c Pleiades Publishing, Ltd., 2009. ISSN 1063-7788, Physics of Atomic Nuclei, 2009, Vol. 72, No. 6, pp. 911–916. c G.S. Karapetyan, A.R. Balabekyan, N.A. Demekhina, J. Adam, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 6, pp. 955–960. Original Russian Text
NUCLEI Experiment
Multimode Approach to 241 Am and 237Np Fission Induced by 660-MeV Protons G. S. Karapetyan* , A. R. Balabekyan, N. A. Demekhina1), 2) , and J. Adam2) Yerevan State University, Alex Manoogian str. 1, 375049 Yerevan, Republic of Armenia Received October 17, 2008
Abstract—The results obtained by measuring cross sections for the formation of fragments originating from 241 Am and 237 Np fission induced by 660-MeV protons are presented. The charge and mass distributions of fragments are analyzed within the multimode-fission model, symmetric and asymmetric fission channels being separated. The contributions of various fission components are estimated, and the fission cross sections for the 241 Am and 237 Np nuclei are calculated along with the fissilities of these nuclei. PACS numbers: 25.85.Ge DOI: 10.1134/S1063778809060027
INTRODUCTION In recent years, the idea that mass and energy distributions of fission fragments result from a concerted effect of several independent processes led to the development of the multimode-fission model. Via identifying and quantitatively describing individual fission channels, one can better understand and assess the impact of shell effects and the nuclear structure on the nature of the process. The multimode-fission hypothesis was theoretically validated within the model that was described in detail in [1] and according to which experimental mass and energy distributions of fission fragments can be represented in the form of a superposition of individual fission modes. In particular, the mass distribution of fragments in the region of the low-energy fission of heavy nuclei comprises largely three fission components. The symmetric mode (Superlong) describes the yield of fragments whose mass numbers concentrate around Af /2 (Af is the mass of the nucleus undergoing fission), while the components associated with the distribution of asymmetric fission fragments take into account (i) the effect of spherical shells in which Z and N are close to the magic numbers of 50 and 82 in a heavy fragment whose average mass is 132 and 134 (Standard I) and (ii) fission leading to the formation of fragments containing ZH ≈ 52, NH ≈ 86–88 deformed shells and having
masses in the range AH ≈ 138–140 (Standard II), where ZH and NH are the numbers of, respectively, protons and neutrons in a heavy fragment and AH is the heavy-fragment mass. The presence of multimode-fission components was confirmed experimentally in studying mass and energy distributions of fragments originating from Table 1. Parameters of the charge and mass distributions of fission fragments Parameters K1as K1as σ1as σ1as D1as K2as K2as σ2as σ2as D2as Ks σs A¯s
1)
Yerevan Physics Institute, Alikhanyan Brothers Str. 2, 375036 Yerevan, Republic of Armenia. 2) Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia. * E-mail:
[email protected]
µ1 µ2 γ1 γ2 911
241
237 Am Np Standard I 45.0 ± 0.2 49.0 ± 0.3 45.8 ± 0.2 49.0 ± 0.3 4.2 ± 0.5 4.5 ± 0.4 4.2 ± 0.5 4.5 ± 0.4 20.0 ± 0.4 21.3 ± 0.4 Standard II 220.5 ± 1.5 252.0 ± 1.3 220.5 ± 1.5 252.0 ± 1.3 7.0 ± 0.5 6.5 ± 0.6 7.0 ± 0.5 6.5 ± 0.6 25.5 ± 1.0 26.3 ± 0.5 Superlong 2970.0 ± 20.5 2590.0 ± 23.3 15.0 ± 0.9 13.7 ± 1.0 113.5 ± 0.6 111.7 ± 0.9 Charge distribution 4.1 ± 0.6 5.0 ± 0.8 0.38 ± 0.01 0.37 ± 0.01 0.92 ± 0.08 0.59 ± 0.02 0.003 ± 0.0001 0.005 ± 0.0002
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spontaneous [2] and low-energy induced [3, 4] fission. The application of this hypothesis in the cases where the fission of uranium, neptunium, and americium isotopes was induced by thermal neutrons [5–7] and 12-MeV protons [8] made it possible to determine the positions of peaks and their widths for each fission mode, along with the spectrum and the multiplicity of emitted neutrons. In the region of intermediate energies, this hypothesis was used in studying the fission of pre-actinide and actinide nuclei that was induced by nucleons [9–12], photons [13, 14], and heavy ions [15, 16]. In the present study, the predictions of the multimode-fission model are used for the first time to analyze the mass distributions of fragments originating from 241 Am and 237 Np fission induced by a beam of 660-MeV protons.
was used in monitoring the proton beam. The yields of fission fragments were measured in the off-line mode by the induced-activity method. Data used to identify fragments (gamma-transition energies and intensities along with half-lives) were borrowed from [18]. The experiment in question was described in detail elsewhere [19].
EXPERIMENTAL RESULTS
The method of consecutive fits to all experimental data (both independent and cumulative data) made it possible to extract independent yields from cumulative data [20].
241 Am
and Our experiment consisted in exposing targets to a beam of protons accelerated to an energy of 660 MeV at the phasotron of the Laboratory of Nuclear Problems at the Joint Institute of Nuclear Research (JINR, Dubna). The cross section for the reaction 27 Al(p, 3pn)24 Na [17] at the same energy 237 Np
The mass distributions of fission fragments were analyzed on the basis of the multicomponent-fission model. As individual components in the mass distribution of fission fragments, we took into account the contributions of symmetric (Superlong) and asymmetric (Standard I and Standard II) fission. The yields from different fission channels were represented by normal distributions whose parameters were determined from basic features obtained in analyzing the charge and mass distributions of fission fragments [1, 8].
The decomposition of the curves representing the charge and mass yield into the aforementioned components is taken here in the form [9, 21]
2 2 A − A¯s − Dias A − A¯s + Dias Kias Kias √ exp − σ (A, Z) = + √ exp − 2 2 2σias 2σias σias 2π σias 2π i=1,2 2 A − A¯s (Z − j − Zp )2 1 Ks √ exp − , + √ exp − 2σs2 πΓZ Γ2Z σs 2π j
where σ (A, Z) is the experimental value of the cross section for the production of a fragment having a charge number Z and a mass number A, A¯s is the average mass number of fragments for the symmetric mode, σ stands for standard deviations, D is the deviations of the centers of the modes from A¯s , K stands for the normalization of the modes, Zp is the most probable charge of the charge distribution, and ΓZ is the width of this distribution. The parameter j determines the contribution of radioactive precursors (j = 0 refers to the yield of independent products, while positive and negative values of j determine the fraction of, respectively, the β + and the β − branches of the decay of neighboring unstable isobars). The indices “s” and “as” label, respectively, the symmetric and asymmetric components. The analysis performed in [9] revealed that Zp and
(1)
ΓZ can be represented by slowly changing functions of the fission-fragment mass numbers as Zp = µ1 + µ2 A,
ΓZ = γ1 + γ2 A,
(2)
where γ1 , γ2 , µ1 , and µ2 are adjustable parameters. The validity of the decomposition procedure and of the results obtained in the present study is confirmed by (i) the application of the standard χ2 criterion, the χ2 value for this decomposition being 1.2, and (ii) agreement between the sum of all fission components found in this study and the experimental values of the total fission cross section σf from [22, 23]. The values that were obtained for the parameters in the decomposition in (1) that are associated with the above components of charge and mass distributions of fission fragments are given in Table 1. PHYSICS OF ATOMIC NUCLEI Vol. 72 No. 6
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Am AND
237
Np FISSION
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Table 2. Cross sections for symmetric, asymmetric, and complete fission Target
σf , mb
σs , mb
σas , mb
σs /σas
241
Am
1763.7 ± 265.0
1487.7 ± 223.0
276.0 ± 41.0
5.4 ± 1.0
237
Np
1600.2 ± 240.0
1298.0 ± 195.0
302.2 ± 45.0
4.3 ± 1.0
1520 ± 160 [22]
1520 ± 160 [22]
1647 ± 100 [23]
1674 ± 102 [23]
Our analysis made it possible to determine the positions of peaks, the standard deviation, and the contribution of each mode to the total mass yield. The total fission cross section determined by summing all fission modes with allowance for the formation of two fragments in one fission event is given in Table 2 along with data from [22, 23]. Also quoted in this table are the cross sections associated with symmetric and asymmetric fission components. DISCUSSION OF THE RESULTS Approximations of the mass distributions of fragments originating from 241 Am and 237 Np fission induced by 660-MeV protons are presented in Figs. 1a and 1b, respectively. In the case of interaction with intermediate- and high-energy particles, the fission process is considered at a slow reaction stage after the completion of the internuclear cascade and the formation of an excited after-cascade nucleus. Neutron evaporation is a process that competes with the fission process (proton emission is suppressed). These processes proceed sequentially in several steps, depending on the excitation energy. At each step, the residual nucleus may undergo fission or emit a neutron. The number of neutrons emitted within the period spanning the commencement of the preequilibrium stage of interaction and the ultimate disintegration of the nucleus into two fragments is classified as the mean multiplicity of prefission neutrons νpre = ACN − 2A¯s = ACN − [AH + AL ], where ACN is the compound-nucleus mass and AH and AL are the masses of complementary heavy and light fragments, respectively, at the peaks of asymmetric fission [24– 26]. For either target under study, Table 3 presents the relative contribution of each fission mode (σi /σf ) and the mean multiplicity of prefission neutrons (these PHYSICS OF ATOMIC NUCLEI Vol. 72
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Table 3. Features of various fission modes: σi /σf (in percent) and νpre 241
Am
237
Np
σ1as /σf
2.6 ± 0.5
3.1 ± 0.6
σ2as /σf
13.0 ± 3.0
15.8 ± 3.0
σs /σf
84.4 ± 17.0
81.1 ± 16.0
νpre
15.0 ± 2.0
14.6 ± 2.0
quantities characterize various fission modes). These data indicate that, in the energy region under study, the symmetric component is dominant, which confirms the trend toward the enhancement of symmetric fission with increasing projectile energy [21, 27, 28]; at the same time, the low-energy fission of nuclei in the Th–Cf range [29, 30] is predominantly asymmetric by nature. In [9, 13, 14, 31, 32], the probabilities of various fission channels were estimated on the basis of an empirical relation for the critical fissility parameter. This relation was obtained from an analysis of symmetric- and asymmetric-fission contributions for a broad range of nuclei and is given by 2 (3) Z /A cr = 35.5 + 0.4 (Zf − 90) . The symmetric and asymmetric fission modes are dominant in the cases of Z 2 /A > (Z 2 /A)cr and Z 2 /A < Z 2 /A cr , respectively. Within the statistical model [10], the contribution of the evaporation process leads to the production of neutron-deficient nuclei, which predominantly undergo symmetric fission. The presence of the asymmetric fission component in the energy region being
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σ, mb 102 (a)
101
100
102 (b)
101
100
60
80
100
120
140
160 A
Fig. 1. Components of the mass distributions of fragments originating from (a) 241 Am and (b) 237 Np fission: (closed circles) Superlong, (open circles) Standard I, and (inverted open triangles) Standard II. The solid curve represents the total fission cross section σf , and the closed boxes stand for experimental data.
considered may be attributed to a large scatter of excitation energies of residual nuclei. Since the ratio of the number of neutrons to the number of protons has nearly identical values in 241 Am and 237 Np targets, the relative fractions of the different components of their fission are close in magnitude. On the basis of our data, we have estimated the fissility parameters of the 241 Am and 237 Np nuclei. As is well known, the fissility is defined as the ratio of the fission cross section (σf ) and the total cross section for inelastic interaction on a given nucleus (σin ) [33]: σf . (4) D= σin
In order to determine σin , we have employed here model calculations performed in [34]. The values of the fissility for 241 Am and 237 Np proved to be 0.91 ± 0.14 and 0.85 ± 0.13, respectively. These values agree within the errors. In [35], Fukahori and his coauthors systematized data on the fission of actinide and lighter nuclei that was induced by protons, neutrons, and photons in the region of excitation energies from several tens of MeV units to 10 GeV. As a supplement to their systematics, they used data computed according to the FISCAL code. The objective of their study was to create a universal database for employing it in applied problems associated with the transmutation of fission PHYSICS OF ATOMIC NUCLEI Vol. 72 No. 6
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fragments in subcritical systems. On the basis of systematizing experimental data and employing computed values, Fukahori et al. [35] proposed an empirical formula for estimating fissilities of nuclei that is independent of the sort of interacting particles. The estimates obtained in the present study for the fissilities are in satisfactory agreement with experimental and computed data on reactions induced by protons, neutrons, and monoenergetic photons [35, 36]. A comparison of fissilities obtained in reactions induced by particles of different species makes it possible to exclude special features of primary interaction and to single out general regularities of the fission process. The problem of the effect of primary interaction in the fission of Z 2 /A > 30 nuclei that was induced by photons, protons, and pions in the energy range extending up to 200 MeV was discussed in detail in [37]. The analysis performed there revealed that, in the case of similar properties of after-cascade nuclei, the fissility value, which determines the probability of fission at the stage of evaporation, depends only slightly on the sort of incident particles. Thus, the mechanism of fission is determined by the properties of an excited fissile nucleus and is universal with respect to the nature of interacting particles. The fissility of heavy nuclei at excitation energies above 40 MeV reaches a plateau, remaining below unity. This fact can be explained by the contribution of competing processes, such as the evaporation of neutrons, protons, and heavier particles at the preequilibrium stage of the interaction.
241
Am AND
237
Np FISSION
915
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CONCLUSIONS On the basis of the above analysis of experimental data on the charge and mass distribution of fragments originating from 241 Am and 237 Np fission induced by 660-MeV protons, we have obtained the decomposition of the total mass yield into individual components of symmetric and asymmetric fission. A determination of basic properties of individual components of the mass distribution and the contributions of these components has made it possible to establish a dominant role of the symmetric fission mode and to estimate the absolute fissilities of the 241 Am and 237 Np nuclei. At the above proton energy, the results proved to be 0.91 ± 0.14 and 0.84 ± 0.13, respectively.
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Translated by A. Isaakyan
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