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Shake-off processes in photoionization and Auger transition for rare gases irradiated by soft X-rays
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Physica Scripta. Vol. 49, 80-85, 1994
Shake-off Processes in Photoionization and Auger Transition for Rare Gases Irradiated by Soft X-Rays Norio Saito and Isao H. Suzuki Electrotechnical Laboratory, Tsukuba-shi, Ibaraki 305 Japan Received June 7,1993; accepted in revised form July 28, I993
Abstract Branching ratios of multiply charged Ne, Ar, Kr and Xe ions produced following soft X-ray absorption by the rare gases have been measured using a time-of-eight mass spectrometer and monochromatized synchrotron radiation. Ratios of double, triple and quadruple valence photoionization to single valence photoionization, of multiple Auger transitions to the normal Auger transition from a core hole or core-valence two-hole state, and of the multiple photoionization with a core hole to single core photoionization have been determined using the measured branching ratios of the multiply charged ions.
1. Introduction Soft X-ray absorption by an atom usually results in a multiply charged ion. This multiply charged ion is produced via three dominant processes, i.e., (1) simultaneous multiple photoionization of valence electrons, (2) single photoionization of a core electron followed by an Auger transition, (3) simultaneous multiple photoionization of valence electrons and a core electron followed by an Auger transition. The vacancy in the inner-shell resulting from the core photoionization is filled primarily by a normal Auger transition in which an electron from an outer orbital fills the core hole accompanied by the ejection of a second electron from an outer orbital, yielding a doubly charged ion. Two or more electrons are occasionally ejected simultaneously in the Auger transition, a process called a multiple Auger transition, which generates a triply or more highly charged ion. It is important to investigate the multiple photoionization processes and multiple Auger processes in detail because these processes are considered to originate from electronelectron correlation effects. Several experimental studies of multiple photoionization in the rare gases have been reported previously [l-71. Partial cross sections for multiple photoionization of the rare gases in the photon energy range of 50-280eV were measured by Holland et al. using monochromatized synchrotron radiation [l]. Hayaishi and coworkers studied in detail multiple photoionization following Ar L-shell excitation, Kr M-shell excitation and Xe N-shell excitation [2]. Carlson et al. measured branching ratios of multiply charged ions produced from the rare gases irradiated by photons from X-ray line sources in the 0.2-17.5 keV range [3]. Multiply charged ions from Ar in the K-shell ionization region [4] and from Xe in the L-shell ionization region [5] were measured using monochromatized synchrotron radiation. Branching ratios of multiply charged ions from Ne and Ar [6] and Kr and Xe [7] were measured using an electron energy-loss technique. Physica Scripta 49
These previously reported photoionization data are inadequate for clarification of the shake-off and Auger processes, however, as they do not cover a sufficient energy range and/or the scatter in the data is too large to be conclusive. In addition to the experimental work, there have been a few theoretical studies of the shake-off processes accompanying valence and core ionization of the rare gases reported [8-113. In the present study, yields of multicharged ions resulting from the irradiation of Ne, Ar, Kr and Xe with photons in the soft X-ray region have been measured using a time-of-flight mass spectrometer (TOF) and monochromatized synchrotron radiation [12, 131.
2. Experimental The experimental procedures employed in this study have been described previously in detail [14], however a brief explanation is helpful in the discussion of the present results. Monochromatized soft X-rays were obtained using synchrotron radiation from TERAS at the Electrotechnical Laboratory [l5] and a Grasshopper monochromator [16]. The monochromatized soft X-rays crossed an effusive beam of the gas at right angles in the center of a TOF mass spectrometer with a 140" long drift tube. The spectrometer was operated in a pulsed mode in which ions were extracted by a pulsed electric field, where the start of the pulse provides the origin of the flight time. The dependence of the branching ratios of the rare gas ions on the time width and interval of the pulsed field was measured to obtain the optimum experimental settings. Thin Al, In and Be films were used to reduce contributions of diffusely scattered light to the monochromatized photon beam. TERAS was operated at appropriate electron energies to reduce higher orders in the photon beam. (The ring energy was set at 300 MeV or lower for photon energies below 100eV, at 400MeV or lower for photon energies between 100 and 300eV and at 750 MeV for photon energies above 300 eV.) Figure 1 compares the present results (dots) of the ratio of the yields of NeZ+ to Ne' over the photon energy range from 60-150eV with the ratios of doubly to singly ionized Ne obtained by other experiments and calculations. The present results are similar to the data obtained by Wight and van der Wiel [6] and by Becker et al. [20] and are centered among the other experimental data and the calculations, suggesting that the present data and hence methods employed are reliable.
81
Shake-of Processes in Photoionization and Auger Transition for Rare Gases
0.2 I
I
I
I
I
I
0.2 1
T
I
01 0 .rl
c> rd
0.1
I
t i
0
I
I
I
Ne 3t/Ne'
{
Ne4t/Net
{
e
I n v
-
100
0.002
200
Photon Energy (eV) Fig. I. Comparison of the ratio of the double ionization yield to the single ionization yield of Ne from the photon energy of 60-220eV of this work (dots) to the ratios obtained by other works. The open squares represent data by Carlson [17], the open triangles data by Samson and Haddad [18], the filled triangles data by Schmidt et al. [19], and the open circles data by Holland et al. [l], all of which were obtained from photoion yield measurements. The electron impact measurement of Wight and van der Wiel [6] is given by filled squares. Filled circles denote data by Becker et al. [20] determined from the complete photoelectron spectra. The solid curve shows calculations by Chang and Poe Ell]. The short broken and long broken curves represent dipole-length and dipole-velocity calculations by Carter and Kelly [9].
3. Results and discussion 3.1. Multiple photoionization of the valence electrons The ratio of the doubly charged ion yield to the singly charged ion yield at photon energies below the first core ionization energy gives the ratio of double valence photoionization to single valence photoionization. Figure 2 shows the ratios of the doubly, triply and quadruply charged ion yields to the singly charged ion yield for Ne over the photon energy range of 44-800eV. The ratios of the doubly and triply charged ion yields increase with increasing photon energy until they become saturated at about 250 and 300eV, respectively. The values of the ratios at their saturation levels are 0.16 f 0.02 for double photoionization and 0.014 & 0.003 for triple photoionization. Although it is dif€icult to determine the saturated ratio of quadruple to single photoionization owing to large scatter of the experimental data, the average ratio just below the 1s ionization threshold (the average between 650 and 850eV) is about 0.002 0.001. Figure 3 shows the ratios of the doubly charged ion yields to the singly charged ion yields for Ar, Kr and Xe from a photon energy of 44eV to energies just below their first core-ionization thresholds. The ratios for Ar and Kr increase with increasing photon energy until they reach saturated values at about 70 and 80 eV, respectively. This behaviour is similar to that observed for the ratio of double to single photoionization in Ne. The ratio of Xe seems to be already saturated in this photon energy range. The double photoionization thresholds of Ne, Ar, Kr and
200
400 600 Photon Energy (eV)
800
Fig. 2. Ratios of the double, triple and quadruple photoionization yields to the single photoionization yield of Ne. The bars with hatching show the ground states of Ne2+,Ne3+ and Ne4*.
Xe are 62.528, 43.39, 38.36 and 33.11eV, respectively [21]. The saturated values of the ratios of double to single photo-. ionization for Ar, Kr and Xe are 0.21 & 0.02, 0.22 & 0.03 and 0.44 f 0.04, respectively. Although the ratios of double to single valence photoionization for Ar and Kr are close, the ratios for rare gases increase with atomic number. Since the number of valence electrons involved in the double photoionization is the same in these atoms, outer most np electrons mainly, the binding energies of the electrons,
0.22...,....'..;.,: . .:;. . .
.. . . .
*
'
80 90 Photon Energy (eV)
50
60
70
lA0
Fig. 3. Ratios of the double photoionization yields to the single photoionization yield of (a) Ar, (b) Kr and (c) Xe. Physica Scripta 49
82
N. Saito and I. H . Suzuki
which decrease with increasing atomic number, are pre- values. The trend in the ratios calculated by this method is reverse to that obtained experimentally for Ne through Xe. sumed to affect the probability of double photoionization. Table I lists the saturated values of the ratio of multiple This disagreement is a result of approximations in calcuphotoionization to single photoionization in the valence lation, which did not consider electron-electron correlation. shell of Ne, Ar, Kr and Xe obtained here together with previously determined experimental and theoretical values. The 3.2. Multiple Auger transitions ratios of triple photoionization are about 1/10 those of Radiative decay of the core hole is neglected in the present double photoionization and the ratios of quadruple photo- study because the probabilities of the radiative processes are ionization are about 1/100 those of double photoionization small in the sub-keV region. Whereas the normal Auger in the present data. A similar trend was obtained in the process produces doubly charged ions, the multiple Auger ratios of multiple photoionization among Ne, Ar and Kr process generates triply or more highly charged ions. If the obtained by Holland and coworkers [11. Although the ratio core hole is produced in a deep inner-shell, the atomic ion of the double photoionization of Ne is lower and that of Kr after the first Auger transition may have enough energy to is higher than the present results, the ratio for Ar deter- deexcite through another Auger transition, resulting in a mined previously is close to the present value. The double cascade of Auger transitions and a highly charged ion. Since and triple photoionization ratios for Kr obtained by Mura- only core holes in the shallowest inner-shell are discussed in kami et al. [22] are also significantly larger than the values this study, successive Auger transitions are energetically obtained here. Since the photoabsorption cross section of impossible. The ratios of the multiply charged ion yields to Kr in the photon energy just below the 3d ionization thresh- the doubly charged ion yield at photon energies above the olds is very small [23], higher order contributions to the first inner-shell ionization threshold therefore include informonochromatized photon beam may have resulted in mation about multiple Auger transitions. greater ratios of double photoionization obtained by those Figure 4 shows the ratios of Ne3+/Ne2+and Ne4+/Ne2+ studies. above the Ne K-shell ionization edge, Fig. 5, the ratio of Wight and van der Wiel [6] measured the multiple Ar3+/Ar2+above the Ar L-shell ionization edges, Fig. 6, the photoionization cross sections of Ne and Ar using a high ratio of Kr3+/Kr2+above the Kr M-shell ionization edges, energy electron impact coincidence technique. Their results and Fig. 7, the ratio of Xe3'/Xe2+ above the Xe N-shell for Ne and Ar agree with the present results within experi- ionization edges. In these figures, the yields of multiple mental uncertainties. El-Sherbini and van der Wiel [7] also photoionization of valence electrons have been subtracted measured the multiple photoionization cross sections of Kr using the probability ratios in Table I and the yield curve of and Xe using the electron impact coincidence technique. the singly charged ion. Profiles of the ratios all exhibit plaAlthough the ratios of the multiple photoionization for Kr teaus just above the core edge, and increase at a photon obtained by them agree with the present data, their ratio for energy 10 or 20eV above the core ionization threshold. This double photoionization of Xe is larger than the value in this increase results from other processes which will be discussed work. The ratio of the double photoionization for Xe by in the next section. Values of the multiply charged to doubly Adam [24] agrees with the present ratio. The ratios of the charged ion yield ratios in the plateau regions provide the double photoionization for Ne and Ar calculated by Carter ratios of the multiple Auger process to the normal Auger and Kelly [9] using many-body perturbation theory are process. The plateau values of the ratio of the triply charged very close to the present results. Chang and Poe [11] calcu- ion to the doubly charged ion (the ratio of the double Auger lated the double photoionization of Ne using many-body transition) for Ne, Ar, Kr and Xe are 0.06, 0.11, 0.38 and perturbation theory and obtained a ratio value of 0.13. This 0.25, respectively. The ratio of the triple Auger transition for value is also in agreement with the present result. The ratios Ne is 0.003. Table I1 shows the ratios of the double Auger transitions calculated by Carlson and Nestor [8] using the sudden approximation are significantly lower than the experimental to the normal Auger transition for Ne, Ar, Kr and Xe
Table I. Ratios of the multiple valence ionizations to the single valence ionization. D, T and Q denote double, triple and quadruple photoionization, respectively. Exp. Present work Ne
0.09
0.18
Q
0.21 0.025 0.0025
D T
0.22 0.02
0.55
D
0.44
Q Ar
Kr
Xe
a
0.16 0.014 0.002
D T D T
Cal. b -
f
g
h
0.15
0.15
0.13
0.044
0.19
0.19
C
d
e
0.035
0.05
0.01
0.59 0.13
0.19 0.60
0.033 0.46
0.031
~~~~~~
a : Holland et al. [l], b: Murakami et al. [22], c: Wight and van der Wiel [6], d : El-Sherbini and van der Wiel [7], e: Adam [24], f: Carter and Kelly [9], g: Chang and Poe [ll], h : Carlson and Nestor [8] Physica Scripta 49
Shake-off Processes in Photoionization and Auger Transition for Rare Gases I
0.4
IIK
1
I
I
83
!a2,3 . . . . . . .. ... . ....................... ..
0.2 0 c,
0 0.04 0.02
I1:
0.003 ......
0
.. . .: . .... . . . . . .. . . . . ....
Ne4t/Ne2t
o'loo'
1
I
900
1
1000 1100 1200 Photon Energy (eV)
Fig. 4. Ratios of the triple and the quadruple photoionization yields to the
'
'
'
200 '
'
'
'
Photon Energy (eV)
'
Fig. 6. Ratio of the triple photoionization yield to the double photoionization yield of Kr. Contributions from valence multiple photoionization have been subtracted from the multiple photoionization yields. The bars with hatching denote the M4,and M,, ionization thresholds.
,
double photoionization yield of Ne. Contributions from valence multiple photoionization have been subtracted from the multiple photoionization yields. The bars with hatching denote the K and KL,, ionization thresholds.
of the valence double photoionization. Due to the decrease in electron-electron repulsion and shielding in the higher charge states, the remaining bound electrons are attracted more strongly to the nucleus and thus they are less likely to together with the previous experimental and calculated be shaken-off than the more loosely bound electrons in results. The ratios of the double Auger process are lower lower charge states. The ratios of the double Auger tranthan the ratios of the double valence photoionization for all sition for Kr obtained by Murakami et al. [22] and Elof the rare gases except Kr. This low ratio may be related to Sherbini and van der Wiel [7] are close to the present result, the fact that both the initial and the final charge states of 0.38, the largest value of the ratio in the four atoms. This the double Auger process are one charge higher than those ratio is significantly larger than the ratio of the valence
,
O.4
I
!L293
0.105
O "250'
0
350 " Photon Energy (eV) "
300
"
"
"
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PBrt ' ' ' ' 100
50
Photon
Fig. 5. Ratio of the triple photoionization yield to the double photoionization yield of Ar. Contributions from valence multiple photoionization have been subtracted from the multiple photoionization yields. The bars with hatching denote the L2, and L , ionization thresholds.
' '
' ' ' ' ' '
150 Energy (eV)
'
200
Fig. 7. Ratio of the triple photoionization yield to the double photoionization yield of Xe. Contributions from valence multiple photoionization have been subtracted from the multiple photoionization yields. The bars with hatching denote the N4. and N2, ionization thresholds.
Table 11. Ratios of multiple Auger transitions to the normal Auger transition. D and T denote the double Auger transition and the triple Auger transition, respectively. Experimental Initial hole state
Present work
ls2p
D T D
0.06 0.003 0.03
2P
D
Ne
Is
Ar
2P3P
D
0.1 1 0.0035 0.07
3d
D D
0.38 0.25
T Kr Xe
4d
a
b
Calculation d
C
0.04
0.34
0.21
0.36 0.14
0.29
a: Murakami et al. [22], b: Becker et al. [25], c: El-Sherbini and van der Wiel[7], d: Amusia et al. [ l o ] Physica Scripta 49
84
N . Saito and I. H . Suzuki
double photoionization, 0.22. At present the reason for this exception for Kr cannot be clarified. The ratios of the double Auger transition for Xe obtained by Becker et al. [25] and El-Sherbini and van der Wiel [7] are also close to the present result. The ratio of the double Auger transition of Ne calculated by Amusia et al. [lo] using many-body perturbation theory is 0.04, in reasonable agreement with the present result of 0.06. The probability of the triple Auger transition from the outer-most core hole state is very low. The ratios for the triple Auger process have been estimated from the intensity ratios of quadruply to doubly charged ions for Ne and Ar (see Table 11). Triple Auger transitions from the 3d hole of Kr and the 4d hole of Xe do not occur as they are energetically impossible. The ratios of triple Auger transition range from about 1/20 to 1/30 of those for the double Auger transition as seen in Table 11.
3.3. Multiple ionization of core and valence electrons and double Auger transition from this two hole state When the photon energy is greater than about 15eV above the core ionization threshold, a core electron and a valence electron can be simultaneously ejected in the initial photoabsorption step (core photoionization shake-off process). This core and valence hole state de-excites through an Auger transition, yielding triply charged ion. Triply charged ions are therefore produced by two processes, the double Auger process after a core ionization and the normal Auger transition after a core photoionization shake-off process. In Fig. 4, the ratio of Ne3+/NeZ+starts increasing at about 900eV, which corresponds to the threshold of the K-'L-' state. This increase in the ratio is therefore presumed to result from the normal Auger process following a core photoionization shake-off process. The ratio of the quadruply to the triply charged ion yield provides information on the double Auger transition from the two hole state involving a core and valence orbital. Figure 8 shows the ratio of the yields of quadruply charged ions to triply charged ions of Ne over the photon energy of 850-1 250 eV. Contributions from the valence multiple ionization and the multiple Auger transition from the single core ionization have been subtracted from the data in the figure using the probability ratios in Tables I and I1 and the singly and doubly charged ion yields. The profile of the
0.2
I
0 .rl
Y
a
m
0.1
-
Soft X-rays
-
Ne
I
0 . 1 2 . .. .. . . .. . . .. . .: ...- .. . . .
.....: ;... ...... - .
0.03
..
transition
-
Ne4t/Ne3t
Photon Energy (eV) Fig. 8. Ratio of the quadruple photoionization yield to the triple photoionization yield of Ne. Contribution from valence multiple photoionization and 1s photoionization have been subtracted from the multiple photoionization yields. The bars with hatching denote the K L and K L L ionization thresholds. Physica Scripta 49
ratio in Fig. 8 is similar to the ratio of the triply charged ion yield to the doubly charged ion yield (Fig. 4). This ratio shows a plateau in the energy region just above the threshold of the K L double ionization and increases around the threshold of the K LL triple ionization. Near the threshold of K L L ionization in the ratio curve in Fig. 8 the observed increase in the ratio probably originates from the process in which a core electron and two valence electrons are simultaneously ejected in the initial photoabsorption step. The ratio at the first plateau, 0.03, represents the ratio of the double Auger transition to the normal Auger transition from the K L hole state. The ratios of the double Auger transition to the normal Auger transition from the two hole state of a core and a valence orbital are also listed for Ne and Ar in Table 11. Double Auger transitions from the 3d4p hole state of Kr and the 4d5p hole state of Xe are not allowed energetically. The ratios of the double to single Auger transition from the two hole state are lower than those of the double to single Auger transition from a core hole state. This feature is reasonable on account of the difference of the charge states in the two kinds of the double Auger transition as explained previously. Next, the ratios of photoionization shake-off to single core ionization are discussed. Figure 9 illustrates a summary of the ratios obtained for Ne. The saturated value of the ratio of the triply to doubly charged ion yields for Ne from Fig. 4 is 0.30. Since the ratio of the double Auger process for Ne is 0.06, the ratio of the normal Auger transition from the core and valence two hole state to the normal Auger transition from the core hole state is therefore 0.24. The ratios of the normal Auger from a K hole state : double Auger from a K hole state :triple Auger from a K hole state: normal Auger from a K L hole state are then 100 : 6 : 0.3 : 24. From the plateau ratios between the K L and the K L L states shown in Fig.' 8, the ratio of the normal Auger transition from the three hole K L L state to the normal Auger transition from the two hole K L state is 0.09. Ratios of the
Ne+
Ne3+
Fig. 9. Summary of the ratios of multiple photoionization processes for Ne. a: the ratios of the multiple valence ionizations to the single valence photoionization obtained from Fig. 2. b: the ratios of the multiple Auger transitions from a K state and the normal Auger transition from a KL hole state to the normal Auger transition from a K hole state obtained from Fig. 4. c: the ratios of the multiple Auger transitions from a K L hole state and the normal Auger transition from a K L L hole state to the normal Auger transition from a K L hole state obtained from Fig. 8.
Shake-off Processes in Photoionization and Auger Transition for Rare Gases
85
Table 111. Ratios of multiple photoionization generating a single core photoionization for Ne, Ar, Kr and Xe have been core hole to single core photoionization. determined from the branching ratios of yields of the multiply charged ions. Triple and quadruple valence photoionizaHole Gal.' Present Exp. tion occur with probabilities of about 1/10 and 1/100 that of state work a b the double valence photoionization, respectively. The problsL/ls 0.23 0.18 Ne ability of triple photoionization generating a core hole is 1SLLllS 0.02 about 1/10 that of double photoionization generating a core Ar 2PMI2P 0.17 0.15 hole. Kr 3dN/3d 0.21 (0.25) 0.12 Xe a: Murakami
4d0/4d et
0.16
0.10
al. [22] (estimated from Fig. 4), b: Carlson and Nestor [8]
normal Auger from a K L hole state : the double Auger from a KL hole state : the normal Auger from a K L L hole state are 100 : 3 : 9, which corresponds to 24 : 0.7 : 2 normalized to the probability of the single Auger transition from a K hole state of 100. The ratios for the creation of K : K L : K L L hole states in the initial photoabsorption step of Ne are therefore 106.3 : 24.7 : 2. The ratios of the double and triple photoionizations involving a core electron (core ionization with shake-off and double shake-off respectively) to the single photoionization of a core electron are therefore 0.23 and 0.02 for Ne, respectively. In the heavier rare gases, Ar, Kr and Xe, there are additional core edges beyond the first core level which complicate the analysis of the data. The ratios of the triply charged to doubly charged ion yields increase sharply at the energies of these edges, as shown in Figures 5-7. De-excitations from these sub-shells are beyond the scope of this study, however, and are not discussed. Table I11 lists the ratios of the multiple photoionizations including a core electron to the single photoionization of a core electron for Ne, Ar, Kr and Xe. Theoretical results obtained by Carlson and Nestor [8] are also listed in the table. Calculated value of the ratios of the multiple photoionizations including a core electron decrease with increasing atomic number, which agrees with the present results except for the case of Kr. These theoretical ratios are relatively close to the present results, although their data for the valence double ionization are not in agreement with our experimental results. These theoretical results were calculated using the sudden approximation which only applies when the electrons are ejected with relatively high kinetic energies. As only the ratios of multiple photoionization well above threshold are considered in this experiment, this approximation is valid for comparison with these results. 4. Summary
The ratios of valence multiple photoionization to single valence photoionization, of multiple Auger transitions to the normal Auger transition from a core hole state and a corevalence two-hole state, and of simultaneous multiple photoionization of a core and multiple valence electrons to the
Acknowledgements The authors are grateful to the staff of the accelerator group at ETL for their continued operation of the TERAS electron storage ring. We wish to express sincere thanks to Dr. J. D.Bozek for his comments and assistance with the language in this paper. The readers could be referred to the recent result on the double photoionization of the Ne (Bartlett, R. J., Walsh, P. J., He, Z. X., Chung, Y., Lee, E-M. and Samson, J. A. R., Phys. Rev. A46,5574 (1992)).
References 1. Holland, D. M. P., Codling, K., West, J. B. and Man, G. V., J. Phys. B12,2485 (1979). 2. Hayaishi, T., Morioka, Y., Watanabe, M., Suzuki, I. H., Mikuni, A., Isoyama, G., Asaoka, S.and Nakamura, M., J. Phys. B17,3511(1984). 3. Carlson, T. A., Hunt, W. E. and Krause, M. O., Phys. Rev. 151, 41 (1966). 4. Ueda, K., Shigemasa, E.;Sato, Y., Yagishita, A., Ukai, M., Maezawa, H., Hayaishi, T. and Sasaki, T., J. Phys. B24,605 (1991). 5. Tonuma, T., Yagishita, A., Shibata, H., Koizumi, T., Matsuo, T., Shima, K., Mukoyama, T. and Tawara, H., J. Phys. BZO, L31(1987). 6. Wight, G. R. and van der Wiel, M. J., J. Phys. B9, 1319 (1976). 7. El-Sherbini, Th. M. and van der Wiel, M. J., Physica 62,119 (1972). 8. Carlson, T. A. and Nestor, C. W. Jr, Phys. Rev. AB, 2887 (1973). 9. Carter, S. L. and Kelly, H. P., Phys. Rev. A16, 1525 (1977). 10. Amusia, M. Ya., Lee, I. S. and Win, V. A., Phys. Rev. A45, 4576 (1992). 11. Chang, T. N. and Poe, R. T., Phys. Rev. A12, 1432 (1975). 12. Saito, N. and Suzuki, I. H., J. Phys. B E , 1785 (1992). 13. Saito, N. and Suzuki, I. H., Physica Scripta 45,253 (1992). 14. Saito, N. and Suzuki, I. H., Int. J. Mass Spectrom. Ion Proces. 115, 157 (1992). 15. Tomimasu, T., Noguchi, T., Sugiyama, S., Yamazaki, T., Mikado, T. and Chiwaki, M., IEEE Trans. Nucl. Sci. 30,3133 (1983). 16. Saito, N., Suzuki, I. H., Onuki, H. and Nishi, M., Rev. Sci. Instrum. 60,2190 (1989). 17. Carlson, T. A., Phys. Rev. 156,142 (1967). 18. Samson,J. A. R. and Haddad, G. N., Phys. Rev. Lett. 33,875 (1974). 19. Schmidt, V., Sandner, N., Kuntzemiiller, H., Dhez, P., Wuilleumier, F. and Kiillne, E., Phys. Rev. A13, 1749 (1976). 20. Becker, U., Wehlitz, R., Hemmers, O., Langer, B. and Menzel, A., Phys. Rev. Lett. 63, 1054 (1989). 21. Radzig, A. A. and Smirnov, B. M., “Reference Data on Atoms, Molecules and Ions” (Springer-Verlag, Berlin 1985). 22. Murakami, E., Hayaishi, T., Yagishita, A. and Morioka, Y., Physica Scripta 41,468 (1990). 23. Marr, G. V. and West, J. B., At. Data Nucl. Data Tables 18, 497 (1976). 24. Adam, M. Y., Ph.D. thesis, Universite de Paris-Sud, 1978. 25. Becker, U., Szostak, D., Kerkhoff, H. G., Kupsch, M., Langer, B., Wehlitz, R., Yagishita, A. and Hayaishi, T., Phys. Rev. A39, 3902 (1989).
Physica Scripta 49
