ЯДРА
SYMMETRIC AND ASYMMETRIC FISSION MODES IN PROTON-INDUCED FISSION AT 660 MeV OF 238U
© 2010 A. R. Balabekyan1)*, G. S. Karapetyan1), N. A. Demekhina2)'3), J. Adam2), K. Katovsky4)
Received February 8, 2010
Fission product cross sections of intermediate-energy fission of 238 U were used in order to construct the charge and mass yield distributions. Enriched target of 238 U was irradiated by proton beam with energy 660 MeV for several hours at the LNP Phasotron, Joint Institute for Nuclear Research (JINR), Dubna, Russia. The charge distribution of the fission fragments was analyzed for calculation of isobaric cross sections. The mass yield curves were expanded into symmetric and asymmetric components according multimodal fission approach. The fissility values of actinides were calculated at given proton energy. The obtained results have been compared to the same data for targets 237 Np and 241 Am.
INTRODUCTION
Fission product cross sections of 241 Am, 238 U, and 237Np actinides are the subject of interest, because they are essential data in management of radioactive waste from nuclear power plants. Fission cross section in the intermediate energy range has an important role as well as the emitted neutron number per fission reaction and fission neutron spectrum. On the other hand, experimental studies of fission cross section are recently available. However, the experimental data are not enough for actinide nuclei, especially for minor actinides.
The excitation energy of the fissioning system plays an important role in the dynamics of the fission process. Asymmetric fission, which is dominant at low energies, is characterized by a clear-cut manifestation of shell effects [1—6], whereas symmetric division is consistent with a classical liquiddrop picture of the fissioning nucleus [7, 8]. Among various information associated with nuclear fission phenomenon the problem of mass division has evoked interest. Particularly, this question is related to the intermediate energy region between the low and high energies, where the transition between the different fission modes (from asymmetric to symmetric) is supposed. The growth of the actinide fissility at this energy range, in spite of the wide-spread assumption
''Yerevan State University, Armenia.
2)JINR, Dubna, Russia.
3)Yerevan Physics Institute, Armenia.
4)Department of Nuclear Reactors, Czech Technical University in Prague, Czech Republic.
E-mail: balabekyan@ysu.am
about the fission saturation, causes interest to this question.
According to theoretical presentation, the correlation of different fission channels depends on the configuration and position of the saddle and scission points on energy surface [9, 10]. The application of the hypothesis of the multicomponent fission have allowed to extract different components on the base of the decomposition of the mass yield curve [11, 12].
In the present paper the multimodal analysis of fission has been performed at the research energies at first. The experimental fragment cross sections are used to extract the characteristics of the charge and mass distributions of the fission fragments. The obtained fission cross section has allowed to estimate the fissility of actinides at low and intermediate energy ranges.
EXPERIMENTAL
Bombardment of the 238U target by protons with energy 660 MeV was performed at LNP Phasotron, Joint Institute for Nuclear Research (JINR), Dubna, Russia. Fission fragment cross sections were measured by 7-ray spectrometry using high-purity Ge detector. The identification of the fission products was conducted by means of the definition of the half-lives, of the energies and intensities of the nuclear y transitions of the radioactive fragments [13]. In the absence of radioactive precursors the cross section of fission fragments was determined by using the following form:
ANX
a
NpNnкец(1 - e-Xtl )e-Xt^ (1 - e-Xt^)
(1)
1865
a, mb 102 r
Fig. 1. Mass-yield curves for proton-induced fission of 238U at Ep = 660 MeV. (■) Experimental points; solid curve is total fission yield af ; (•) Superlong I mode; (o) Standard I mode; (y ) Standard II mode.
where a is the cross section of the reaction product; AN is the area under the photopeak; Np — the intensity of proton beam (part./s); Nn — the number of target nuclei on unit surface (1/cm2); t1 — the irradiation time; t2 — the time of exposure between the end of irradiation and the beginning of measurements; t3 — the time of measurement; À — the decay constant (s—1 ); n — the intensity of nuclear 7 transitions; k — the total coefficient of the 7-ray absorption in the target and detector materials; e — the detection efficiency. In this way the isotope formation in the nuclear reaction is determined as an independent (I) cross section directly.
To deduce the independent cross section from the measured radioactivity it is necessary to correct the contribution from precursors, if the precursor has a half-life period of the same order or more than daughter nucleus. Knowing the precursor cross section the independent cross section of the daughter can be calculated by the relation from [14]
as =
Àb
(1
— p — ^B)p~Xbt2 (1 — e~XBt3
e
AN
l)e—XBt2 (1 - aafab
)
(2)
__ aAjAB ^A^B ^
NpNnksT] XB ~ A a
'(1 - e~XAtl)e~XAt2(l - e~XAts)
,
(1
— ^B)e — ^Bt2
)e—XB t2 (1
— ^B t3 ^
xb
where symbols A and B refer to, respectively, the parent and the daughter isotopes; fAB designates the fraction of decay from nuclide A to B; AN determines the area under the photopeak.
RESULTS AND DISCUSSION
The unmeasurable product cross sections were estimated in the present paper by means of the fragment charge distribution. Empirically, the charge distribution of fission products has been well represented by a Gaussian function, therefore, in the present work the analysis of the charge distribution is performed by the following function in the fitting procedure [15]:
aaz =
v(A)
(Cn)
1/2
exp
(Z
ZP )2
C
(3)
where aAzZ is the independent experimental cross section of the nuclide (Z, A); a (A) — the total isobar cross section for mass number A; Zp — the most probable charge for isobars, and C — the width parameter. The isobaric cross sections for different mass numbers are used for construction of the fission mass yield. The total mass yield af = ^A a (A)/2 was
x
x
SYMMETRIC AND ASYMMETRIC FISSION MODES 1867
Table 1. Symmetric, asymmetric, total fission cross sections and the average number of pre-scission neutrons
Target Energy, MeV 07, mb as, mb a as, mb o"s/o"as
241 Am 660 1763.7 ± 265.0 1487.7 ±223.0 276.0 ±41.0 5.4 ± 1.0
238 у 660 1226.5 ±183.9 [18] 1110 ±300 [19] 1040 ± 75 [20] 698.3 ± 104.7 528.2 ± 79.2 1.32 ±0.2
237Np 660 1600.0 ±240.0 1520 ± 160 [21] 1647 ± 100 [22] 1674 ± 102 [22] 1298.0 ± 195.0 302.0 ±45.0 4.3 ± 1.0
evaluated by summing all isobaric cross sections and multiplying by factor 0.5, because in the sum give the contribution both fragments formed in each fission event.
The application of the hypothesis of the multicom-ponent fission allowed to extract the different components on the base of the decomposition of the mass yield curve. According to this model [12], the mass-yield curve can be decomposed into three distinct fission components: one symmetric "Superlong I" and two asymmetric "Standard I", "Standard II". "Superlong" mode fragments are strongly elongated with masses around Af/2. "Standard I" mode is characterized by influence of spherical neutron shell NH — 82 and proton shell ZH — 50 in the heavy fragments with masses MH — 132—134. "Standard II" mode is characterized by influence of the deformed neutron shell closure NH = 86—88 and proton shell ZH — 52 in the heavy fragments with masses MH — - 138-140.
The Gaussians were used for presentation of the different fission modes with parameters depending on nuclear characteristics of fission fragment [12, 16]. The mass-yield distribution of the fission fragments is usually described by five-Gaussian fit of the form [17] (Fig. 1):
a =
kias У2тг
aias
exp
K '
H—;—1ASr— exp
a
+
1AS^ K2AS
exp
+
K'
2AS
a
2ASV2tt Ks
exp
(A - AÎs - Dias)
2
^¡AS
(A - As+ DlAsf
42as
(A - As — D2as)2
2 rr2 2a2as
(A - As+ D2Asf
2a2as
+
(Ту л/2тг
exp
{A — Asf 2 4
Table 2. Contribution of symmetric fission mode and pre-scission neutron multiplicity
Target Energy, MeV crs/o-f, % ^pre
241 Am 660 84.4 ± 17.0 15.0 ±2.0
238 у 660 57.0 ± 10.0 12.0 ± 1.7
237Np 660 81.1 ± 16.0 14.6 ±2.0
+ (4)
+
+
+
where as is the mean mass number, the asymmetric components are characterized by the positions of the peaks (a4s ± DiAs), each components are characterized by the dispersions aiAs,s(^[As S) and the normalization factors KiAs,s(K'iAs s). The indexes AS, S designate the asymmetric and symmetric components.
The results of the fit allow to determine the total fission cross section and the cross sections of different fission components. These data are represented in Table 1 as well as for 241 Am and 237Np from our recent work [18], where the total fission cross sections are compared with the data from [19—22]. The good agreement in the overlap energy region is found. The relative contributions of symmetric fission mode as well as the average number of neutrons prior to the fission for investigated nuclei are shown in Table 2. One can see from Table 2, the symmetric fission gives the appreciable contribution to the total fission cross section. With increasing excitation energy of fissioning nucleus, the symmetric fission component grows too, and attributes its to increasing neutron evaporation opening new fission channels, there exists a set of various fissioning nuclides. Therefore, the symmetric component is linked with the more neutron-deficient fissioning systems.
In Fig. 2 the ratio of symmetric to asymmetric fission (or the valley-to-peak ratio, V/P) depending on excitation energy (E*) of fissioning nuclei is presented in the charge range 96 ^
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