Isotopic dependence of the cross section for the induced fission of heavy nuclei
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CLEI Theory
Isotopic Dependence of the Cross Section for the Induced Fission of Heavy Nuclei O. N. Bolgova1), G. G. Adamian1), 2) , N. V. Antonenko1) , А. S. Zubov1) , S. P. Ivanova†1) , and W. Scheid3) Received May 26, 2008; in final form, October 8, 2008
Abstract—The cross sections for the induced fission of 211−223 Ra, 203−211 Rn, and 221−231 Th nuclei undergoing peripheral collisions with 208 Pb nuclei are calculated on the basis of the statistical model. The role of the N = 126 neutron shell is studied. The level density in excited nuclei is determined within the Fermi gas model and a model that takes into account the collective enhancement of the level density. The inclusion of a particle–hole excitation in addition to a collective Coulomb excitation makes it possible to obtain a satisfactory description of experimental cross sections for the fission of radium isotopes. The calculated ratios of the cross sections for the induced fission of 236 U (237 U) and 238 U (239 U) nuclei agree with experimental data. PACS numbers: 25.70.Jj DOI: 10.1134/S1063778809060040
1. INTRODUCTION The effect of the shell structure of nuclei on the fission process has been studied for a long time. Since closed-shell heavy nuclei are more stable against spontaneous fission and alpha decay than their neighbors, it is natural to assume their higher stability against induced fission as well. This assumption is supported by experimental data on the synthesis of superheavy nuclei in hot-fusion reactions [1] induced by 48 Ca beams. From the respective experimental results, it follows that the survival probability of excited superheavy nuclei grows as they approach the N = 184 neutron shell, this being in accord with the predictions of the shell model. Of particular interest is the shell structure of nuclei far from the drip line. Magic numbers may change in these nuclei. The present study is devoted to exploring the impact of the shell structure in the vicinity of the N = 126 neutron shell on the probability of the fission of excited neutron-deficient radium isotopes. Experiments that studied the fissility of these nuclei †
Deceased. Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia. 2) Institute of Nuclear Physics, Uzbek Academy of Sciences, pos. Ulughbek, Tashkent, 702132, Republic of Uzbekistan. 3) ¨ Theoretische Physik, Justus-Liebig-Universitat, ¨ Institut fur Heinrich-Buff-Ring 16, 35392 Giessen, Germany. 1)
¨ Schwerionenwere performed at the Gesellschaft fur forschung (GSI, Darmstadt) [2]. Although fragmentation products had low angular momenta, an increase in the survival probability in relation to fission at N = 126 can hardly be observed, radium isotopes presumably undergoing Coulomb collective excitation. In [2], this unexpected effect was explained in part by the effect of collective excitations on the level density. Nevertheless, the calculated cross section for 214 Ra fission proved to be nearly two orders of magnitude smaller than its experimental counterpart. In the present study, we will try to reveal the reaso
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