Eligibility of spherical-well approximation for calculations of nucleon-transfer matrix elements
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NUCLEI Theory
Eligibility of Spherical-Well Approximation for Calculations of Nucleon-Transfer Matrix Elements* R. K. Utamuratov1), 2) , A. I. Muminov2) , and A. K. Nasirov1), 2) Received September 11, 2006
Abstract—Single-particle matrix elements of nucleon transfer were calculated by the Woods–Saxon potential wave functions. The results are compared with the ones calculated by the spherical-well approximation. The eligibility of the approximation of the mean field of nuclei by the spherical well to study the initial stage of nuclear reactions at heavy-ion collisions is demonstrated. PACS numbers: 25.40.Hs, 25.70.Lm DOI: 10.1134/S1063778807090025
INTRODUCTION The role of shell structure of colliding nuclei in the reaction mechanism at low energies was demonstrated in a theoretical analysis of a nonequilibrium share (out of proportion to masses of fragments) of an excitation energy between reaction fragments at heavy-ion collisions [1–3] and of the observed fine structure in a mass distribution of fission products [4]. These phenomena indicate that the nuclear-shell structure plays an important role in nuclear reaction and in formation of the reaction fragments [5, 6]. So, the theoretical methods used to describe and analyze the above-mentioned phenomena should contain realistic schemes of the single-particle states, the nucleon separation energy, and single-particle matrix elements of the particle–hole excitations in nuclei and nucleon exchange between interacting nuclei. One of these models was developed and applied to describe and interpret the experimental data [2–4, 7–11]. The calculations were performed on the basis of the dinuclear-system concept [6, 8] which implies conservation of shell structure of the interacting nuclei. To simplify calculations of the matrix elements of nucleon transfer, the authors of the above-mentioned model used the wave functions of a spherical symmetric well in the internal part of nuclei [9] instead of the Woods–Saxon wave functions. But the effect of shell structure was taken into account by using the eigenvalues of the Woods–Saxon potential as singleparticle energies in the interacting nuclei. Nevertheless, the results obtained in the framework of this ∗
The text was submitted by the authors in English. Joint Institute for Nuclear Research, Dubna, Moskow oblast, 141980 Russia. 2) Institute of Nuclear Physics, Tashkent, Uzbekistan. 1)
model for the observable quantities are in good agreement with the experimental data and allowed one to explain the nonequilibrium distribution of excitation energy between reaction products [2]. The matrix elements calculated by the above-mentioned method were used in calculations of the collective-transition coefficients of the master equation describing the yield of the fission [4] and quasifission [10, 11] products. In this paper, we compare the results which were obtained by the above-mentioned approximation and by using the Woods–Saxon energy eigenvalues and wave functions for the single-particle states in both interacting nuclei. Our aim is to sh
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