β--decay half-lives for waiting point nucleiaround N=82

Abstract

Based on the exponential formula of β--decay half-lives for nuclei far from stable line, the half-lives of nuclei around N=82 (R-process waiting point nuclei) are calculated. The results are compared with recent theoretical and experimental data. It is shown that compared with the complicated and time-consuming microscopic calculation, the exponential formula including the shell effect can give the results of β--decay half-lives for R-process waiting point nuclei quicker and better. The results can be used as reliable inputs for the network calculation for nuclei synthesis in cosmos.

Generalizing the Liquid Drop Model (LDM) to Assess (Q_β^+-value) for Nuclei in the Range of 10≤Z≤98.

“…Table (2), shows the standard deviation (𝛿) for the average nuclear binding energy in the range of (10 ≤ 𝑍 ≤ 98) according to the (LDM). The results indicated the accuracy of the new equation (8) in determining the (𝑄 𝛽 + − 𝑣𝑎𝑙𝑢𝑒) in terms of nuclear binding energy instead of masses difference as it is usual, thus, indicates high possibility of (LDM) in determining the nuclear binding energy for all studied nuclei.…”

“…When we applied the above equation on all studied nuclei, it showed an acceptable match between the experimental and theoretical values with acceptable standard deviation. The equation (8) we will be denoted as modified liquid drop model (MLDM).…”

“…Many alternative models have been developed to assess the half-life of beta decay in addition to the global quasiexperimental models, and many of these are dubbed micro computations inside the reactive shell model [5][6][7], while others employ the random quasi-particle approximation. Between the decay energy and the halflife, the spectrum of nuclei located on the Valley of Stability has been closely studied to create an experimental law of beta decay [8]. Several researchers have looked into this extensively and have begun to characterize the energy of beta decay [9,10].…”

The contribution of the first forbidden transitions to the nuclear β−-decay half-life *

“…Sargent [22] proposed a fifth power law between the decay half-life and decay energy. Recently, we systematically analyzed the experimental data for decay halflife and found an exponential law for the decay halflife for nuclei far from stability, which is similar to the relation between the decay half-life and decay energy [23][24][25]. The calculations with an empirical formula based on this exponential law reproduce the experimental data well.…”

“…It can be seen from the two panels that the ratio has a minimum value around the shell (N = 82) and subshell closures (N = 92). To consider the shell correction, we use the form to describe empirically, where S represents the shell correction described by the Gaussian function [24]. The expression for including the proton number Z and the neutron number N can be written as…”