Description of nucleon-transfer and fusion reactions within time-dependent approaches and coupled-channel method
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CLEI Theory
Description of Nucleon-Transfer and Fusion Reactions within Time-Dependent Approaches and Coupled-Channel Method V. V. Samarin* Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia Received January 13, 2014
¨ Abstract—The time-dependent Schrodinger equation and the method of perturbed stationary states that is based on the expansion of the total wave function for the system of two nuclear cores and a nucleon in a set of nucleon two-center functions are used to describe nucleon transfers and fusion in low-energy nuclear reactions. A set of multichannel equations that couple the relative motion of nuclei to the motion of the nucleon is obtained. The kinetic-energy coupling matrix is similar to the coupling matrix for collective excitations of nuclei. DOI: 10.1134/S1063778814120151
1. INTRODUCTION Reactions involving neutron-rich nuclei open new possibilities for the production and investigation of new isotopes—in particular, for the synthesis of new superheavy elements [1, 2]. Special features of the tunnel effect under conditions of the interplay between the outer-neutron energy and the energy of the relative motion of nuclei are of particular interest in reactions of near-barrier fusion of nuclei [2, 3]. An extension of neutron wave functions for outer neutron shells over a long distance is known to be responsible for large values of neutron-transfer cross sections at near-barrier energies. A significant enhancement of cross sections for the fusion of nuclei was observed in a number of reactions involving 18 O and 96 Zr neutron-rich nuclei [4, 5] (Fig. 1). The transition of outer neutrons of one of the nuclei involved to unoccupied lower lying levels of the other nucleus may be a source of the increase in the energy of the relative motion of these nuclei, and this would in turn enhance the probability for overcoming the Coulomb barrier [2]. The interplay between the processes of the formation of two-center (molecular) states, the transition of neutrons between such states, and neutron transfer between nuclei in the 18 O+58 Ni system was studied on the basis of the time-dependent semiclassical three-dimensional model [6]. Here, an analysis of the role of two-center states in this model is supplemented with calculations performed within a simpler and more transparent semiclassical model and within a quantum three-body one-dimensional model. A set of multichannel equations for wave functions that describe the relative motion of nuclei *
with the aid of a microscopic renormalized symmetric kinetic-energy matrix is obtained by the method of excited stationary states [7]. The matrix in question is determined by the two-center wave functions, and the accuracy of the method proposed in [8] is improved here in order to calculate these functions. The resulting set of equations makes it possible to take into account coupling to single-particle degrees of freedom by a method that is similar for that used in [9] to take into account coupling to collective excitations of nuclei. 2. TIME-DEPENDENT
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