Special features of the structure of the beta-stability line for nuclei
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CLEI Theory
Special Features of the Structure of the Beta-Stability Line for Nuclei Yu. S. Lutostansky* and V. N. Tikhonov National Research Center Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia Received October 25, 2016
Abstract—The mass-number (A) dependence Zβ (A) for nuclei lying on the beta-stability line (BSL) is calculated for A and Z values in the ranges of A = 2–258 and Z = 1–100, respectively. The calculated values are compared with experimental data. The deviations ΔZ = Zexpt − Zβ are analyzed. This analysis of ΔZ reveals that there are three regions of A values in which the A dependence of ΔZ is parabolic. The possible forms of the A dependence of ΔZ are analyzed, and it is shown that the majority of nuclei belong to several parabolas simultaneously. DOI: 10.1134/S106377881703019X
1. INTRODUCTION It is well known that the experimental betastability line (BSL) for nuclei is determined from tables of nuclear masses [1] via finding Zexpt (A) by minimizing the nuclear mass for each isobaric chain (A = const). By means of calculations, the values of Zβ (A) versus the mass number are also determined by finding a minimum of nuclear masses at a constant value of A. In the region of low- and medium-mass nuclei, those that lie on the beta-stability line are stable, but, in the region of heavy nuclei, where alpha decay and spontaneous fission are possible, not all of the nuclei on this line are long-lived. The simplest way to calculate the dependence Zβ (A) is to rely on the liquid-drop model of the nucleus [2]. In this model, a dominant contribution to Zβ comes from the symmetry energy and the Coulomb energy of the nucleus being studied. Below, we consider two forms of the expression for the Coulomb energy and analyze special features associated with the symmetry energy. A procedure for describing the beta-stability line was developed many years ago (see, for example, [2]), and no changes have been introduced in it to date. On the basis of this procedure, one of the present authors derived an expression for the dependence Zβ (A) [3]. This expression was used in studying processes that accompany the beta decay of neutron-rich nuclei. A similar expression for Zβ (A) was obtained recently in [4] in studying various approaches to describing nuclear masses. A determination of the beta-stability *
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line is of particular importance in calculating the nucleosynthesis process, especially the formation of heavy nuclei in intense neutron flows (r-process). In the case of the r-process, the BSL position, together with the position of the neutron drip line [5, 6], determines the trajectories of equilibrium neutron-capture processes [7], and this is also of importance in calculating the half-lives of neutron-rich nuclei involved in the r-process [8]. In the present article, methods for calculating the dependence Zβ (A) on the beta-stability line are described for two versions of the description of the Coulomb energy, the influence of exchange effects in the region of light nuclei being a
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