Nucleon states of strongly deformed nuclei and dinuclear systems in the nonoscillator two-center model
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CLEI Theory
Nucleon States of Strongly Deformed Nuclei and Dinuclear Systems in the Nonoscillator Two-Center Model V. V. Samarin* Cheboksary Polytechnic Institute, Moscow State Open University, ul. Karla Marksa 54, Cheboksary, Chuvash Republic, 428000 Russia Received December 28, 2009
¨ Abstract—A new method for numerically solving the Schrodinger equation for an arbitrary axisymmetric field with allowance for spin–orbit interaction is used to study neutron and proton states in strongly deformed nuclei and dinuclear systems produced at the first step of the fusion of nuclei. A quadrupole– octupole parametrization is proposed for the shape of a dinuclear system and for the potential energy of nucleons in this system. The experimentally observed deformations of the 26,27,28 Mg nuclei and the difference in the cross sections for the fusion of nuclei in the 18 O + 58 Ni and 16 O + 60 Ni systems are explained qualitatively. DOI: 10.1134/S1063778810080156
1. INTRODUCTION In recent years, much attention has been given to studying the fusion of heavy nuclei, which is able to lead to the synthesis of new superheavy elements [1– 3], and to reactions involving exotic (neutron- and proton-rich) nuclei [4–7] in the vicinities of the N and Z drip lines on the chart of nuclei in the (N −Z) plane [8]. Such nuclei are characterized by a strong deformation and by a shell structure substantially different from that of spherical nuclei. Therefore, investigation of nucleon states in strongly deformed nuclei is of importance for analyzing existing experimental data and for forecasting the results of new experiments devoted to superheavy and exotic nuclei. Such investigations are also necessary for exploring the properties of fission and fusion barriers [9, 10] for nuclei and their isomeric states. The shell model of spherical and weakly deformed nuclei (Nilsson model) [11, 12] has been successfully used for more than half a century. The inclusion of two-body nucleon–nucleon interactions for spherical nuclei [13, 14] and selfconsistent Skyrme–Hartree–Fock and relativisticmean-field models for superheavy nuclei [15, 16] are important lines of the development of this model along with the generalization of the Woods–Saxon model to strongly deformed nuclei [17, 18] and to two-center systems [18–21], which are initial stages of the fusion of nuclei or final stages of their fission. It is noteworthy that, in the case of an appropriate choice of set of parameters [22, 23], even the independent-particle *
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approach of the spherical shell model [11, 12], albeit being relatively simple, makes it possible to attain satisfactory agreement with such experimentally observable properties of nuclei as nucleon-separation energies and spin–parities of ground and low-lying excited states. Difficulties in extending this approach to strongly deformed and two-center nuclear systems are associated with the choice of optimum numerical ¨ method for solving the Schrodinger equation for an axisymmetric field and with the choice of description a
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