 , C2 H4 , C2 H2 , C3 H8 , and C3 H6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Lists Papers in the Previous Volumes of The Collected Works of Tatsuo Tabata . . . . .

98

Previous Issues of Institute for Data Evaluation and Analysis Technical Reports (IDEA-TR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

i

Preface The present volume contains two papers, published by Tatsuo Tabata and his coworkers in 2002 and 2006, in the form of the post-print re-edited by the use of LATEX. The studies described were made at Osaka Prefecture University and Institute for Data Evaluation and Analysis1 under the joint research program of data compilation at Japan Atomic Energy Research Institute (JAERI; presently Japan Atomic Energy Agency, JAEA), and belong to the category of atomic and molecular collision cross sections. A “Commentary” section written by the present editor is attached to the end of each paper. When minor errors in the published version are mentioned in the “Commentary” section, those are corrected in this volume.

1

A virtual institute established in 1999 by Tabata after his retirement from Osaka Prefecture Univer-

sity.

ii

Paper published in Atomic Data and Nuclear Data Tables, Vol. 80, Issue 2, March 2002, Pages 147–204 (doi:10.1006/adnd.2001.0878) Copyright © 2002 by Elsevier Science (USA)

Analytic Cross Sections for Electron Collisions with Hydrocarbons: CH4 , C2 H6 , C2 H4 , C2 H2 , C3 H8 , and C3 H6 Toshizo Shirai Department of Fusion Plasma Research, Japan Atomic Energy Research Institute, Naka-machi, Ibaraki 319-0193, Japan; and Advanced Photon Research Center, Japan Atomic Energy Research Institute, Kizu-cho, Kyoto 619-0215, Japan

Tatsuo Tabata Osaka Prefecture University, Gakuen-cho, Sakai, Osaka 599-8531, Japan; and Institute for Data Evaluation and Analysis, Kami, Sakai, Osaka 593-8311, Japan

Hiroyuki Tawara Physics Department, Kansas State University Manhattan, Kansas 66506-2604 and

Yukikazu Itikawa Institute of Space and Astronautical Science, Sagamihara, Kanagawa 229-8510, Japan

Cross sections for 138 processes in collisions of electrons with hydrocarbons, based on available literature sources, are critically compiled. The literature has been surveyed up to September 2000. A short comment is given for each measurement. The recommended data sets are presented in separate graphs for each process. Analytic fits to the recommended cross sections are also presented.

1

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons

CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methane (CH4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ethane (C2 H6 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ethylene (C2 H4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acetylene (C2 H2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propane (C3 H8 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propene and Cyclopropane (C3 H6 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analytic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 3 5 6 6 6 7 7

EXPLANATION OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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EXPLANATION OF GRAPHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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TABLES I. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Methane (CH4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethane (C2 H6 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethylene (C2 H4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Acetylene (C2 H2 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propane (C3 H8 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propene and Cyclopropane (C3 H6 ) . . . . . . . . . . . . . . . . . . . GRAPHS Cross Section vs Electron Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

12 16 18 20 22 24 26


INTRODUCTION Cross section data for collision processes involving electron impact of hydrocarbons (CH4 , C2 H6 , C2 H4 , C2 H2 , C3 H8 , and C3 H6 ) are necessary for understanding and modeling diverter plasmas (e.g., Janev [1]), where such molecules are produced through protoninduced chemical sputtering of graphite tiles used for the first walls of present-day and future tokamak fusion devices. Moreover, these data are also needed to elucidate the mechanisms of astrophysical phenomena (e.g., Perry et al. [2]) and to control plasma processing employed in industry (e.g., Morgan [3]). For these processes, Tawara et al. [4] have previously surveyed the literature through 1990 and made a comprehensive compilation of cross section data. Since then, quite a large number of works have produced relevant cross section data. Taking these new data into account, the previous compilation has been updated and the results are presented here. With the help of IAEA publications [5] and other bibliographies the literature was surveyed through September 2000. The recommended data in the previous compilation [4] have been replaced by the new ones only when more reliable data are available. Otherwise, the previous conclusion is adopted. The previous recommended data are indicated as Tawara et al. (1992) [4] in the present graphs. In such cases, the discussions in the previous paper should be consulted for the quality of the data shown, and the references for those data are not repeated here. As in the previous compilation, only experimental data are considered here. In cases where only a single set of measured cross sections is available, it is adopted as the recommended data, unless it is deemed unreliable. When a disagreement exists among different data sets, a renormalization of the data is made in some cases to the most reliable one to obtain the recommended data set for an energy range as wide as possible. In order to facilitate practical use of the data, an analytic formula fitted by the method of least squares is given for each set of cross section data recommended in the present paper. The values of threshold energy have been taken from tables of standard thermodynamic properties of chemical substances for molar enthalpy of formation and of ionization energies of gas-phase molecules [6]. Data Sources Methane (CH4 ) For methane, Kanik et al. [7] reviewed cross section data and determined the recommended values as of 1992 for total scattering, elastic, vibrational, and total ionization cross sections. Since 1990 (see Graph 1), the total cross section has been measured by Zecca et al. [8], Kanik et al. [9], and García and Mareno [10] using a beam attenuation method. The agreement among these cross sections is, in general, good within a few percent, but the result of Zecca et al. [8] seems to decrease too fast with increasing energy above 1 keV. In this range we have adopted the results of García and Mareno [10]. The elastic scattering cross section is available from Boesten and Tanaka [11], Bundschu et al. [12], and Iga et al. [13] (Graph 2). All those results are in good agreement with the previous recommended data [4] within 20%. The result of Boesten and Tanaka [11] 3

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons shows the highest maximum of the resonance at 7.5 eV, but seems to be too small at 100 eV. Above 100 eV, the recommended data of Kanik et al. [7] are used here. The momentum transfer cross section was obtained from the beam experiments mentioned above [11–13] and, at low energies below 2 eV, from a swarm method used by Schmidt [14] (Graph 3). We see a pronounced Ramsauer minimum at about 0.3 eV, which is deeper than that in the previous compilation [4]. Cross sections for the vibrational excitation of the (v1 +v3 ) and (v2 +v4 ) unresolved normal modes were reported by Tanaka et al. [15], Schmidt [14], Shyn [16], and Bundschu et al. [12]. Graphs 4 and 5 show these data together with the values recommended in the previous paper [4]. The cross section data scatter so widely that no recommended values can be determined. No recent data are available for the electron attachment cross section and the previous recommendation is adopted (Graph 6). For total ionization, cross sections were measured by Djurić et al. [17], Nishimura and Tawara [18], Vallance et al. [19], and Tian and Vidal [20]. The agreement among these measurements is generally good, except for the result of Vallance et al. [19], which shows a rapid fall-off of the cross section at energies above 100 eV. Nishimura and Tawara [18] measured total ionization cross section systematically for the hydrocarbon molecules. In the present paper, the use of their cross section is recommended as far as available (Graph 7). A calculation by Hwang et al. [21] based on the binary-encounter Bethe model is also shown for comparison. Straub et al. [22] measured partial cross sections for the + production of CH+ x (x=0–4) and Hx (x=1–2) (Graphs 8–14) for the electron energies from threshold to 1000 eV. The experimental uncertainty of their cross sections is estimated to be as small as ±3.5%.We have adopted their results here. Another recent measurement of the partial ionization cross sections, the result of which agrees well with those of Straub et al. [22] within 5%, was done by Tian and Vidal [20]. The total dissociation cross section determined by Winters [23] was recommended in the previous compilation [4] (Graph 15). The cross section for the production of CH3 radical due to the neutral dissociation and dissociative ionization was given by Motlagh and Moore [24] (Graph 16), who derived the absolute values with the help of information on the total dissociation cross section of Winters [23] and the dissociative ionization cross sections by Straub et al. [22]. The cross section for the H (2s) production was first measured along with the Lyman-α emission cross section by Vroom and de Heer [25]. We found that the latter cross section values are too high compared with a recent measurement of Motohashi et al. [26]. Therefore, the result for the former cross section is also considered to be too high and has been reduced by the factor obtained from the comparison of the latter cross section (Graph 17). Motohashi et al. [26] also measured the cross sections for the emission from the various fragments produced at the dissociation (Graphs 18–25, 27, 28): the Lyman series of H with n=2–4, the Balmer series of H with n=3–6, CH (A 2 ∆ → X 2 Π) at 420–440 nm, C (2p3s → 2p2 ) at 165.7 nm, and C (2s2p3 → 2s2 2p2 ) at 156.1 nm. The cross section value of 7.3 × 10−18 cm2 for the Lyman-α emission upon the electron impact dissociation of H2 at 100 eV was employed for the intensity calibration. The uncertainties of the resulting cross sections are estimated to be ±20% for the Lyman-α emission, ±12% for the Balmer-α emission, ±20% for the CH band emission, and ±50% for the C-line emission. We have adopted these results. Motohashi et al. [26] did not measure the emission of C (2p3s → 2p2 ) at 193.1 nm (Graph 26). 4

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons While not directly involving the collision of electrons with the neutral methane molecule (CH4 ), related cross sections for processes involving CH+ x (x=1–4) and CDx (x=1–3) are shown in Graphs 29–41. No recent measurements are available for the total dissociative recombination cross sections for the CH+ x (x=1–4) ions (Graphs 29–32). Absolute cross sections for the total ionization and the dissociative ionization of the deuterated methane molecule CD4 and the radicals CDx (x=1–3) (Graphs 33–41) were measured by Tarnovsky et al. [27] in the energy range from threshold to 200 eV, using a fast-neutral beam technique. The uncertainties are estimated to be ±15% for the ionization cross sections of the parent molecules and ±18% for the dissociative ionization cross sections. Their results agree well with the previous recommended data [4]. A comparison of the cross sections for the total ionization and dissociative ionization of CD4 with the corresponding data of CH4 indicates no isotope effects. It should be noted that the cross section for the production of CD+ 2 due to dissociative ionization of CD4 in the energy range above 70 eV is somewhat larger than that in the case of CH4 . However, this difference is due not to isotope effect, but to a better collection of energetic fragment ions in the CD4 experiment. In conclusion, the CH4 results can be used for CD4 in the energy range above 30 eV, where the presence of vibrationally excited molecules in the neutralized CD4 beam does not affect the cross section. The total ionization cross sections of the radicals CDx (x=1–3) are also compared with the calculations, based on the binary-encounter Bethe model, by Hwang et al. [21] for the radicals CHx (x=2–3) and by Kim [28] for the CH radical. Ethane (C2 H6 ) The total scattering cross section was determined by Nishimura and Tawara [29] and Kimura et al. [30] in the energy range 1–400 eV (Graph 42). These two sets of cross sections agree with each other and with the earlier measurements in Ref. [4] within the respective uncertainties. The cross section for elastic scattering was newly measured by Merz and Linder [31] in the energy range 0.3–10 eV with an estimated uncertainty of ±25% (Graph 43). In the energy range 1–2 eV, the present total cross section seems too small compared with the elastic one. However, considering the uncertainty of the latter, there is no inconsistency between the two cross sections. Shishikura et al. [32] analyzed a swarm experiment and derived the momentum transfer cross section in the range 0.1–100 eV. Merz and Linder [31] also derived the momentum transfer cross section with the phase shift determined from their elastic cross section measured and using the modified effective range theory. They estimated the value at zero energy to be 3.2 × 10−15 cm2 . The two sets of momentum transfer cross sections (Graph 44) are in fairly good agreement with each other at energies around 0.1 eV, but the result of Shishikura et al. [32] seems to be too high at the lower energies. In the lower energy range, only the result of Merz and Linder [31] has been adopted. As stated in the case of CH4 , the total ionization cross section measured by Nishimura and Tawara [18] (Graph 45) is plotted along with the calculation by Hwang et al. [21] based on the binary-encounter Bethe model. The partial ionization cross sections for the + + production of C2 H+ x (x=0–6), CHx (x=0–3), and Hx (x=1–3) were determined by Tian and Vidal [33] (Graphs 46–59). The uncertainties are estimated to be ±10%. These data sets are more reliable than those of Grill et al. [34], because all the ionic fragments are 5

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons believed to be collected properly. No recent data are available for the cross sections for the total dissociation (Graph 60), H (2s) production (Graph 61), and photon emission (Graph 62–66). The previous recommended values [4] are reproduced here. It should be noted that the cross sections for H (2s) production and the Lyman-α emission are renormalized as in the case of CH4 (Graph 61). Ethylene (C2 H4 ) The total scattering cross section in the previous compilation [4] is in good agreement with that of Nishimura and Tawara [29] (Graph 67). No recent measurements are available for momentum transfer cross section (Graph 68). As stated in the case of CH4 , total ionization cross section measured by Nishimura and Tawara [18] is recommended here (Graph 69). Tian and Vidal [35] obtained the + dissociative ionization cross sections for the production of C2 H+ x (x=0–4), CHx (x=0–3), and H+ x (x=1–2) in the energy range from threshold to 600 eV (Graphs 70–80). Their experimental uncertainty is estimated to be ±10%. We have adopted these results. The sum of the partial cross sections is consistent with the present recommended values of total ionization cross section. No recent measurements are available for the cross sections for H (2s) production (Graph 81) and photon emission (Graphs 82–87). It should be noted that the cross section values of the H (2s) production and Lyman-α emission are renormalized as in the case of CH4 (Graph 81). Acetylene (C2 H2 ) The total cross section was provided by Kimura et al. [30] in the energy range 1–400 eV and by Xing et al. [36] in the range 400–2600 eV, both using a beam attenuation technique (Graph 88). The uncertainties of the two experiments are estimated to be ±3% and ±5%, respectively. We have adopted these results. A measurement of the elastic scattering cross section was made by Khakoo et al. [37] in the energy range 3–100 eV with an estimated uncertainty of about 20% (Graph 89). A relative flow method was employed for normalization. Their result is consistent with the difference between the total scattering cross section and the total ionization one presented here. No recent measurements are available for momentum transfer cross section (Graph 90). + Cross sections for the dissociative ionization to form C2 H+ x (x=0–2), CHx (x=0–1), and H+ were determined by Tian and Vidal [20] (Graphs 92–97). The corresponding data obtained by Zheng and Srivastava [38] are too low, probably because of incomplete collection of energetic fragment ions. Since there is no reliable direct measurement of total ionization cross section, the sum of the partial cross sections of Tian and Vidal [20] is recommended here as the total ionization cross section (Graph 91). The results are plotted along with a calculation by Kim et al. [28] based on the binary-encounter Bethe model. No recent measurements are available for photon emission cross sections (Graphs 98– 105). Propane (C3 H8 ) 6

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons The total scattering cross section has been taken from Kimura et al. [30] (Graph 106), which is in good agreement with the earlier works shown in the previous compilation [4]. The elastic scattering (Graph 107) and momentum transfer (Graph 108) cross sections were measured by Boesten et al. [39] in the energy range 1.5–100 eV. The cross section for total ionization was reported by Djurić et al. [17], Grill et al. [40], and Nishimura and Tawara [18] (Graph 109). As in the case of CH4 , we have adopted the result of Nishimura and Tawara [18], which is shown in comparison with a calculation by Hwang et al. [21] based on the binary-encounter Bethe model. Absolute partial ionization cross sections were determined by Grill et al. [40] for the 2+ + + production of C3 H+ x (x=0–8), C2 Hx (x=0–5), CHx (x=0–3), and C3 Hx (x=2–5) in the energy range from threshold to 950 eV. They used the total ionization cross section at 100 eV of Djurić et al. [17], which is by about 18% smaller than that of Nishimura and Tawara [18], to normalize their relative cross sections. In the present paper, therefore, the partial cross sections of Grill et al. [40] are multiplied by 1.18 and plotted as recommended values (Graphs 110–132). The uncertainties are estimated to be ±15% for the dominant ions and ±20% for minor ones. No measurements are available for photon emission except for Balmer-β emission (Graph 133). Propene and Cyclopropane (C3 H6 ) The total scattering (Graphs 134 and 137) and total ionization (Graphs 135 and 138) cross sections were measured by Nishimura and Tawara [18, 29]. No measurements are available for photon emission except for Balmer-β emission (Graph 136). Analytic Expressions The functional forms of the analytic expressions used for the cross sections except for ionization are those derived semiempirically by Green and McNeal [41] with such modifications as adopted in our previous work [42, 43]. For the ionization cross section, use is made, in most cases, of the function with an asymptotic form of lnE/E (E being the incident electron energy), as proposed by Lotz [44], and with a near-threshold form used in the previous work [43] [see Eq. (14) below]. First we introduce three different functions in the form f1 (x; c1 , c2 ) = σ0 c1 (x/ER )c2

(i)

.h

1 + (x/c3 )c2 +c4

.h

1 + (x/c3 )c2 +c4 + (x/c5 )c2 +c6

f2 (x; c1 , c2 , c3 , c4 ) = f1 (x; c1 , c2 )

f3 (x; c1 , c2 , c3 , c4 , c5 , c6 ) = f1 (x; c1 , c2 )

i

(ii) i

(iii)

with σ0 =1 × 10−16 cm2 and ER =1.361 × 10−2 keV (Rydberg constant). The symbols x and ci (i=1, 2, . . . , 6) in Eqs. (i)–(iii) denote dummy parameters. The cross sections recommended in the present paper are expressed by one of the following forms involving the combination of the above functions, σ = f1 (E1 ; a1 , a2 ) σ = f2 (E1 ; a1 , a2 , a3 , a4 ) σ = f1 (E1 ; a1 , a2 ) + f2 (E1 ; a3 , a4 , a5 , a6 )

(1) (2) (3) 7

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons σ σ σ σ σ σ σ σ σ σ

= f2 (E1 ; a1 , a2 , a3 , a4 ) + a5 f2 (E1 /a6 ; a1 , a2 , a3 , a4 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a4 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a8 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a4 ) + f2 (E1 ; a8 , a9 , a10 , a4 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a8 ) + f2 (E1 ; a9 , a10 , a11 , a12 ) = f3 (E1 ; a1 , a2 , a3 , a4 , a5 , a6 ) = f1 (E1 ; a1 , a2 ) + f3 (E1 ; a3 , a4 , a5 , a6 , a7 , a8 ) = f3 (E1 ; a1 , a2 , a3 , a4 , a5 , a6 ) + a7 f3 (E1 /a8 ; a1 , a2 , a3 , a4 , a5 , a6 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f3 (E1 ; a5 , a6 , a7 , a8 , a9 , a4 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f3 (E1 ; a5 , a6 , a7 , a8 , a9 , a10 ) + f2 (E1 ; a11 , a12 , a13 , a10 )

σ = σ0 a1 [ln (E/Eth ) + a2 ]

.

Eth E [1 + (a3 /E1 )a4 ] ,

(4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

where E1 =E − Eth with E the incident electron energy in keV and Eth the threshold energy of reaction in keV. Depending on the formula chosen from Eqs. (1)–(14) above, the value of E1 or E1 /ai (i=6 or 8) is substituted for x, and a1 , a2 , etc. are substituted for ci . The tables (read across two facing pages) give the values of the fitting parameters (a1 , a2 , . . . ), which have been determined by least-squares fits to the recommended data with some additional constraints to guarantee reasonable behavior outside the energy range of the available data. The present expressions allow one not only to interpolate but also to extrapolate the data to some extent. This is in contrast to polynomial fits, which frequently show physically unreasonable behavior just outside the energy range of the available data. The resulting analytic expressions are shown in the graphs together with the recommended data. Normally the present forms fit the data quite well. To show the agreement quantitatively, the root-mean-square and the maximum deviations of the expressions from the data are also given in the tables. Acknowledgment We express our thanks to Dr. A. Kitsunezaki, Dr. H. Ninomiya, and Dr. T. Ozeki of Naka Fusion Research Establishment, and Dr. Y. Kato, Dr. S. Nagai, and Dr. T. Tajima of Advanced Photon Research Center for their support and encouragement during this work. One of the authors (H.T.) was supported in part by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy. References 1. R. K. Janev, in Atomic and Plasma–Material Interaction Processes in Controlled Thermonuclear Fusion, edited by R. K. Janev and H. W. Drawin (Elsevier, Amsterdam, 1993) p. 27 2. J. J. Perry, Y. H. Kim, J. L. Fox, and H. S. Porter, J. Geophys. Res. 104, 16, 541 (1999) 3. W. L. Morgan, Adv. At. Mol. Opt. Phys. 43, 79 (2000) 4. H. Tawara, in Atomic and Molecular Processes in Fusion Edge Plasmas, edited by R. K. Janev (Plenum, New York, 1995) p. 461; H. Tawara, Y. Itikawa, H. Nishimura, H. Tanaka,

8

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons and Y. Nakamura, Suppl. Nucl. Fusion 2, 41 (1992) 5. International Bulletin on Atomic and Molecular Data for Fusion, 42 (1992)–58 (2000), published by International Atomic Energy Agency (Vienna, Austria) 6. D. R. Lide, Ed., CRC Handbook of Chemistry and Physics (CRC Press, New York, 1999) Sections 5 and 10 7. I. Kanik, S. Trajmar, and J. C. Nickel, J. Geophys. Res. 98, 7447 (1993) 8. A. Zecca, G. Karwasz, R. S. Brusa, and C. Szmytkowski, J. Phys. B 24, 2747 (1991) 9. I. Kanik, S. Trajmar, and J. C. Nickel, Chem. Phys. Lett. 193, 281 (1992) 10. G. García and F. Manero, Phys. Rev. A 57, 1069 (1998) 11. L. Boesten and H. Tanaka, J. Phys. B 24, 821 (1991) 12. C. T. Bundschu, J. C. Gibson, R. J. Gulley, M. J. Brunger, S. J. Buckman, N. Sanna, and F. A. Gianturco, J. Phys. B 30, 2239 (1997) 13. I. Iga, M.-T. Lee, M. G. P. Homem, L. E. Machado, and L. M. Brescansin, Phys. Rev. A 61, 022708 (2000) 14. B. Schmidt, J. Phys. B 24, 4809 (1991) 15. H. Tanaka, M. Kubo, N. Onodera, and A. Suzuki, J. Phys. B 16, 2861 (1983) 16. T. W. Shyn, J. Phys. B 24, 5169 (1991) 17. N. Djurić, I. Čadež, and M. Kurepa, Int. J. Mass Spectrom. Ion Processes 108, R1 (1991) 18. H. Nishimura and H. Tawara, J. Phys. B 27, 2063 (1994) 19. C. Vallance, S. A. Harris, J. E. Hudson, and P. W. Harland, J. Phys. B 30, 2465 (1997) 20. C. Tian and C. R. Vidal, J. Phys. B 31, 895 (1998) (Tian and Vidal (1998a) in Graph legends) 21. W. Hwang, Y.-K. Kim, and M. E. Rudd, J. Chem. Phys. 104, 2956 (1996) 22. H. C. Straub, D. Lin, B. G. Lindsay, K. A. Smith, and R. F. Stebbings, J. Chem. Phys. 106, 4430 (1997) 23. H. F. Winters, J. Chem. Phys. 63, 3462 (1975) 24. S. Motlagh and J. H. Moore, J. Chem. Phys. 109, 432 (1998) 25. D. A. Vroom and F. J. de Heer, J. Chem. Phys. 50, 573 (1969) 26. K. Motohashi, H. Soshi, M. Ukai, and S. Tsurubuchi, Chem. Phys. 213, 369 (1996) 27. V. Tarnovsky, A. Levin, H. Deutsch, and K. Becker, J. Phys. B 29, 139 (1996) 28. Y.-K. Kim, M. A. Ali, and M. E. Rudd, J. Res. Natl. Inst. Stand. Technol. 102, 693 (1997) 29. H. Nishimura and T. Tawara, J. Phys. B 24, L363 (1991) 30. M. Kimura, O. Sueoka, A. Hamada, and Y. Itikawa, Adv. Chem. Phys. 111, 537 (2000) 31. R. Merz and F. Linder, J. Phys. B 31, 4663 (1998) 32. Y. Shishikura, K. Asano, and Y. Nakamura, J. Phys. D 30, 1610 (1997) 33. C. Tian and C. R. Vidal, J. Chem. Phys. 109, 1704 (1998) (Tian and Vidal (1998b) in Graph legends)

9

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons 34. V. Grill, G. Walder, P. Scheier, M. Kurdel, and T. D. Märk, Int. J. Mass Spectrom. Ion Processes 129, 31 (1993) 35. C. Tian and C. R. Vidal, Chem. Phys. Lett. 288, 499 (1998) (Tian and Vidal (1998c) in Graph legends) 36. S. L. Xing, Q. C. Shi, X. J. Chen, K. Z. Xu, B. X. Yang, S. L. Wu, and R. F. Feng, Phys. Rev. A 51, 414 (1995) 37. M. A. Khakoo, T. Jayaweera, S. Wang, and S. Trajmar, J. Phys. B 26, 4845 (1993) 38. S.-H. Zheng and S. K. Srivastava, J. Phys. B 29, 3235 (1996) 39. L. Boesten, M. A. Dillon, H. Tanaka, M. Kimura, and H. Sato, J. Phys. B 27, 1845 (1994) 40. V. Grill, G. Walder, D. Margreiter, T. Rauth, H. U. Poll, P. Scheier, and T. D. Märk, Z. Phys. D 25, 217 (1993) (Grill et al. (1993b) in Graph legends) 41. A. E. S. Green and R. J. McNeal, J. Geophys. Res. 76, 133 (1971) 42. Y. Nakai, T. Shirai, T. Tabata, and R. Ito, Atomic Data and Nuclear Data Tables 37, 69 (1987) 43. T. Tabata and T. Shirai, Atomic Data and Nuclear Data Tables 76, 1 (2000) 44. W. Lotz, Z. Phys. 206, 205 (1967)

10


EXPLANATION OF TABLES TABLE I.

Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Methane (CH4 )

TABLE II.

Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethane (C2 H6 )

TABLE III. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethylene (C2 H4 ) TABLE IV. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Acetylene (C2 H2 ) TABLE V.

Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propane (C3 H8 )

TABLE VI. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propene and Cyclopropane (C3 H6 ) Number label identifying a particular reaction process in the same sequence as in the Graphs. The relevant reaction process. Process Minimum energy (in keV) of experimental data. Emin Maximum energy (in keV) of experimental data. Emax Root-mean-square relative deviation (in %) of the δrms analytic expression from the data. Maximum relative deviation (in %) of the analytic δmax expression from the data. Eδmax Energy (in keV) at which the relative deviation takes on the value δmax . Eq. The identifying number of the equation to be used for deriving the recommended cross sections. n Number of applicable fit parameters. Threshold energy of the reaction (in keV). Eth ai (i = 1, 2, . . . , 13) Fit parameters. The notation 1.23−1 means 1.23×10−1 . No.

EXPLANATION OF GRAPHS GRAPHS.

Cross Section vs Electron Energy Graphs are numbered in order of the entries in Table I through VI. Cross section in cm2 . Ordinate Electron energy in eV in the center-of-mass system. Abscissa Recommended data from the analytic formula of the Solid line present work. Symbols Experimental data from sources as explained in the legends. 11

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE I. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Methane (CH4 ) See page 11 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

1

Total scattering

8.00−5

5.00

4.8

1.1+1

3.00−3

2

Elastic scattering

2.00−4

1.00

9.9

3.4+1

1.00−1

3

Momentum transfer

1.00−6

5.00−1

1.4+1

3.6+1

7.00−4

4

Vibrational excitation (v2 +v4 )

5

Vibrational excitation (v1 +v3 )

6

Attachment

8.00−3

1.30−2

1.3

2.7

9.50−3

7

Total ionization

1.50−2

3.00

3.3

1.2+1

3.00

8

CH+ 4 production

1.50−2

1.00

2.0

6.9

1.75−2

9

CH+ 3 production

1.50−2

1.00

3.1

1.0+1

1.75−2

10

CH+ 2 production

1.75−2

1.00

9.1

2.8+1

2.25−2

11

CH+ production

2.50−2

1.00

5.9

2.1+1

3.00−2

12

C+ production

3.00−2

1.00

3.3

6.9

4.00−2

13

H+ 2 production

2.50−2

1.00

1.8+1

8.3+1

2.50−2

14

H+ production

2.50−2

1.00

1.6

4.1

4.50−2

15

Total dissociation

1.10−2

5.00−1

5.1

1.4+1

1.20−2

16

CH3 production

1.01−2

5.03−1

2.7

8.6

2.38−2

17

H (2s) production

1.00−1

6.00

2.5

6.3

3.00

18

Ly-α emission

2.06−2

9.86−1

1.1+1

2.4+1

2.37−2

19

Ly-β emission

2.03−2

9.88−1

5.0

1.5+1

2.17−2

20

Ly-γ emission

2.15−2

9.94−1

5.9

1.8+1

2.23−2

21

H-α emission

2.16−2

6.00

4.7

1.1+1

2.66−2

22

H-β emission

2.07−2

6.00

6.5

2.5+1

2.13−2

23

H-γ emission

1.88−2

6.00

1.0+1

3.2+1

1.99−2

24

H-δ emission

2.02−2

6.00

9.3

2.5+1

2.02−2

25

CH (A 2 ∆–X 2 Π) emission at 420–440 nm

1.46−2

5.00

7.0

1.6+1

2.50−2

26

C (2p3s 1P 0 –2p2 1D) emission at 193.1 nm

2.75−2

4.00−1

3.0

8.4

4.50−2

12


Eq.

n

1

10

8

0.0

2

3

6

0.0

3

6

8

6

9

7

Eth

a1 a7

a2 a8

a3 a9

a4 a10

a5 a11

a6 a12

3.330−2 1.660−2 2.930−2

−9.850−1 1.090 −1.030

2.330+2

1.849

5.450−3

4.580−1

3.280+2

2.190

5.400−3

7.920−1

0.0

3.300 6.670−3

−2.060−1 1.318

6.020−5

2.620

1.360+2

1.789

6

7.750−3

2.857+1

3.065

3.669−4

−4.317−1

2.090−3

7.759

14

4

1.300−2

3.539−3

3.600−2

3.730−2

9.060−1

8

9

6

1.299−2

4.886

1.627

7.420−3

−4.500−2

3.300−2

1.040

9

9

6

1.424−2

2.350

1.435

1.130−2

7.400−2

5.500−2

1.200

10

9

6

1.520−2

1.210−1

1.868

3.440−2

3.000−1

5.520−2

1.000

11

9

6

2.414−2

1.038−1

1.161

4.000−2

6.700−1

1.400−1

1.600

12

9

6

2.820−2

6.400−2

1.430

1.330−2

−3.300−1

4.240−2

1.181

13

9

6

2.023−2

4.900−3

3.610

2.570−2

−3.900−2

4.400−2

1.290

14

9

6

1.800−2

4.949−2

2.855

3.180−2

−3.300−1

5.130−2

1.155

15

4

6

4.510−3

4.590

3.590

1.321−2

3.450−1

6.200−1

3.700

16

9

6

4.510−3

1.385+2

5.790

5.880−3

−6.070−1

9.280−3

6.150−1

17

9

6

1.470−2

3.430−1

9.700

6.100−3

−1.900

1.164−2

9.989−1

18

9

6

1.470−2

8.540−3

2.820

2.720−2

−1.900−1

5.950−2

1.600

19

9

6

1.660−2

5.210−2

4.650

5.910−3

−1.237

1.660−2

1.100

20

9

6

1.730−2

2.240−2

4.210

5.800−3

−1.120

1.780−2

1.158

21

9

6

1.660−2

1.330−2

2.410

1.040−2

−1.190

3.350−2

1.040

22

9

6

1.730−2

1.550−2

3.540

6.400−3

−1.060

1.900−2

1.052

23

9

6

1.760−2

1.330−3

1.980

2.300−2

−4.000−1

4.080−2

1.084

24

9

6

1.770−2

4.050−4

2.310

2.490−2

−3.200−1

4.060−2

1.106

25

11

8

1.220−2

−1.191

1.184−2

9.090−1

11

8

2.350−2

1.600+1 2.770−1 4.350 4.990

8.400−3

26

1.070 3.270 1.080−2 1.745

8.080−3

−2.300−1

1.370−2

1.810

4 5

13


Process

Emin

Emax

δrms

δmax

Eδmax

27

C (2p3s 3P 0 – 2p2 3P ) emission at 165.7 nm

2.43−2

9.80−1

1.8+1

6.0+1

2.43−2

28

C (2s2p3 3D0 – 2s2 2p2 3P ) emission at 156.1 nm

2.62−2

1.00

2.1+1

7.3+1

2.62−2

29

Dissociative recombination/CH+ 4

2.00−5

1.00−3

0.4

0.6

5.00−4

30


2.00−5

2.00−3

1.4+1

2.1+1

1.00−4

31


2.00−5

2.00−3

6.3

9.5

1.00−4

32

Dissociative recombination/CH+

2.00−5

2.00−3

1.3+1

2.1+1

1.00−3

33

Total ionization/CD3

1.10−2

2.00−1

4.3

8.6

1.60−2

34

CD+ 3 production/CD3

1.10−2

2.00−1

3.0

7.8

2.00−2

35


1.60−2

2.00−1

2.4

4.9

1.90−2

36

Total ionization/CD2

1.10−2

2.00−1

3.8

8.7

3.00−2

37


1.10−2

2.00−1

1.9

4.5

1.20−2

38

CD+ production/CD2

1.60−2

2.00−1

3.9

1.4+1

1.70−2

39

Total ionization/CD

1.20−2

2.00−1

6.1

1.4+1

1.50−2

40

CD+ production/CD

1.20−2

2.00−1

3.7

9.4

1.50−2

41

C+ production/CD

1.70−2

2.00−1

6.4

1.8+1

1.90−2

14


Eq.

n

Eth

a1 a7

a2 a8

a3 a9

27

11

8

1.570−2

2.100−1

2.500−2

1.800

11

8

2.500−2

1.160−2

9.500−1

1.870−2

9.500−1

29

2

4

0.0

6.550 3.160 2.200 5.850 −9.260−1

1.720−2

28

6.880−4 1.220 3.360−3 1.820 1.941

2.830−4

1.994

30

2

4

0.0

1.820

−1.000

1.600−4

1.520

31

1

2

0.0

9.440−1

−1.007

32

1

2

0.0

7.530−1

−9.420−1

33

14

4

9.840−3

1.811−3

0.0

4.620−2

1.015

34

9

6

9.840−3

9.250+1

3.010

1.810−3

−9.180−1

5.900−3

4.480−1

35

9

6

1.530−2

4.040

1.773

5.490−3

−1.620−1

4.380−2

1.990

36

14

4

1.040−2

2.036−3

4.500−3

7.810−2

8.210−1

37

9

6

1.040−2

3.770

1.670

8.140−3

−3.630−1

1.940−2

5.500−1

38

9

6

1.490−2

7.190−1

1.458

1.640−2

1.430−1

7.700−2

1.280

39

14

4

1.060−2

1.221−3

0.0

2.810−2

1.077

40

9

6

1.060−2

1.610

4.200−1

6.400−3

−2.180

6.700−2

6.400−1

41

9

6

1.470−2

6.180−1

1.500−4

1.770−2

−1.760

2.600−1

9.300−1

15

a4 a10

a5 a11

a6 a12

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE II. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethane (C2 H6 ) See page 11 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

42

Total scattering

1.00−3

4.00−1

3.9

1.7+1

1.00−3

43

Elastic scattering

5.00−5

1.00−1

2.6

7.7

9.95−3

44

Momentum transfer

1.58−6

9.75−1

9.7

2.7+1

2.01−4

45

Total ionization

2.50−2

6.00−1

1.7

5.2

3.00−2

46

C2 H+ 6 production

1.75−2

6.00−1

3.5

1.0+1

2.00−2

47

C2 H+ 5 production

1.75−2

6.00−1

3.8

1.2+1

2.00−2

48

C2 H+ 4 production

1.75−2

6.00−1

4.0

1.4+1

2.00−2

49

C2 H+ 3 production

1.75−2

6.00−1

4.0

1.4+1

2.00−2

50

C2 H+ 2 production

1.75−2

6.00−1

4.8

1.6+1

2.00−2

51

C2 H+ production

3.50−2

6.00−1

1.2

3.0

2.25−1

52

C+ 2 production

4.50−2

6.00−1

2.2

6.2

3.50−1

53

CH+ 3 production

1.75−2

6.00−1

5.2

1.5+1

3.50−2

54

CH+ 2 production

3.00−2

6.00−1

3.1

7.8

3.50−2

55

CH+ production

4.00−2

6.00−1

2.9

6.4

1.75−1

56

C+ production

4.50−2

6.00−1

3.6

8.8

5.50−1

57

H+ 3 production

3.50−2

6.00−1

4.8

1.3+1

6.00−2

58

H+ 2 production

2.50−2

6.00−1

2.2

6.0

4.50−2

59

H+ production

2.50−2

6.00−1

2.3

7.2

3.50−2

60

Total dissociation

1.50−2

6.00−1

1.5

2.5

3.00−2

61

H (2s) production

5.00−2

6.00

1.4

2.6

2.00−1

62

Ly-α emission

5.00−2

6.00

3.0

7.3

2.00−1

63

H-α emission

5.00−2

6.00

3.8

6.2

8.00−1

64

H-β emission

5.00−2

6.00

1.2

2.3

2.00−1

65

H-γ emission

5.00−2

6.00

4.3

6.9

2.00−1

66

H-δ emission

5.00−2

6.00

3.2

5.5

2.00−1

16

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE II. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethane (C2 H6 ) See page 11 for Explanation of Tables No.

Eq.

n

42

7

10

0.0

43

8

12

0.0

44

8

12

0.0

45

14

4

46

9

47

Eth

a1 a7

a2 a8

a3 a9

2.980 1.070+1 −5.800−1 6.000−1 −5.770−1 1.010 0.0

4.960−4 2.950−1 4.700−5 1.950+2 4.690−5 3.890+2 4.520−2

7.640−1 8.600−2 1.790 2.060 5.000 2.710 1.030

2.660−3

2.250

1.150−2

1.370+5 5.930−3 4.050−1 7.300−4 1.650−1 1.040−3 5.350−3

1.060+3 7.010−3 3.190+2 5.090−3

1.390 8.040−1 1.180 1.140

6

1.150−2

1.010

3.050

1.281−2

−5.400−2

2.840−2

9.200−1

9

6

1.280−2

8.290−1

2.500

1.270−2

3.570−2

3.950−2

1.110

48

9

6

1.270−2

2.960

2.390

1.420−2

7.130−2

4.120−2

1.080

49

9

6

1.540−2

6.290−1

1.265

3.060−2

4.490−1

1.900−1

1.700

50

2

4

1.530−2

3.238−1

1.161

4.640−2

7.100−1

51

9

6

2.880−2

1.560−1

2.070

1.120−2

−4.700−1

3.150−2

1.131

52

9

6

3.400−2

4.090−2

5.200

9.700−3

−9.520−1

2.140−2

1.250

53

2

4

1.400−2

8.170−2

1.116

8.390−2

9.450−1

54

2

4

2.580−2

6.290−2

1.043

6.560−2

9.380−1

55

9

6

3.000−2

5.240−2

3.620

1.130−2

−7.000−1

2.780−2

1.347

56

9

6

3.200−2

1.051−2

7.220

1.327−2

−9.570−1

2.230−2

1.203

57

2

4

3.320−2

1.712−2

1.092

5.540−2

8.420−1

58

9

6

1.800−2

9.720−3

2.336

4.860−2

−1.750−1

6.220−2

1.140

59

9

6

2.050−2

3.420

4.330

3.450−3

−1.479

1.520−2

1.004

60

9

6

3.900−3

4.900

4.120

1.360−2

−6.700−1

2.150−2

5.940−1

61

2

4

1.440−2

3.530−3

9.240−1

6.640−2

9.944−1

62

2

4

1.440−2

2.550−2

9.000−1

6.810−2

9.980−1

63

2

4

1.630−2

8.350−3

1.110

6.390−2

1.000

64

2

4

1.700−2

3.260−3

8.390−1

7.180−2

1.037

65

2

4

2.730−2

1.860−3

7.300−1

6.780−2

1.039

66

2

4

2.740−2

1.035−3

7.760−1

6.240−2

1.030

17

a4 a10

a5 a11

a6 a12

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE III. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethylene (C2 H4 ) See page 11 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

67

Total scattering

1.00−3

4.00−1

1.6

3.4

2.00−2

68

Momentum transfer

1.03−5

1.00

5.9

1.1+1

2.64−2

69

Total ionization

1.10−2

1.20+1

6.7

2.6+1

1.10−2

70

C2 H+ 4 production

1.75−2

6.00−1

1.2

2.4

8.00−2

71

C2 H+ 3 production

1.75−2

6.00−1

2.5

6.9

2.00−2

72

C2 H+ 2 production

1.75−2

6.00−1

1.9

4.4

3.00−2

73

C2 H+ production

2.00−2

6.00−1

8.9

2.6+1

3.00−2

74

C+ 2 production

3.00−2

6.00−1

3.6

1.0+1

6.00−1

75

CH+ 3 production

2.50−2

6.00−1

9.9

2.3+1

3.00−1

76

CH+ 2 production

2.50−2

6.00−1

2.7

6.3

4.50−1

77

CH+ production

2.50−2

6.00−1

7.7

2.5+1

2.50−2

78

C+ production

3.00−2

6.00−1

9.0

3.1+1

4.00−2

79

H+ 2 production

3.00−2

6.00−1

6.2

1.5+1

3.00−2

80

H+ production

3.00−2

6.00−1

2.2

4.5

4.00−2

81

H (2s) production

5.00−2

6.00

2.9

4.5

2.00−1

82

Ly-α emission

5.00−2

6.00

3.6

5.4

8.00−2

83

H-α emission

5.00−2

6.00

3.7

7.5

1.00

84

H-β emission

5.00−2

6.00

4.0

6.4

6.00

85

H-γ emission

5.00−2

6.00

3.2

4.8

1.00

86

H-δ emission

5.00−2

6.00

1.5

2.7

2.00

87

CH (A 2 ∆ – X 2 Π) emission at 420–440 nm

5.00−2

6.00

1.0

2.2

2.00−1

18

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE III. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Ethylene (C2 H4 ) See page 11 for Explanation of Tables No.

Eq.

n

Eth

a1 a7

a2 a8

a3 a9

a4 a10

a5 a11

a6 a12

1.020 5.260−1 −5.920−1 −5.510−1 3.900−1

2.270−3

6.600

1.036+2

1.087

6.140−5 2.750−4 5.640−2

9.400 1.494 1.265

4.090+11 1.890+1

5.180 6.730−1

67

6

8

0.0

68

13

13

0.0

69

14

4

1.050−2

1.257+2 6.860−3 1.420−1 1.103−4 3.500−3

70

9

6

1.050−2

4.760

3.950

1.017−2

−2.830−1

1.860−2

8.340−1

71

9

6

1.320−2

1.510

2.350

1.220−2

−8.900−2

3.830−2

1.110

72

9

6

1.320−2

9.690−1

2.004

1.650−2

6.600−2

5.500−2

1.260

73

2

4

1.830−2

1.049−1

1.037

6.150−2

9.290−1

74

9

6

1.950−2

2.680−2

4.080

1.440−2

−8.200−1

2.920−2

1.157

75

2

4

1.700−2

7.770−3

8.650−1

6.030−2

7.700−1

76

2

4

1.790−2

1.034−1

1.101

6.510−2

8.470−1

77

2

4

1.780−2

3.100−2

1.241

7.820−2

1.094

78

2

4

2.560−2

2.510−2

9.360−1

1.070−1

1.197

79

2

4

1.720−2

5.950−3

1.567

6.660−2

9.590−1

80

2

4

1.820−2

7.610−2

1.541

7.330−2

9.500−1

81

2

4

1.480−2

2.000−3

1.030

5.880−2

9.780−1

82

2

4

1.480−2

3.070−2

9.000−1

6.220−2

9.850−1

83

2

4

1.670−2

1.290−2

9.900−1

6.320−2

1.034

84

2

4

1.740−2

3.580−3

8.100−1

7.240−2

1.048

85

2

4

1.820−2

1.670−3

8.600−1

6.360−2

1.026

86

2

4

1.780−2

7.750−4

9.850−1

6.380−2

1.025

87

2

4

1.010−2

6.240−3

1.017

6.270−2

8.699−1

19

a13

2.050−2

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE IV. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Acetylene (C2 H2 ) See page 11 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

88

Total scattering

1.00−3

2.60

4.4

1.0+1

5.50−3

89

Elastic scattering

5.00−3

1.00−1

4.9

7.2

1.00−1

90

Momentum transfer

1.00−5

9.79−1

5.2

1.1+1

4.85−5

91

Total ionization

1.75−2

6.00−1

3.4

1.1+1

2.50−2

92

C2 H+ 2 production

1.75−2

6.00−1

1.2

3.6

2.50−2

93

C2 H+ production

2.00−2

6.00−1

1.2

2.5

1.25−1

94

C+ 2 production

2.50−2

6.00−1

1.4

3.7

3.50−2

95

CH+ production

2.50−2

6.00−1

1.5

3.0

1.25−1

96

C+ production

3.00−2

6.00−1

2.2

5.0

3.50−2

97

H+ production

2.50−2

6.00−1

4.4

8.8

5.00−2

98

Ly-α emission

2.25−2

4.00−1

2.3

6.6

2.75−2

99

Ly-β emission

2.75−2

4.00−1

1.5

3.0

3.00−2

100

H-β emission

2.49−2

1.53−1

1.3

2.9

1.01−1

101

CH (A 2 ∆ – X 2 Π) emission at 420–440 nm

2.21−2

2.23−1

4.6

8.7

4.80−2

102

C2 (d 3 Πg – a 3 Πu ; δv=0) emission

2.18−2

2.23−1

0.6

1.3

1.57−1

103

C2 (d 3 Πg – a 3 Πu ; δv=1) emission

3.48−2

2.20−1

0.5

0.8

6.18−2

104

C2 (d 3 Πg – a 3 Πu ; δv=−1) emission

2.21−2

2.23−1

0.8

1.6

3.48−2

105

C (2p3s 3P 0 – 2p2 3P ) emission at 165.7 nm

2.00−2

1.00

1.1+1

4.1+1

2.00−2

20

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE IV. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Acetylene (C2 H2 ) See page 11 for Explanation of Tables No.

Eq.

n

88

6

8

0.0

89

2

4

0.0

90

7

10

0.0

91

14

4

92

9

93

Eth

a1 a7

a2 a8

a3 a9

a5 a11

a6 a12

1.000+7 3.300−1 3.291+2

6.400 1.080 2.000

1.772−3

5.800−1

1.400+1

−1.370−1

4.732−3

8.030−1

1.140−2

3.610 7.000−4 4.260−3

−1.080−1 3.270+4 0.0

1.042−1 3.750 4.240−2

1.637 2.149−3 1.129

2.380+2

6.860−1

6

1.140−2

9.550

2.590

8.810−3

−1.970−1

2.370−2

9.130−1

9

6

1.650−2

1.560

2.144

9.790−3

−1.540−1

2.900−2

9.800−1

94

9

6

1.950−2

3.396−1

2.830

1.097−2

−4.050−1

2.370−2

9.550−1

95

9

6

2.060−2

1.010

3.690

6.910−3

−1.030

1.740−2

8.760−1

96

9

6

2.370−2

7.230−2

1.620

4.300−2

−1.900−1

6.300−2

1.100

97

2

4

1.850−2

6.480−2

1.665

6.500−2

8.380−1

98

9

6

1.510−2

6.130−3

3.670

1.880−2

−1.230

3.370−2

9.480−1

99

9

6

1.700−2

1.257−3

4.930

1.499−2

−1.216

2.970−2

1.246

100

9

6

1.760−2

3.080−2

6.110

7.250−3

−1.473

1.600−2

9.500−1

101

2

4

1.290−2

5.760−3

7.240−1

2.280−1

1.500

102

9

6

8.660−3

3.546−3

1.510

2.940−2

1.880−1

5.000−1

1.000

103

9

6

8.460−3

2.614−3

1.240

4.410−2

3.690−1

5.000−1

1.000

104

9

6

8.870−3

2.242−3

1.256

4.330−2

3.980−1

5.000−1

1.000

105

5

7

1.660−2

1.670−3 6.810−2

8.900

1.473−2

9.470−1

5.140−4

2.218

21

a4 a10

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE V. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propane (C3 H8 ) See page 11 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

106

Total scattering

8.00−4

6.00−1

2.7

6.7

5.50−3

107

Elastic scattering

2.00−3

1.00−1

2.0

4.0

7.50−3

108

Momentum transfer

9.79−6

1.00−1

1.0+1

2.1+1

2.00−3

109

Total ionization

1.20−2

1.20+1

2.7

8.9

1.50−2

110

C3 H+ 8 production

1.32−2

9.52−1

4.0

1.5+1

1.69−2

111

C3 H+ 7 production

1.38−2

9.53−1

1.1+1

5.3+1

1.38−2

112

C3 H+ 6 production

1.38−2

9.51−1

1.8

4.3

1.63−2

113

C3 H+ 5 production

1.76−2

9.54−1

4.8

1.6+1

2.63−2

114

C3 H+ 4 production

2.26−2

9.52−1

1.9

4.5

6.40−2

115

C3 H+ 3 production

2.26−2

9.54−1

2.8

9.5

2.51−2

116

C3 H+ 2 production

2.73−2

9.50−1

3.0

1.4+1

3.36−2

117

C3 H+ production

2.78−2

9.51−1

2.1

5.1

4.94−2

118

C+ 3 production

3.92−2

9.49−1

3.9

8.4

5.56−2

119

C2 H+ 5 production

1.43−2

9.51−1

5.9

2.8+1

1.56−2

120

C2 H+ 4 production

1.37−2

9.53−1

7.2

3.6+1

1.37−2

121

C2 H+ 3 production

1.56−2

9.50−1

1.8

6.8

1.81−2

122

C2 H+ 2 production

1.55−2

9.51−1

6.0

2.1+1

2.58−2

123

C2 H+ production

3.09−2

9.52−1

1.0+1

4.4+1

3.09−2

124

C+ 2 production

5.05−2

9.55−1

7.5

2.6+1

8.55−1

125

CH+ 3 production

2.38−2

9.54−1

3.5

1.4+1

3.00−2

126

CH+ 2 production

2.69−2

9.54−1

8.2

2.4+1

3.32−2

127

CH+ production

2.32−2

9.49−1

6.8

2.2+1

2.01−1

128

C+ production

3.77−2

9.49−1

1.3+1

3.8+1

3.91−2

129

C3 H2+ 5 production

3.32−2

9.48−1

6.7

2.6+1

4.51−2

130

C3 H2+ 4 production

3.65−2

9.54−1

8.8

2.0+1

1.42−1

131

C3 H2+ 3 production

4.03−2

9.53−1

7.1

3.1+1

5.32−2

132

C3 H2+ 2 production

4.00−2

9.52−1

7.9

3.4+1

4.78−2

133

H-β emission

5.43−2

5.28−1

3.5

6.9

5.28−1

22

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE V. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propane (C3 H8 ) See page 11 for Explanation of Tables No.

Eq.

n

106

12

9

0.0

107

6

8

0.0

108

6

8

0.0

109

14

4

110

9

111

Eth

a1 a7

a2 a8

a3 a9

a4 a10

a5 a11

3.300−1 7.600−2 9.100−1 7.700−1 −1.120 1.250 1.510−1

5.900−3 1.030−2 9.400−4

1.077

2.410+3

4.270

5.100−1

1.640+3

3.750

6.700−5

6.000

5.140+1

5.350−1

1.100−2

4.090+1 5.150−3 3.550+2 5.400−3 1.210−2 1.020−2 7.863−3

6.090−2

1.034

6

1.095−2

2.020

2.280

7.560−3

−2.800−1

1.960−2

7.110−1

9

6

1.160−2

3.080

2.760

6.100−3

−2.900−1

1.710−2

8.100−1

112

9

6

1.100−2

1.995−1

1.823

1.239−2

−4.900−2

4.220−2

1.040

113

9

6

1.480−2

3.240−1

1.349

2.180−2

3.120−1

1.530−1

1.620

114

9

6

1.274−2

5.360−2

2.090

2.110−2

1.600−1

5.500−2

1.100

115

9

6

1.450−2

6.430−1

4.150

1.402−2

−6.600−1

2.090−2

7.330−1

116

9

6

1.780−2

2.738−2

5.500

2.003−2

−9.370−1

3.034−2

1.038

117

9

6

2.180−2

3.050−2

3.326

2.360−2

−7.010−1

4.200−2

1.133

118

9

6

3.280−2

3.160−2

5.030

1.040−2

−1.126

2.320−2

1.157

119

9

6

1.190−2

7.050

2.140

7.200−3

−2.800−1

2.350−2

8.600−1

120

9

6

1.140−2

3.190

1.990

8.000−3

−1.400−1

2.840−2

9.200−1

121

9

6

1.450−2

1.239

1.082

3.130−2

4.100−1

1.520−1

1.430

122

2

4

1.410−2

1.478−1

1.718

4.590−2

7.060−1

123

2

4

3.040−2

2.418−2

1.075

8.490−2

1.111

124

9

6

4.050−2

1.863−3

1.870

6.250−2

6.900−1

2.190−1

3.740

125

9

6

1.400−2

5.460−2

4.410

2.298−2

−3.900−1

3.440−2

1.043

126

9

6

2.370−2

4.770

5.900

5.320−3

−1.229

1.170−2

9.430−1

127

9

6

1.890−2

8.470−3

1.781

6.070−2

4.600−1

1.110−1

1.760

128

9

6

3.490−2

6.000−3

1.380

7.400−2

4.300−1

1.480−1

2.160

129

2

4

3.240−2

3.061−4

1.163

5.480−2

8.260−1

130

9

6

3.140−2

3.890+1

1.350+1

6.330−3

−1.600

9.210−3

8.640−1

131

9

6

3.540−2

2.970−3

2.860

2.760−2

−8.700−2

4.960−2

1.250

132

9

6

3.460−2

5.140−3

2.240

3.720−2

2.300−1

7.200−2

1.330

133

2

4

1.850−2

1.740−3

8.100−1

1.130−1

1.210

23

a6 a12

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE VI. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propene and Cyclopropane (C3 H6 ) See page 11 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

134

Total scattering/propene

4.00−3

5.00−1

1.4

3.6

4.50−1

135

Total ionization/propene

1.00−2

3.00

1.2+1

5.9+1

1.00−2

136

H-β emission/propene

5.34−2

5.20−1

2.5

4.9

5.20−1

137

Total scattering/cyclopropane

3.96−3

4.93−1

1.8

3.9

8.92−2

138

Total ionization/cyclopropane

1.00−2

3.00

1.4+1

7.8+1

1.00−2

24

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons TABLE VI. Energy Ranges of Data, Fitting Errors, and Parameters of the Analytic Expressions for Propene and Cyclopropane (C3 H6 ) See page 11 for Explanation of Tables No.

Eq.

n

134

9

6

0.0

1.388+3

135

14

4

9.730−3

136

2

4

137

9

138

14

Eth

a1 a7

a2 a8

a3 a9

a4 a10

a5 a11

a6 a12

2.650

3.970−3

2.150−1

1.370−2

1.274

5.790−3

3.500−1

7.680−2

1.130

1.900−2

1.690−3

1.010

8.230−2

1.161

6

0.0

5.976+2

2.300

4.380−3

3.390−1

1.940−2

1.475

4

9.860−3

5.610−3

2.100−1

6.430−2

1.210

25


GRAPHS. Cross Section vs Projectile Energy See page 11 for Explanation of Graphs

26

88. Analytic Cross Sections for Electron Collisions with Hydrocarbons GRAPHS. Cross Section vs Projectile Energy See page 11 for Explanation of Graphs

27


28


29


30


31


32


33


34


35


36


37


38


39


40


41


42


43


44


45


46


47


48


49


50



51


52


53



54


55


56


57


58


59


Commentary Typos on pages of the published version: Page 151 154 157 162

Place Eq. (iii) line 2 from bottom value of No. for the last entry but two δmax value for No. 69

60

Now reads c6 = 12 23 3.

Should read c6 ) = 13 24 3.4

Paper published in Atomic Data and Nuclear Data Tables, Vol. 92, Issue 3, May 2006, Pages 375–406 (doi:10.1016/j.adt.2006.02.002) Copyright © 2006 by Elsevier Inc.

Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules Tatsuo Tabata

a,b

, Toshizo Shirai

c,∗

, Masao Sataka d , Hirotaka Kubo

c,†

a

Osaka Prefecture University, Gakuen-cho, Sakai, Osaka 599-8531, Japan Institute for Data Evaluation and Analysis, Kami, Sakai, Osaka 593-8311, Japan Department of Fusion Plasma Research, Japan Atomic Energy Research Institute, Naka-shi, Ibaraki 319-0193, Japan d Department of Materials Science, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-1195, Japan b

c

Abstract Cross sections for 74 processes in collisions of electrons with nitrogen molecules (N2 ) and singly ionized nitrogen molecules (N2+ ) have been collected. The literature has been surveyed through the middle of 2004. The data sets collected are presented in separate Graphs for each process. Recommended cross sections are expressed by analytic expressions.

∗ †

Deceased. Corresponding author. Fax: +81 0 29 270 7419. E-mail address: [email protected] (H. Kubo).

61

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1. The Nitrogen molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2. The singly ionized nitrogen molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Analytic expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62 63 63 66 67

Explanation of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Explanation of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Tables 1. Energy ranges of data, fitting errors, and parameters of the analytic expressions for nitrogen molecules, N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Energy ranges of data, fitting errors, and parameters of the analytic expressions for singly ionized nitrogen molecules, N2+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Graphs 1–75. Cross section vs. electron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76 78

1. Introduction Cross section data on collision processes of electrons with nitrogen molecules (N2 ) and singly ionized nitrogen molecules (N2+ ) are important in studying low-temperature plasmas in nature and industrial techniques of gaseous electronics and plasma processing. In the field of thermonuclear fusion research, the use of N2 , Ne, Ar, and other gases is being studied. The deliberate introduction of these impurities is intended to solve the problems of reducing the peak power loads and erosion of diverter components to acceptable levels. Thus, this also makes the accurate knowledge of the above data a necessity. The latest review of these data were included in articles by Trajmar et al. [1], Itikawa et al. [2], and Majeed and Strickland [3]. Trajmar et al. surveyed experimental techniques for measuring electron–molecule cross sections and available experimental data on electron scattering by various molecules including N2 , and numerically presented recommended cross sections applying renormalization when necessary. Itikawa et al. graphically gave recommended cross sections for collisions of electrons and photons with N2 . Majeed and Strickland numerically reported surveyed sets of total ionization and excitation cross sections of electrons in collisions with N2 , O2 , and O. Bibliographies of low-energy electron cross section data are included in [4–8]. Hayashi [9] published an extensive bibliography of original and review reports on experiments and theories of electron collisions with N2 covering the period 1906–2000. In the present work, we have updated the compilation of cross sections for collisions of electrons with N2 and have made a new compilation of cross sections for collisions of electrons with (N2+ ) surveying the literature through the middle of 2004. Threshold phenomena, resonances, dissociative attachment, and coincidence measurements are not covered in the present compilation. To facilitate dissemination of numerical data for practical applications we present the recommended data in the form of analytic expressions obtained by least-squares fits to the collected data. In evaluating the recommended data, 62

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules no general criteria for the screening of data have been applied, but considerations for rejecting some data points or data sets are described individually in the next subsection. This work has been done as part of the work at Japan Atomic Energy Research Institute to expand the Japanese Evaluated Atomic and Molecular Data Library (JEAMDL; http://www-jt60.naka.jaeri.go.jp/JEAMDL/index.html) (see [10,11] for the latest work). 1.1. Data sources 1.1.1. The Nitrogen molecule (N2 ) The total cross section (Graph 1) was measured by Nickel et al. [12] in the energy range 4–300 eV within a total error of 4.1%, by Nishimura and Yano [13] in the 7–500 eV range within a statistical error of 19%, by Hoffman et al. [14] in the 2.2–700 eV range within a statistical uncertainty of 3%, by Brennan et al. [15] from the integration of differential cross sections measured by a crossed-beam technique in the 1.5–5.0 eV range within an overall uncertainty of 25%, and by Garcia et al. [16] in the 600 eV–5 keV range within an error of 3%. The method used by Nickel et al. [12], Nishimura and Yano, Hoffman et al., and Garcia et al. is a beam attenuation technique. Itikawa et al. [2] gave a recommended data set in the energy range 0.05 eV–5 keV by revising the earlier recommendation by Hayashi [17]. The present compilation also includes the data set of Itikawa et al. All the data sets are quite consistent. The total cross section has fine structure around the 2.3-eV shape resonance, but this structure has been smoothed out in the present treatment. The same also applies to the fine structure in other cross sections. Data on the elastic scattering cross section (Graph 2) are available from Brennan et al. [15] in the energy range 1.5–5.0 eV and Shi et al. [18] at energies of 0.55 and 1.5 eV. The latter authors used the integration of differential cross sections measured by the relative flow technique, and the standard deviation of the results are ±6%. We have also used the recommended data of Itikawa et al. [2] obtained in the 0.05–2 keV range revising the earlier recommendation by Hayashi [17]. All the data sets are consistent. The data for the momentum transfer cross section (0.01 eV–3.4 keV) (Graph 3), and the cross section for rotational excitation of J=0 → 2 (0.03–3 eV) (Graph 4) were also taken from the recommendation by Itikawa et al. While the former is the revision of Hayashi’s recommendation [17], the latter is based on Onda’s calculation [19]. The cross section for vibrational excitation for v=0 → 1 (Graph 5) has been taken from Itikawa et al. [2] in the energy range 1–50 eV. The cross sections for vibrational excitation for v= 0 → 2 and for v=0 → 3 (Graphs 6 and 7) were measured by Brennan et al. [15] at energies 2.1 and 3.0 eV and by Sweeney and Shyn [20] by a crossed-beam technique in the energy range 1.9–2.6 eV within a total error of about 20%. Sweeney and Shyn also measured the cross section for vibrational excitation for v=0 → 4 (Graph 8) in the 2.1–2.6 eV range. The energy range in which the last three cross sections are available are so narrow that we have not made analytic expressions for those cross sections. We have used the compilation by Majeed and Strickland [3] for the total vibrational excitation cross section (Graph 9; here “total” means sum over final vibrational states) in the 1.3– 6 eV range. To make an analytic expression for this cross section, the contributions of vibrational excitation for v=0 → 1 at lower and higher energies (Graph 5) have been taken into account. Cross sections for excitation to the triplet states A3 Σu+ , B 3 Πg , W 3 ∆u , and B 03 Σu− and the singlet states a01 Σu− , a1 Πg , and w1 ∆u (Graphs 10–16) in the energy range from around 10 to 50 eV were taken from recommendations by Trajmar et al. [1], and those 63

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules in the energy range from threshold to 200 or 1 keV, from Majeed and Strickland [3]. The former authors applied renormalization to original data, when necessary, to take into account newer N2 elastic scattering cross sections. The two recommendations agree well in the overlapping energy range. Recently Campbell et al. [21] reported values for all these cross sections in the energy range from 15 to 50 eV. They obtained those values from the earlier crossed-beam differential cross section measurements of their group. While being roughly in agreement with the two sets of recommendations, the data points of Campbell et al. show rather large scatter. Therefore, we have not used them for determining the parameters of analytic expressions, though they are shown in the Graphs of the present compilation. The results of Finn and Doering [22], obtained by an inelastic electron scattering technique in the energy range 13–100 eV within a total expected uncertainty of ±50%, were added to the cross section for excitation to a1 Πg , and also agree with the two sets of recommended data (Graph 15). Hereafter no mention is made about the comparison among plural numbers of data sets except when there are discrepancies. James et al. [23] measured the cross sections for excitation to (b1 Πu ; v=2), (b1 Πu ; v=3), (b1 Πu ; v=4), (b1 Πu ; v=7), and (b1 Πu ; sum over v) (Graphs 17–21) in the energy range 14–400 eV by a crossed-beam technique. The data recommended by Majeed and Strickland [3] in the 13–30 eV range were also used (Graph 21). Ajello et al. [24] measured the cross sections for excitation to (b01 Σu+ ; v=12), (b01 Σu+ ; v=14), (b01 Σu+ ; v=15), (b01 Σu+ ; v=16), (b01 Σu+ ; v=17), and (b01 Σu+ ; sum over v), (Graphs 22–27) in the energy range from 14 or 16 to 400 eV. Data for (b01 Σu+ ; sum over v) in the energy range of 15 eV–1 keV was also taken from the compilation of Majeed and Strickland [3] (Graph 27) as well as the cross section data for excitation to (c1 Πu ; sum over v) (Graph 28) in the energy range 13 eV–1 keV. Ajello et al. [24] also measured the cross sections for excitation to (c04 1 Σu+ ; v=0), (c04 1 Σu+ ; v=4), and (c04 1 Σu+ ; sum over v) (Graphs 29–31) in the energy range 14–400 eV. The data recommended by Majeed and Strickland [3] in the energy range 14 eV–1 keV were also used (Graph 31). Zubek [25] measured cross sections for excitation to (C 3 Πu ; v=0), (C 3 Πu ; v=1), (C 3 Πu ; v=2), and (C 3 Πu ; sum over v) (Graphs 32–35) in the energy range from threshold to 17.5 eV with an electron impact spectrometer. Data for (C 3 Πu ; sum over v) have also been taken from the experimental results of Zubek and King [27] at energies of 17.5 and 20 eV, from the compilation by Trajmar et al. [1] in the 15–50 eV range, and from the compilation by Majeed and Strickland [3] in the 12–200 eV range (Graph 35). The cross section for excitation to E 3 Σg+ (Graph 36) was measured by Brunger et al. [26] in the energy range 11.87–12.69 eV with an estimated uncertainty of 40%. Experimental data of Zubek and King [27] at energies of 17.5 and 20 eV and the data from the compilation by Majeed and Strickland [3] in the 15–50 eV range were also included. Data on the cross section of excitation to a001 Σg+ (Graph 37) have been taken from the compilation of Trajmar et al. [1] for the energy range 15–50 eV and from the recommendation of Majeed and Strickland [3] for the range 13 eV–1 keV. Campbell et al. [21] also reported the cross sections for excitation to C 3 Πu , E 3 Σg+ , and a001 Σg+ (Graphs 35–37) in the energy range from 15 to 50 eV. Their data, obtained from the earlier differential cross section measurements of their group, are in moderate agreement with the results of other authors, except that two data points around the 10 eV peak of the cross section for excitation to E 3 Σg+ show a large discrepancy. We have not used the data of Campbell et al. for determining the parameters of analytic expressions. In a crossed-beam experiment by the use of an electron impact emission chamber 64

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules in tandem with two UV spectrometers, Ajello and Shemansky [28] measured the cross section for emission from a1 Πg → X 1 Σg+ summed over 120.0–260.0 nm (Graph 38) in the energy range 9.8–200 eV. In the present compilation, their data have been renormalized by a multiplicative factor of 0.892. This factor has been determined by the use of the new data on the emission cross section of the Lyman α line in the collision of electrons with hydrogen molecules (van der Burgt et al. [29]). The cross section for emission from (a1 Πg → X 1 Σg+ ; v=3 → 3) at 149.3 nm (Graph 39) was measured by Ajello [30] in the energy range 10.6–200 eV and by Mumma and Zipf [31] in the 10–17.8 eV range. The cross sections for emission from b01 Σµu+ → X 1 Σg+ summed over 83.7–96.5 nm (Graph 40) was measured by Ajello et al. [24] in the energy range 14–400 eV. The cross section for emission from (C 3 Πu → B 3 Πg ; v=0 → 0) at 337.03 nm (Graph 41) was measured by Shemansky and Broadfoot [32] in the energy range from threshold to 50 eV. However, only the data up to 18.5 eV have been used in the present compilation, because those authors noted that the results above 25 or 30 eV appeared to be untrustworthy because of the presence of low energy electrons reflected from the collector of the electron gun. The same cross section was also measured by Imami and Borst [33] in the energy range from threshold to 1 keV, by Zubek [25] in the range up to 17.5 eV, and by Shemansky et al. [34] up to 40 eV. The data in the energy range 15–50 eV compiled by Trajmar et al. [1] were also used for this cross section, as deduced from the excitation cross section, by applying the branching ratio of 0.251 for the emission. The branching ratio has been taken from Shemansky et al. [34]. Shemansky et al. [34] also measured the cross section for emission from (C 3 Πu → B 3 Πg ; v=1 → 0) at 315.80 nm (Graph 42) in the energy range 11.4–40 eV. The cross section for emission from (C 3 Πu → B 3 Πg ; v=0 → 2) at 380.4 nm (Graph 43) was measured by Shaw and Campos [35] in the energy range from threshold to 400 eV. Shemansky and Broadfoot [32] provided experimental data on the cross section for emission from (B 3 Πg → A3 Σu+ ; v=3 → 1) at 762.6 nm (Graph 44) in the energy range 8.5–28 eV. The total ionization cross section (Graph 45) was measured by Rapp and EnglanderGolden [36] in the energy range from threshold to 1 keV, by Straub et al. [37] in the same energy range within an uncertainty of ±3.5%, and by Tian and Vidal [38] in the range from threshold to 600 eV within an error of about 10%. Straub et al. also measured the cross section for (N2+ ) production (Graph 46) in the energy range 17 eV–1 keV. Tian and Vidal provided the cross sections for N+ production (Graph 47), N+ +N production (Graph 48), and N+ +N+ production (Graph 49), all in the range from threshold to 600 eV. The cross section for N+ production (Graph 47) was measured by Straub et al. [37], as well, in the energy range from threshold to 1 keV. There are minor discrepancies between the data of Tian and Vidal and those of Straub et al. Considering the behavior of the results from the threshold energy, the data of the latter authors seem to be more reliable. Therefore, the data of Tian and Vidal at the lowest four energies have not been used in the present formulation of the analytic expression. Straub et al. [37] and Tian and Vidal [38] provided the cross section for N2+ production (Graph 50) in the range from threshold to 1 keV. The cross section for N2+ +N production (Graph 51) was measured by Tian and Vidal in the range from threshold to 600 eV, and the cross section for N+ +N2+ production (Graph 52), by Tian and Vidal in the 100–450 eV range. There are more sets of old data on partial ionization cross sections of N2 . However, the review article by Tawara and Kato [39] indicates that those data show much scatter, so that we have adopted only the newest data. 65

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules The cross section for N2+ (X 2 Σg+ production (Graph 53) was measured by Abramzon et al. [40] by the use of electron scattering and laser-induced fluorescence techniques in the range from threshold to 180 eV with an uncertainty of 7%. The cross section for the excitation of [N2+ (B 2 Σu+ → X 2 Σg+ ; v=0 → 0] at 391.4 nm (Graph 54) was measured by Borst and Zipf [41] in the energy range from threshold to 3 keV. They extrapolated the cross section to 10 keV by fitting the Bethe–Oppenheimer relation to the data in the range 200 eV–3 keV. In the present compilation, both their experimental data and the Bethe– Oppenheimer curve read off at discrete energies from their Graph have been adopted. The same cross section was measured by Skubenich and Zapesochnyy [42] in the range from threshold to 400 eV. These authors also measured cross sections for the excitation of [N2+ (B 2 Σu+ → X 2 Σg+ ; v=0 → 1] at 427.8 nm (Graph 55), [N2+ (B 2 Σu+ → X 2 Σg+ ; v=0 → 2] at 470.9 nm (Graph 56), [N2+ (B 2 Σu+ → X 2 Σg+ ; v=1 → 0] at 358.2 nm (Graph 57), [N2+ (A2 Πu+ → X 2 Σg+ ; v=1 → 0] at 918.3 nm (Graph 58), [N2+ (A2 Σu+ → X 2 Σg+ ; v=2 → 0] at 785.4 nm (Graph 59), and [N2+ (A2 Πu+ → X 2 Σg+ ; v=3 → 0] at 687.4 nm (Graph 60), all in the energy range from threshold to 400 eV. The cross section for N+N production (Graph 61) has been taken from Cosby’s recommendation [43] in the energy range 12–200 eV. The emission cross section for N(4D0 → 4P ) at 868.0 nm (Graph 62) was measured by Aarts and de Heer [44] in the energy range 100–500 eV and by Filippelli et al. [45] in the range 22.4–193 eV. The emission cross section for N(4P → 4S 0 ) at 120.0 nm (Graph 63) was measured by Aarts and de Heer [44] in the energy range 100 eV–5 keV, by Mumma and Zipf [31] in the range 22.5–350 eV, by Forand et al. [46] at an energy of 200 eV, by Ajello et al. [24] at energies 100 and 200 eV, and by James et al. [23] in the 20–200 eV range. The Mumma–Zipf and Aarts–de Heer papers also include the results of measurements of cross sections for emission from N(2P → 2D0 ) at 149.3 nm (Graph 64) and emission from N(2D → 2 0 D ) at 124.3 nm (Graph 65). The energy range of the Mumma–Zipf data is 100 eV–5 keV and that of the Aarts–de Heer data is from threshold to 350 eV. The emission cross section for N(2P → 2P 0 ) at 174.3 nm (Graph 66) was measured by Ajello [30] in the energy range from threshold to about 200 eV. The emission cross sections for N(4P → 4S 0 ) at 113.4 nm (Graph 67) and N+ (3D0 → 3P ) at 108.4 nm (Graph 68) were measured by Aarts and de Heer [44] in the energy range 60 eV–3 keV and 50–5 keV. Low energy data are deficient for these two cross sections. 1.1.2. The singly ionized nitrogen molecule (N2+ ) Bahati et al. [47] measured the single ionization cross section (Graph 69) in the energy range from threshold to 2.5 keV. The N+ production cross section (Graph 70) was measured by Van Zyl and Dunn [48] in the energy range from threshold to about 500 eV. Peterson et al. [49] measured the N+ +N production (dissociative excitation or dissociation) cross section (Graph 71) with an ion storage ring in combination with an imaging technique in the energy range from threshold to 54.3 eV. Bahati et al. [47] measured the same cross section by the animated crossed electron–ion beam method in the energy range from threshold to 2.5 keV. The two sets of results show large discrepancies of a factor of about three. Considering that the discrepancies might be partly due to the two experimental methods, Bahati et al. performed many tests to check the possible reason, without reaching a definitive conclusion. At energies below the single-ionization and dissociativeionization thresholds (about 30 eV), however, one expects the dissociative-excitation cross section to be the same as the N+ production cross section as observed by Van Zyl and Dunn [48] (Graph 70). The data of Peterson et al. agree with those of Van Zyl and 66

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules Dunn, while those of Bahati et al. do not. Thus, we adopted the results of Peterson et al., and used only the high-energy trend of the data of Bahati et al. to make an analytic expression. Bahati et al. also measured the N+ +N+ production (or dissociative ionization) cross section (Graph 72) from threshold to 2.5 keV. The N2+ +N production (asymmetrical dissociative ionization) cross section (Graph 73) was measured by Siari et al. [50] by the animated crossed beams method in the energy range from threshold to approximately 2 keV within the total uncertainty of ±5.5% at the cross section maximum. The N+N production (or dissociative recombination) cross section (Graph 74) was measured by Peterson et al. [49] in the 0.012–1.18 eV range. Older data obtained by Noren et al. [51] are generally much lower than the results of Peterson et al., and are about five times lower at 0.07 eV. We have not included the data of Noren et al. in the present compilation. Though undulations seen in the data of Peterson et al. are also seen in the data of Noren et al., the present analytic expression neglected this minor behavior. Crandall et al. [52] measured the cross sections for electron impact excitation (Graph 75) by a crossed-beam technique. The total uncertainty of their results at high confidence is about 18%. 1.2. Analytic expressions The functional form of the analytic expressions used in the present work are the same as, or similar to, those used in the previous work [10,11]. For cross sections except for ionization, modified forms of equations derived semiempirically by Green and McNeal [53] have been used. For ionization cross sections, use is made of the function with an asymptotic form of ln E/E (E being the incident electron energy), as proposed by Lotz [54], and with a modified near-threshold form [see Eq. (7) below]. In writing modified Green–McNeal equations, we introduce three different functions of the form: f1 (x; c1 , c2 ) = σ0 c1 (x/ER )c2 ,

(i)

f2 (x; c1 , c2 , c3 , c4 ) = f1 (x; c1 , c2 )

1 + (x/c3 )c2 +c4 ,

.h

i

.h

f3 (x; c1 , c2 , c3 , c4 , c5 , c6 ) = f1 (x; c1 , c2 )

(ii)

1 + (x/c3 )c2 +c4 + (x/c5 )c2 +c6 , i

(iii)

with σ0 = 1 × 10−16 cm2 and ER = 1.361 × 102 keV (one Rydberg). The symbols x and ci (i = 1, 2, 3, . . . , 6) in Eqs. (i)–(iii) denote dummy parameters. The cross sections recommended in the present paper are expressed by one of the following forms involving the combination of the above functions: σ σ σ σ σ σ

= f2 (E1 ; a1 , a2 , a3 , a4 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a4 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a8 ) = f2 (E1 ; a1 , a2 , a3 , a4 ) + f2 (E1 ; a5 , a6 , a7 , a8 ) + f2 (E1 ; a9 , a10 , a11 , a12 ) = f3 (E1 ; a1 , a2 , a3 , a4 , a5 , a6 ) = f3 (E1 ; a1 , a2 , a3 , a4 , a5 , a6 ) + f2 (E1 ; a7 , a8 , a9 , a10 )

σ = σ0 a1 [ln (E/Eth ) + a2 ]

.

Eth E [1 + (a3 /E1 )a4 ] ,

(1) (2) (3) (4) (5) (6) (7)

where E1 = E − Eth with E the incident electron energy in keV and Eth the threshold 67

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules energy of reaction in keV. Depending on the formula chosen from Eqs. (1)–(6) above, a1 , a2 , etc., are substituted for c1 , c2 , etc., in f2 and f3 given by Eqs. (ii) and (iii). Tables 1 and 2 (read across two facing pages) give the values of the fitting parameters (a1 , a2 , . . .), which have been determined by least-squares fits to the collected data (in some cases with additional constraints to guarantee reasonable behavior outside the energy range of the available data). The present expressions allow one not only to interpolate but also to extrapolate the data to some extent. This is in contrast to polynomial fits, which frequently show physically unreasonable behavior just outside the energy range of the available data. The resulting analytic expressions are shown in Graphs together with the compiled data. Normally the present forms fit the data quite well. To show the agreement quantitatively, the root-mean-square and the maximum deviations of the expressions from the data are also given in Tables. Acknowledgments We are indebted to Professor Y. Itikawa of the Institute of Space and Astronautical Science for his critical reading of the manuscript and invaluable comments. Thanks are due to Dr. T. Ozeki of Japan Atomic Energy Research Institute for his encouragement and support of this work. This paper has been prepared as an account of work supported partly by a research contract of Japan Atomic Energy Research Institute with Osaka Nuclear Science Association. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.adt.2006.02.002. References [1] S. Trajmar, D.F. Register, A. Chutjian, Phys. Rep. 97 (1983) 219. [2] Y. Itikawa, M. Hayashi, A. Ichimura, K. Onda, K. Sakimoto, K. Takayanagi, M. Nakamura, H. Nishimura, T. Takayanagi, J. Phys. Chem. Ref. Data 15 (1986) 985. [3] T. Majeed, D.J. Strickland, J. Phys. Chem. Ref. Data 26 (1997) 335. [4] L.J. Kieffer, “Bibliography of Low Energy Electron and Photon Cross Section Data (through December 1974),” NBS Special Publication 426, Natl. Bureau of Standards, 1976. [5] L.J. Kieffer, J.R. Rumble, E.C. Beaty, “Bibliography of Low Energy Electron and Photon Cross Section Data (January 1975 through December 1977),” NBS Special Publication 426, Suppl. 1, Natl. Bureau of Standards, 1979. [6] J.W. Gallagher, E.C. Beaty, “Bibliography of Low Energy Electron and Photon Cross Section Data (1978),” Univ. Colorado JILA Information Center Rep. No. 18, 1980. [7] J.W. Gallagher, E.C. Beaty, “Bibliography of Low Energy Electron and Photon Cross Section Data (1979),” Univ. Colorado JILA Information Center Rep. No. 21, 1981. [8] Y. Itikawa, “Bibliography on Electron Collisions with Molecules: Rotational and Vibrational Excitations, 1980–2000,” Natl. Inst. Fusion Sci. Rep. NIFS-DATA-63, 2001. [9] M. Hayashi, “Bibliography of Electron and Photon Cross Sections with Atoms and Molecules Published in the 20th Century – Nitrogen Molecule,” Natl. Inst. Fusion Sci. Rep. NIFS-DATA-77, 2003. [10] T. Shirai, T. Tabata, H. Tawara, At. Data Nucl. Data Tables 79 (2001) 143. [11] T. Shirai, T. Tabata, H. Tawara, Y. Itikawa, At. Data Nucl. Data Tables 80 (2002) 1.

68

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules [12] J.C. Nickel, I. Kanik, S. Trajmar, K. Imre, J. Phys. B 25 (1992) 2427. [13] H. Nishimura, K. Yano, J. Phys. Soc. Jpn. 57 (1988) 1951. [14] K.R. Hoffman, M.S. Dababneh, Y.-F. Hsieh, W.E. Kauppila, V. Pol, J.H. Smart, T.S. Stein, Phys. Rev. A 25 (1982) 1393. [15] M.J. Brennan, D.T. Alle, P. Euripides, S.J. Buckman, M.J. Brunger, J. Phys. B 25 (1992) 2669. [16] G. García, A. Pérez, J. Campos, Phys. Rev. A 38 (1988) 654. [17] M. Hayashi, “Recommended Values of Transport Cross Sections for Elastic Collision and Total Collision Cross Section for Electrons in Atomic and Molecular Gases,” Inst. Plasma Phys. Nagoya Univ. Rep. IPPJ-AM-19, 1981. [18] X. Shi, T.M. Stephen, P.D. Burrow, J. Phys. B 26 (1993) 121. [19] K. Onda, J. Phys. Soc. Jpn. 54 (1985) 4544. [20] C.J. Sweeney, T.W. Shyn, Phys. Rev. A 56 (1997) 1384. [21] L. Campbell, M.J. Brunger, A.M. Nolan, L.J. Kelly, A.B. Wedding, J. Harrison, P.J.O. Teubner, D.C. Cartwright, B. McLaughlin, J. Phys. B 34 (2001) 1185. [22] T.G. Finn, J.P. Doering, J. Chem. Phys. 64 (1976) 4490. [23] G.K. James, J.M. Ajello, B. Franklin, D.E. Shemansky, J. Phys. B 23 (1990) 2055. [24] J.M. Ajello, G.K. James, B.O. Franklin, D.E. Shemansky, Phys. Rev. A 40 (1989) 3524. [25] M. Zubek, J. Phys. B 27 (1994) 573. [26] M.J. Brunger, P.J.O. Teubner, S.J. Buckman, Phys. Rev. A 37 (1988) 3570. [27] M. Zubek, G.C. King, J. Phys. B 27 (1994) 2613. [28] J.M. Ajello, D.E. Shemansky, J. Geophys. Res. 90 (1985) 9845. [29] P.J.M. van der Burgt, W.B. Westerveld, J.S. Risley, J. Phys. Chem. Ref. Data 18 (1989) 1757. [30] J.M. Ajello, J. Chem. Phys. 53 (1970) 1156. [31] M.J. Mumma, E.C. Zipf, J. Chem. Phys. 55 (1971) 5582. [32] D.E. Shemansky, A.L. Broadfoot, J. Quant. Spectrosc. Radiat. Transf. 11 (1971) 1401. [33] M. Imami, W.L. Borst, J. Chem. Phys. 61 (1974) 1115. [34] D.E. Shemansky, J.M. Ajello, I. Kanik, Astrophys. J. 452 (1995) 472. [35] M. Shaw, J. Campos, J. Quant. Spectrosc. Radiat. Transf. 30 (1983) 73. [36] D. Rapp, P. Englander-Golden, J. Chem. Phys. 43 (1965) 1464. [37] H.C. Straub, P. Renault, B.G. Lindsay, K.A. Smith, R.F. Stebbings, Phys. Rev. A 54 (1996) 2146. [38] C. Tian, C.R. Vidal, J. Phys. B 31 (1998) 5369. [39] H. Tawara, T. Kato, At. Data Nucl. Data Tables 36 (1987) 167. [40] N. Abramzon, R.B. Siegel, K. Becker, J. Phys. B 32 (1999) L247. [41] W.L. Borst, E.C. Zipf, Phys. Rev. A 1 (1970) 834. [42] V.V. Skubenich, I.P. Zapesochnyy, Geomag. Aeron. 21 (1981) 355. [43] P.C. Cosby, J. Chem. Phys. 98 (1993) 9544. [44] J.F.M. Aarts, F.J. de Heer, Physica 52 (1971) 45. [45] A.R. Filippelli, F.A. Sharpton, C.C. Lin, R.E. Murphy, J. Chem. Phys. 76 (1982) 3597. [46] J.L. Forand, S. Wang, J.W. Woolsey, J.W. McConkey, Can. J. Phys. 66 (1988) 349. [47] E.M. Bahati, J.J. Jureta, D.S. Belic, H. Cherkani-Hassani, M.O. Abdellahi, P. Defrance, J. Phys. B 34 (2001) 2963. [48] B. Van Zyl, G.H. Dunn, Phys. Rev. 163 (1967) 43. [49] J.R. Peterson, A. Le Padellec, H. Danared, G.H. Dunn, M. Larsson, A. Larson, R. Peverall, C. Strömholm, S. Rosén, M. af Ugglas, W.J. van der Zande, J. Chem. Phys. 108 (1998) 1978. [50] A. Siari, D.S. Belic, P. Defrance, S. Rachafi, J. Phys. B 32 (1999) 587. [51] C. Noren, F.B. Yousif, J.B.A. Mitchell, J. Chem. Soc. Faraday Trans. 85 (1989) 1697.

69

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules [52] D.H. Crandall, W.E. Kauppila, R.A. Phaneuf, P.O. Taylor, G.H. Dunn, Phys. Rev. A 9 (1974) 2545. [53] A.E.S. Green, R.J. McNeal, J. Geophys. Res. 76 (1971) 133. [54] W. Lotz, Z. Phys. 206 (1967) 205.

70


Explanation of Tables Table 1.

Energy ranges of data, fitting errors, and parameters of the analytic expressions for nitrogen molecules, N2 Number label identifying a particular reaction process in the same sequence as in the Graphs The relevant reaction process. Process Minimum energy (in keV) of experimental data Emin Maximum energy (in keV) of experimental data Emax Root-mean-square relative deviation (in %) of the δrms analytic expression from the data Maximum relative deviation (in %) of the analytic δmax expression from the data Eδmax Energy (in keV) at which the relative deviation takes on the value δmax Eq. The identifying number of the equation to be used for deriving the recommended cross sections n Number of applicable fit parameters Threshold energy of the reaction (in keV) Eth aj (j = 1, 2, . . . , 12) Fit parameters The notation 1.23−1 means 1.23×10−1 . No.

Table 2.

Energy ranges of data, fitting errors, and parameters of the analytic expressions for singly ionized nitrogen molecules, (N2+ ) Same as for Table 1.

Explanation of Graphs Graphs 1–75.

Cross Section vs Electron Energy Graphs are numbered in the same sequence as in Tables 1 and 2 Ordinate Abscissa Solid line Symbols

Cross section in cm2 Electron energy in eV in the laboratory system Recommended data from the analytic formula of the present work Experimental data from sources as explained in the legends

71

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules Table 1 Energy ranges of data, fitting errors, and parameters of the analytic expressions for nitrogen molecules, N2 . See page 71 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

1

Total scattering

5.14−5

5.00+0

4.7+0

1.5+1

1.50−3

2

Elastic scattering

5.14−5

5.22+0

3.6+0

9.1+0

1.50−3

3

Momentum transfer

1.05−5

3.44+0

6.1+0

1.5+1

8.07−3

4

Rotational excitation J=0 → 2

2.96−5

2.94−3

6.0+0

1.1+1

4.05−4

5

Vibrational excitation v=0 → 1

1.05−3

4.85−2

2.6+1

6.6+1

2.01−3

6 7 8 9

Vibrational excitation v=0 → 2 Vibrational excitation v=0 → 3 Vibrational excitation v=0 → 4 Total vibrational excitation

... ... ... 1.30−3

... ... ... 6.00−3

... ... ... 3.5+1

... ... ... 5.3+1

... ... ... 4.00−3

10 11 12 13

Excitation Excitation Excitation Excitation

A3 Σu+ B 3 Πg W 3 ∆u B 03 Σu−

6.50−3 7.60−3 8.00−3 9.00−3

2.00−1 2.00−1 2.00−1 2.00−1

1.9+1 9.1+0 1.7+1 1.3+1

4.8+1 2.1+1 5.1+1 3.0+1

5.00−2 1.50−1 1.00−2 2.00−2

14

Excitation to a01 Σu−

1.10−2

1.00+0

9.4+0

2.2+1

1.70−2

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation Excitation

1.00−2 9.00−3 1.40−2 1.40−2 1.40−2 1.40−2 1.30−2 1.40−2 1.60−2 1.60−2 1.60−2 1.60−2 1.40−2 1.30−2 1.40−2 1.60−2 1.40−2 1.13−2

1.00+0 2.00−1 4.00−1 4.00−1 4.00−1 4.00−1 4.00−1 4.00−1 4.00−1 4.00−1 4.00−1 4.00−1 1.00+0 1.00+0 4.00−1 4.00−1 1.00+0 1.75−2

1.3+1 1.3+1 0.6+0 0.6+0 0.7+0 0.7+0 1.1+1 0.8+0 0.4+0 0.4+0 0.5+0 0.3+0 1.2+1 3.4+0 0.1+0 0.1+0 1.8+0 0.6+0

3.5+1 3.6+1 1.1+0 0.9+0 1.2+0 1.1+0 3.2+1 1.5+0 0.8+0 0.7+0 1.1+0 0.8+0 3.5+1 7.8+0 0.2+0 0.2+0 4.1+0 1.3+0

1.00−2 2.00−2 6.00−2 6.00−2 1.60−2 6.00−2 1.40−2 2.00−1 1.00−1 1.00−1 1.00−1 1.00−1 1.50−2 5.00−2 1.80−2 6.00−2 1.60−2 1.38−2

33

Excitation to C 3 Πu ; v=1

1.13−2

1.75−2

4.2+0

1.5+1

1.15−2

34

Excitation to C 3 Πu ; v=2

1.18−2

1.70−2

2.2+0

4.9+0

1.20−2

35

Excitation to C 3 Πu

1.13−2

2.00−1

9.5+0

3.4+1

1.30−2

36

Excitation to E 3 Σg+

1.19−2

5.00−2

1.1+1

2.9+1

1.70−2

37

Excitation to a001 Σg+

1.30−2

1.00+0

1.1+1

3.3+1

3.00−2

38 39 40 41

Emission Emission Emission Emission

a1 Πg → X 1 Σg+ over 120.0–260.0 nm a1 Πg → X 1 Σg+ ; v=3 → 3; at 149.3 nm b01 Σu+ → X 1 Σg+ over 85.7–94.5 nm C 3 Πu → B 3 Πg ; v=0 → 0 at 337.03 nm

1.00−2 1.00−2 1.40−2 1.11−2

2.00−1 2.00−1 4.00−1 3.00−1

2.6+0 4.7+0 1.4+0 2.0+1

6.5+0 1.0+1 2.2+0 8.9+1

1.20−2 1.25−2 1.80−2 1.15−2

42

Emission from C 3 Πu → B 3 Πg ; v=1 → 0 at 315.80 nm

1.14−2

4.02−2

5.3+0

1.5+1

1.16−2

to to to to

to to to to to to to to to to to to to to to to to to

a1 Πg w 1 ∆u b1 Πu ; v=2 b1 Πu ; v=3 b1 Πu ; v=4 b1 Πu ; v=7 b1 Πu b01 Σu+ ; v=12 b01 Σu+ ; v=14 b01 Σu+ ; v=15 b01 Σu+ ; v=16 b01 Σu+ ; v=17 b01 Σu+ c1 Πu + c01 4 Σu ; v=0 + ; v=4 c01 Σ u 4 + c01 Σ 4 u C 3 Πu ; v=0

from from from from

72

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules Table 1 (continued) Energy ranges of data, fitting errors, and parameters of the analytic expressions for nitrogen molecules, N2 . See page 71 for Explanation of Tables No.

Eq.

1

n

Eth

a1 a7

6

10

0.00+0

2

6

10

0.00+0

3

6

10

0.00+0

4

2

7

1.50−6

5

4

12

2.90−4

6 7 8 9

... ... ... 4

... ... ... 12

6.130+4 9.170+7 1.440+4 9.140+5 1.370+2 1.960+7 1.120+8 2.071−3 1.83+10 2.087−3

2.90−4

10 11 12 13

1 5 5 3

4 6 6 8

6.17−3 7.35−3 7.36−3 8.16−3

14

3

8

8.40−3

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

1 5 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 3

4 6 4 4 4 4 6 6 6 6 6 6 6 6 6 6 6 8

8.55−3 8.89−3 1.27−2 1.28−2 1.28−2 1.32−2 1.25−2 1.39−2 1.41−2 1.42−2 1.42−2 1.43−2 1.29−2 1.21−2 1.29−2 1.40−2 1.29−2 1.10−2

33

3

8

1.12−2

34

3

8

1.15−2

35

3

8

1.10−2

36

4

12

1.19−2

37

3

8

1.23−2

38 39 40 41

1 1 5 3

4 4 6 8

8.55−3 8.30−3 1.29−2 1.10−2

42

3

8

1.13−2

1.730−2 1.970−3 3.970−1 6.820+0 9.140−1 7.500−1 5.780−2 6.090−1 2.720−2 2.560+0 1.220+0 3.702−2 6.795−2 1.097−1 2.774−2 8.910+4 2.464−2 4.160−2 5.340−2 7.120−2 3.560−2 2.280+0 9.020+4 2.257−1 2.365−2 2.170−1 9.740+2 8.570−3 3.100+4 3.640−3 7.390+2 3.770−3 6.820+2 6.170−3 1.750−2 6.290−4 8.880−1 5.680−3 1.750+0 2.540−2 1.320+0 2.260+1 2.540−2 1.440+2 1.220−2

a2 a8

a3 a9

a4 a10

a5 a11

a6 a12

1.530+0 8.320+0 1.284+0 6.180+0 5.820−1 7.820+0 3.146+0

3.110−5 2.362−3 3.190−5 2.437−3 4.010−4 2.370−3 4.180−5

−1.540−1 6.050+0 1.550−1 5.980+0 1.280−1 5.870+0 2.670−1

9.310−4

8.770−1

9.000−4

8.600−1

9.290−3

1.545+0

4.370+7

8.980+0

1.000+1 7.980+0

9.410−4 1.370−2

4.200−1 9.200+0

1.240+9 1.940−2

1.000+1 6.900+0

5.510−1 6.390+0 9.330−1 1.774+0 1.310+0 1.970+0 3.390+0 1.550+0 1.061+0 2.040+0 1.361+0 9.461−1 9.396−1 9.774−1 9.439−1 6.020+0 1.612+0 1.702+0 1.690+0 1.761+0 1.725+0 3.800+0 7.330+0 2.052+0 1.923+0 2.041+0 4.898+0 1.310+0 7.150+0 9.500+0 5.630+0 3.400+1 4.750+0 1.529+0 −3.280−1 4.350+0 1.860+0 8.930−1 1.937+0 9.090−1 3.995+0 3.090+0 2.730+0 4.440+0 1.580+0

3.510−2 1.530−2 1.330−2 3.310−3 9.900−3 6.700−3

2.320+0 7.970+0 2.503+0 9.150−1 2.230+0 3.030+0

9.070+9 2.020−2

1.000+1 9.150+0

1.300−2 3.100−2 2.120−2

3.650+0 4.500+0 1.500−1

6.230−3

2.630+0

8.260−3

2.100+0

6.690−3 3.770−3 1.618−2 1.646−2 1.599−2 1.689−2 9.880−4 1.118−2 9.080−3 9.120−3 8.430−3 9.020−3 5.030−3 1.700−3 5.650−3 7.747−3 7.830−3 2.617−3

9.300−1 1.430+0 6.094−1 6.126−1 6.037−1 6.113−1 −1.290+0 −2.000−2 −2.930−1 −2.980−1 −3.720−1 −2.990−1 −7.700−1 −1.230+0 −7.270−1 −6.290−1 −5.550−1 2.140+0

2.130−2

4.510+0

2.070−3 3.120−2 1.970−2 1.970−2 1.780−2 1.980−2 9.800−3 2.970−3 1.694−2 2.119−2 2.230−2 2.390−1

5.750−1 8.700−1 6.660−1 6.600−1 6.290−1 6.690−1 5.900−1 5.720−1 5.930−1 6.169−1 7.020−1 8.570−1

2.490−3

8.000−1

1.050−1

7.830−1

2.742−3

1.390+0

1.090−2

4.740−1

3.060−3

3.620+0

1.000+0

1.212+0

3.730−4 1.540−2 3.560−3

9.550+0 1.210+0 3.770+0

7.190+7 1.230−2 1.140+2

6.750+0 2.050+0 8.420+0

6.790−3 3.740−3 3.080−3 2.900−3

8.610−1 3.650−1 −1.128+0 1.587+0

6.600−3 1.070−2

4.740−1 3.900−1

2.580−3

1.820+0

2.540−2

5.520−1

(continued on next paage)

73


Process

Emin

Emax

δrms

δmax

Eδmax

43

Emission from C 3 Πu → B 3 Πg ; v=0 → 2 at 380.4 nm

1.18−2

4.00−1

3.2+0

5.1+0

3.82−2

44

Emission from B 3 Πg → A3 Σu+ ; v=3 → 1 at 762.6 nm

8.50−3

2.78−2

3.6+0

7.5+0

1.07−2

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

Total ionization (N2+ ) production N+ production N+ +N production N+ +N+ production N2+ production N2+ +N production N+ +N2+ production N2+ (X 2 Σg+ ) production Excitation to N2+ (B 2 Σu+ → X 2 Σg+ ; v=0 → 0) Excitation to N2+ (B 2 Σu+ → X 2 Σg+ ; v=0 → 1) Excitation to N2+ (B 2 Σu+ → X 2 Σg+ ; v=0 → 2) Excitation to N2+ (B 2 Σu+ → X 2 Σg+ ; v=1 → 0) Excitation to N2+ (A2 Πu+ → X 2 Σg+ ; v=1 → 0) Excitation to N2+ (A2 Πu+ → X 2 Σg+ ; v=2 → 0) Excitation to N2+ (A2 Πu+ → X 2 Σg+ ; v=3 → 0) N+N production Emission from N(4D0 → 4P ) at 868.0 nm

1.60−2 1.70−2 3.00−2 2.50−2 4.50−2 7.00−2 7.00−2 1.00−1 3.00−2 1.90−2 2.05−2 2.05−2 2.92−2 1.70−2 1.73−2 1.75−2 1.20−2 2.24−2

1.00+0 1.00+0 1.00+0 6.00−1 6.00−1 1.00+0 5.50−1 4.50−1 1.80−1 1.00+1 3.99−1 3.99−1 4.00−1 3.99−1 3.99−1 3.97−1 2.00−1 5.00−1

1.2+1 4.2+0 2.9+0 2.9+0 2.6+0 1.5+1 3.5+0 0.7+0 4.9+0 6.2+0 3.9+0 0.8+0 1.7+0 0.7+0 0.7+0 1.5+0 1.2+1 1.8+0

8.4+1 1.3+1 1.0+1 5.0+0 8.0+0 7.7+1 7.6+0 1.7+0 1.0+1 3.5+1 9.6+0 1.4+0 3.5+0 1.6+0 1.7+0 2.7+0 3.2+1 6.6+0

1.70−2 2.00−2 4.50−2 6.00−1 5.00−2 7.00−2 1.75−1 4.00−1 5.50−2 2.05−2 3.16−2 2.23−1 3.01−1 7.14−2 1.92−1 3.97−1 1.40−2 1.00−1

63

Emission from N(4P → 4S 0 ) at 120.0 nm

2.02−2

5.00+0

8.6+0

3.9+1

2.25−2

64

Emission from N(2P → 2D0 ) at 149.3 nm

2.05−2

5.00+0

2.4+0

4.9+0

2.75−2

65

Emission from N(2D → 2D0 ) at 124.3 nm

2.25−2

5.00+0

3.8+0

9.3+0

4.00+0

66

Emission from N(2P → 2P 0 ) at 174.3 nm

2.17−2

1.98−1

4.9+0

1.2+1

2.21−2

67 68

Emission from N(4P → 4S 0 ) at 113.4 nm Emission from N+ (3D0 → 3P ) at 108.4 nm

6.00−2 5.00−2

3.00+0 5.00+0

3.5+0 2.4+0

1.0+1 4.9+0

8.00−1 4.00−1

at at at at at at at

391.4 427.8 470.9 358.2 918.3 785.4 687.4

74

nm nm nm nm nm nm nm


Eq.

n

Eth

a1 a7

43

3

8

1.10−2

44

6

10

7.97−3

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

7 7 7 7 7 5 5 5 1 5 1 5 1 5 5 1 5 3

4 4 4 4 4 6 6 6 4 6 4 6 4 6 6 4 6 8

1.56−2 1.56−2 2.43−2 1.80−2 3.40−2 5.39−2 5.39−2 6.85−2 1.56−2 1.88−2 1.88−2 1.88−2 1.90−2 1.69−2 1.72−2 1.74−2 9.76−3 2.15−2

63

3

8

2.01−2

64

6

10

2.04−2

65

6

10

2.21−2

66

6

10

2.04−2

67 68

1 1

4 4

2.01−2 3.57−2

9.350−2 2.570−3 2.04+12 4.360+2 3.460−3 2.639−3 5.060−4 5.060−4 2.730−6 1.030−4 6.400−4 1.496−4 3.310−1 9.260−2 2.760−2 1.510−1 6.260−3 6.920−2 5.670−2 6.560−3 1.870+0 1.460−2 3.670−2 2.830−6 7.800−2 5.290−3 3.910−3 1.620+2 8.380−4 6.870−4 1.680−2 7.270−3 2.298−2

a2 a8

a3 a9

2.000+0 7.490−1 1.000+1 1.000+1 7.000−2 0.000+0 4.460+0 2.640−1 3.350+2 5.500+0 2.140+0 2.583+0 1.440+0 1.030+0 5.880−1 2.720+0 7.110−1 8.104−1 1.236+0 7.617−1 3.030+0 1.009+0 5.360−1 8.200+0 7.300−1 1.690+0 2.410−1 1.000+1 2.440−1 1.000+1 7.700−1 7.000−1 3.930−1

75

a4 a10

a5 a11

a6 a12

6.000−3

3.670+0

2.050−1

8.930−1

5.817−4 6.020−3 5.750−2 4.690−2 6.390−2 3.540−2 7.460−2 2.380−2 6.350−2 5.762−2 3.570−2 5.250−2 1.330−1 2.360−3 8.770−2 7.770−2 1.200−2 9.230−2 1.230−2 7.840−3

−6.100−1 1.010+0 1.023+0 9.750−1 1.856+0 2.362+0 2.116+0 −1.730+0 3.500−1 −1.187+0 4.000−1 2.700−1 8.700−1 −8.520−1 6.490−1 6.610−1 −2.850−1 8.280−1 4.700−2 2.930+0

1.340−3

5.600+0

4.470−2 2.000−1 8.596−2

8.700−1 2.400+0 1.096+0

1.050−1

9.100−1

9.840−3

5.640−1

3.360−1 6.070−2

3.880+0 1.160+0

3.500−2 5.350−3

1.100+0 1.610+0

3.970−2

7.800−1

1.093−2

9.800−1

4.600−2 1.281−2 4.010−3 1.420−2 1.757−2 9.400−3 6.630−2 1.200−1

5.300−2 8.300+0 −1.167+0 1.000+1 −8.000−1 8.000−1 8.520−1 9.540−1

5.400−2

8.870−1

6.620−3

8.694−1

2.320−2

8.000−1

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules Table 2 Energy ranges of data, fitting errors, and parameters of the analytic expressions for nitrogen molecules, (N2+ ). See page 71 for Explanation of Tables No.

Process

Emin

Emax

δrms

δmax

Eδmax

69 70 71 72 73 74 75

Single ionization N+ production N+ +N production N+ +N+ production N2+ +N production N+N production Excitation to (B 2 Σu+ ; v=0)

2.90−2 1.00−2 9.11−3 3.30−2 4.42−2 1.23−6 3.40−3

2.50+0 4.99−1 5.43−2 2.50+0 2.00+0 1.18−3 9.10−2

6.2+0 2.9+0 9.4+0 8.4+0 1.1+1 9.0+0 4.3+0

1.4+1 8.6+0 2.0+1 2.3+1 4.2+1 2.0+1 8.6+0

3.30−2 1.92−2 9.95−3 3.90−2 4.52−2 6.18−5 9.10−2

76

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules Table 2 (continued) Energy ranges of data, fitting errors, and parameters of the analytic expressions for nitrogen molecules, (N2+ ). See page 71 for Explanation of Tables No.

Eq.

n

Eth

a1 a7

a2 a8

a3 a9

a4 a10

69 70 71 72 73 74 75

7 5 1 1 5 1 1

4 6 4 4 6 4 4

2.79−2 8.71−3 8.40−3 3.12−2 3.63−2 0.00+0 3.17−3

4.080−5 1.990+1 3.280+0 9.230−2 3.390−3 4.000+0 5.540+0

1.700+2 1.560+0 7.330−1 1.099+0 6.300+0 −6.600−1 1.360−1

2.820−1 2.410−3 1.840−2 6.530−2 1.220−2 1.300−4 3.100−3

1.026+0 −4.210−1 5.760−1 7.670−1 −1.310+0 1.260+0 8.060−1

77

a5 a11

a6 a12

2.000−2

8.750−1

2.050−2

7.680−1


Graphs 1–75. Cross section vs. electron energy.

78


Graphs 1–75. (continued)

79



80



81



82



83



84



85



86



87



88



89



90



91



92



93



94



95



Commentary “Erratum” to this paper was published as follows1 with an additional note on affilia1

Atomic Data and Nuclear Data Tables 98, 74 (2012) (doi:10.1016/j.adt.2011.06.002).

96

89. Analytic Cross Sections for Electron Impact Collisions with Nitrogen Molecules tions for two of the authors2 : Eq. (7) on page 379 [in the published version] should read σ = σ0 a1 [ln (E/Eth ) + a2 ]

.

Eth E [1 + (a3 /E1 )a4 ] .

We thank Justin Yonker of Virginia Tech for pointing out this typo. While preparing the present collection, the editor found additional errors: Page 380 386

Place Ref. [36] Table 2, last line

Now reads J. Chem, Physica 8.60+0

2

Should read J. Chem. Phys. 8.6+0

The affiliations [at the date of the publication of “Erratum”] for Masao Sataka and Hirotaka Kubo are Tokai Research and Development Center, Nuclear Science Institute, Japan Atomic Energy Agency, 2-4 Shirakata-shirane, Tokai-mura, Ibaraki 319-1195, Japan and Fusion Research and Development Directorate, Japan Atomic Energy Agency, 801-1 Mukoyama, Naka-shi, Ibaraki 319-0193, Japan, respectively.

97

Papers in the Previous Volumes of The Collected Works of Tatsuo Tabata ∗ Volume 1: Experimental Nuclear Physics in Master’s Program, 1959–1961 1. Angular Distributions of Protons from the Reaction 12 C(α, p)15 N 2. Lower Excited States in P29 3. Gamma-rays from the 7.56 MeV Level in O15 4. Lower Excited States in P29 from the Si28 (p, γ)P29 Reaction 5. (α, p) Reactions near Z=26 Volume 2: Electron Beam Measurements, 1961–1970 6. Nonobstructive Low Energy Electron Beam Monitor 7. Anomalous Emission in Secondary Emission Beam Monitors 8. Beam Position Monitor for Accelerators 9. Beam Profile Measurement for Electron Accelerators 10. Energy Monitor for Electron Beams 11. Contribution of Obliquely Scattered Electrons to the Irradiation under the Scanner Window 12. Current Profile Monitor for Use in Scanning Electron Beam Irradiations Volume 3: Interactions of Electrons with Matter in Bulk (1), 1967–1971 13. Backscattering of Electrons from 3.2 to 14 MeV 14. A Simple Calculation for Mean Projected Range of Fast Electrons 15. On the Experimental Determination of the Maximum Range of Monoenergetic Electrons 16. Charge Distribution Produced by 4- to 24-MeV Electrons in Elemental Materials 17. Extrapolated and Projected Ranges of 4- to 24-MeV Electrons in Elemental Materials 18. Projected Range Straggling of 4- to 24-MeV Electrons in Elemental Materials Volume 4: Interactions of Electrons with Matter in Bulk (2), 1971–1975 19. An Empirical Equation for the Backscattering Coefficient of Electrons 20. An Empirical Equation for the Average Energy-Loss Fraction of Backscattered Electrons 21. An Empirical Equation for the Average Energy-Loss Fraction of Backscattered Electrons. II 22. Generalized Semiempirical Equations for the Extrapolated Range of Electrons 23. A Fitting Function for Energy Dissipation Curves of Fast Electrons 24. An Algorithm for the Energy Deposition by Fast Electrons 25. Effective Treatment of the Interpolation Factor in Marquardt’s Nonlinear LeastSquares Fit Algorithm ∗

Note added later: For the full list of papers in Vols. 1–20, see Vol. 20. The cover page of each volume has the date of the last modification. All modifications made after the date of publication, however, are mostly of minor editorial styles and the addition of anecdotal descriptions in “Commentary” sections.

98

26. Parametric Representation of the Energy Deposition by Fast Electrons under Oblique Incidence Volume 5: Interactions of Electrons with Matter in Bulk (3), 1975–1977 27. A Generalized Empirical Equation for the Transmission Coefficient of Electrons 28. An Empirical Relation for the Transmission Coefficient of Electrons under Oblique Incidence 29. An Improved Interpolation Formula for the Parameter B in Molière’s Theory of Multiple Scattering 30. Interpolation Formulas for Quantities Related to Radiative Energy-Loss of Electrons 31. Approximation to cos γ Appearing in the Formula for the Coulomb Scattering of Relativistic Electrons 32. Approximations to Landau’s Distribution Functions for the Ionization Energy Loss of Fast Electrons 33. An Algorithm for Electron Depth–Dose Distributions in Multilayer Slab Absorbers 34. Review of the Work at the Radiation Center of Osaka Prefecture on the Passage of Electrons through Matter Volume 6: Measurements, Effects, and Applications of Quantum Beams (1), 1969–1976 35. Pulsed-Radiation-Induced Current in Crystalline and Fused Quartz 36. Effect of Electric Field Direction on Pulsed Radiation-Induced Current in Crystalline Quartz 37. Transient Electron Current Observed in Gas Ionization Chambers 38. Simplification of the Water Bath Method for Calibrating a Ra–Be Neutron Source 39. Fitting Function for the Thermal Neutron Distribution in Water due to a Ra–Be Source Volume 7: Measurements, Effects, and Applications of Quantum Beams (2), 1980–1982 40. Utilization of Natural Mica for Visualization of Electron Isodose Curves in a Medium 41. Varietal Differences in the Repair of Gamma-Radiation-Induced Lesions in Barley 42. Cross Section of the Reaction 9 Be(γ, n) near Threshold 43. Influence of a Dye Film Dosimeter Inserted in a Solid Volume 8: Interactions of Light Ions with Solids (1), 1981–1983 44. Empirical Formulas for the Backscattering of Light Ions from Solids 45. Backscattering Coefficients of H, D, and He Ions from Solids Volume 9: Interactions of Light Ions with Solids (2), 1984–1985 46. Reflection of keV Light Ions from Compound Targets 47. Data Center Activities on Plasma–Wall Interaction at Institute of Plasma Physics at Nagoya University 48. Universal Relations for Reflection of keV Light Ions from Solid Targets 49. Empirical Formulas for the Backscattering Coefficients of Light Ions Obliquely Incident on Solids 50. Unified Empirical Formulas for the Backscattering Coefficients of Light Ions Volume 10: Measurements, Effects, and Applications of Quantum Beams (3), 1985–1989 51. Dosimetry and Processing Anomalies Due to Heterogeneities of Materials Irradiated with High-Energy Electrons

99

52. The Effect of High Gamma-Ray Doses on the Thermal Properties of Muscovite Mica 53. Nondestructive Detection of Small Voids in Solids by Transmission Electron Spectrometry 54. Simple Method of Evaluating Absorbed Dose in Electron-Beam Processing Volume 11: Atomic and Molecular Collision Cross Sections (1), 1987–1992 55. Cross Sections for Charge Transfer of Hydrogen Atoms and Ions Colliding with Gaseous Atoms and Molecules 56. Analytic Cross Sections for Charge Transfer of Hydrogen Atoms and Ions Colliding with Metal Vapors 57. A Semiempirical Formula for Single-Electron-Capture Cross Sections of Multiply Charged Ions Colliding with H, H2 and He 58. Extended Scaling of Cross-Sections for the Ionization of H, H2 and He by Multiply Charged Ions Volume 12: Interactions of Electrons with Matter in Bulk (4), 1988–1994 59. Precision Fitting to Depth–Dose Curves of Electron Beams in the Water Phantom 60. Semiempirical Algorithms for Dose Evaluation in Electron-Beam Processing 61. Analytic Fits to Monte Carlo Calculated Depth–Dose Curves of 1- to 50-MeV electrons in water 62. Reflection of Electrons and Photons from Solids Bombarded by 0.1- to 100-MeV Electrons 63. Energy-Deposition Distributions in Materials Irradiated by Plane-Parallel Electron Beams with Energies between 0.1 and 100 MeV Volume 13: Measurements, Effects, and Applications of Quantum Beams (4), 1992–2002 64. Simple Calculation of the Electron-Backscatter Factor 65. Harvesting Backscatter Electrons for Radiation Therapy 66. A Comparison of Calculated and Measured Absorbed Doses of Electron Beams 67. Detour Factors in Water and Plastic Phantoms and Their Use for Range and Depth Scaling in Electron-Beam Dosimetry 68. A Method to Convert Absolute Depth–Dose Curves of Electrons between Different Phantom Materials 69. Analysis of a Discrepancy in Electron-Beam Dose Comparison between Chemical Dosimeters and a Calorimeter 70. Dose Perturbations at High-Z Interfaces in Kilovoltage Photon Beams: Comparison with Monte Carlo Simulations and Measurements Volume 14: Interactions of Electrons with Matter in Bulk (5), 1994–1996 71. Energy Deposition through Radiative Processes in Absorbers Irradiated by Electron Beams 72. Depth Profile of Charge Deposition by 0.1- to 100-MeV Electrons in Elemental Absorber 73. Depth Profiles of Charge Deposition by Electrons in Elemental Absorbers: Monte Carlo Results, Experimental Benchmarks and Derived Parameters 74. Range Distributions and Projected Ranges of 0.1- to 100-MeV Electrons in Elemental Absorbers

100

75. An Analytic Formula for the Extrapolated Range of Electrons in Condensed Materials Volume 15: Interactions of Electrons with Matter in Bulk (6), 1998–1999 76. Average Depths of Electron Penetration: Use as Characteristic Depths of Exposure 77. An Algorithm for Depth–Dose Curves of Electrons Fitted to Monte Carlo Data 78. Semiempirical Formulas for the Detour Factor of 1- to 50-MeV Electrons in Condensed Materials 79. Fractional Energies of Backscattered Electrons and Photon Yields by Electrons 80. An Expression for the Charge-Deposition Distribution Near the Surface of a SemiInfinite Medium Irradiated by Electrons Volume 16: Interactions of Electrons with Matter in Bulk (7), 1999–2002 81. Average Depths of Electron Penetration (II): Angular Dependence and Use to Evaluate Secondary-Electron Yield by Photons 82. Approximation of Charge-Deposition Density in Thin Slabs Irradiated by Electrons 83. Charge-Deposition in Two-Layer Systems Irradiated by Electrons 84. A Database for Electron–Material Interactions 85. Extrapolated Ranges of Electrons Determined from Transmission and ProjectedRange Straggling Curves Volume 17: Atomic and Molecular Collision Cross Sections (2), 2000–2001 + − 86. Analytic Cross Sections for Collisions of H+ , H+ 2 , H3 , H, H2 , and H with Hydrogen Molecules 87. Analytic Cross Sections for Electron Collisions with CO, CO2 , and H2 O Relevant to Edge Plasma Impurities

101

Previous Issues of Institute for Data Evaluation and Analysis Technical Reports (IDEA-TR) 1. The Passage of Fast Electrons through Matter (2002) 2. Abstracts of Selected Papers Published by Tatsuo Tabata and His Coworkers Volume 1: 1959–1980 (2002) 3. Abstracts of Selected Papers Published by Tatsuo Tabata and His Coworkers Volume 2: 1981–1998 (2002) 4. List of Tatsuo Tabata’s Papers Based on SAO/NASA ADS Collection (2016) 5. The Collected Works of Tatsuo Tabata Volume 1: Experimental Nuclear Physics in Master’s Program, 1959–1961 (2017) 6. The Collected Works of Tatsuo Tabata Volume 2: Electron Beam Measurements, 1961–1970 (2017) 7. The Collected Works of Tatsuo Tabata Volume 3: Interactions of Electrons with Matter in Bulk (1), 1967–1971 (2017) 8. The Collected Works of Tatsuo Tabata Volume 4: Interactions of Electrons with Matter in Bulk (2), 1971–1975 (2018) 9. The Collected Works of Tatsuo Tabata Volume 5: Interactions of Electrons with Matter in Bulk (3), 1975–1983 (2018) 10. The Collected Works of Tatsuo Tabata Volume 6: Measurements, Effects, and Applications of Quantum Beams (1), 1969–1976 (2018) 11. The Collected Works of Tatsuo Tabata Volume 7: Measurements, Effects, and Applications of Quantum Beams (2), 1980–1982 (2018) 12. The Collected Works of Tatsuo Tabata Volume 8: Interactions of Light Ions with Solids (1), 1981–1983 (2018) 13. The Collected Works of Tatsuo Tabata Volume 9: Interactions of Light Ions with Solids (2), 1984–1985 (2018) 14. The Collected Works of Tatsuo Tabata Volume 10: Measurements, Effects, and Applications of Quantum Beams (3), 1985–1989 (2018) 15. The Collected Works of Tatsuo Tabata Volume 11: Atomic and Molecular Collision Cross Sections (1), 1987–1992 (2018) 16. The Collected Works of Tatsuo Tabata Volume 12: Interactions of Electrons with Matter in Bulk (4), 1988–1994 (2018) 17. The Collected Works of Tatsuo Tabata Volume 13: Measurements, Effects, and Applications of Quantum Beams (4), 1992–2002 (2018) 18. The Collected Works of Tatsuo Tabata Volume 14: Interactions of Electrons with Matter in Bulk (5), 1994–1996 (2018) 19. The Collected Works of Tatsuo Tabata Volume 15: Interactions of Electrons with Matter in Bulk (6), 1998–1999 (2018) 20. The Collected Works of Tatsuo Tabata Volume 16: Interactions of Electrons with Matter in Bulk (7), 1999–2002 (2018) 21. The Collected Works of Tatsuo Tabata Volume 17: Atomic and Molecular Collision Cross Sections (2), 2000–2001 (2018)

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The Collected Works of Tatsuo Tabata

The Collected Works of Tatsuo Tabata

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