Improved empirical formulas for α-decay half-lives of heavy and superheavy nuclei

Abstract

The empirical Royer formulas were readjusted with new set of coefficients using the latest experimental data and the recent evaluated α-decay half-lives over a wide range of 573 nuclei between 52 ≤ Z ≤ 118. The effects of the orbital angular momentum, isospin asymmetry, and parity have been examined in improving the adopted formulas. The modified formulas were tested for their accuracy by comparing with the recent experimental data and other theoretical calculations. The prediction of α-decay half-lives of several isotopes of the superheavy nuclei with Z = 120 − 126, which have not yet been experimentally synthesized, are presented and compared with other theoretical approaches. The behavior of log10 Tα in relation to the neutron number variation is explored for about 40 isotopes of each element. Based on the minima found in log10 Tα variation with neutron number, we found neutron stability at N = 184, 190, 196, 200, 202, 204, 210, 216, 218, 220 and 228. The behavior of log10 Tα with neutron variation for heavy and superheavy nuclei is almost the same as that found using more heavy and complicated calculations. The present method can be applied easily to study large number of nuclei.

History of Department of Neurology at S.M.S. Medical College, Jaipur

“…For the selection of α-decay half-lives formula, we have tested few recently fitted/modified empirical/semiempirical formulas [25,34,37,38,60,[89][90][91][92][93][94][95][96][97][98] and the comparison among these formulas is shown in Table 1. For the comparison, we use root mean square error (RMSE) and uncertainty (u), which are calculated by using the following formulas:…”

Half-lives for proton emission and α decay within the deformed Gamow-like model

“…The study of proton emission can extract meaningful information about the nuclear structure beyond the proton drip line, e.g., the shell structure and the coupling between unbound and bound nuclear states [2]. Currently, many models have been used to study α decay, such as the unified model for α decay and α capture [3,4], the empirical formulas [5][6][7][8][9][10][11], the twopotential approach [12,13], the cluster model [14][15][16], the liquid drop model [17][18][19][20][21], the generalized liquid drop model [22,23] and others [24][25][26][27][28][29][30][31][32]. There are also many theoretical models used to study proton emission or the different forms of interactions used to construct these models, such as the single-folding model [33,34], the Coulomb and proximity potential model (CPPM) [35], the distorted-wave Born approximation [36], the R-matrix approach [37], the coupled-channel approach [38][39][40], the relativistic density functional theory [41], the generalized liquid drop model [42][43]…”

An improved unified formula for $$\alpha $$-decay and cluster radioactivity of heavy and superheavy nuclei

“…The study of superheavy nuclei (SHN), having Z ≥ 104, and the quest for an "island of stability" have become a topic of active research over the past several decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. These SHN owe their existence to stabilizing nuclear shell effects [9,12,19].…”

“…Numerous analytical and empirical formulas are suggested to predict the half-lives of these two decay modes [2,[50][51][52][53][54][55][56]. Many of these formulas undergo periodic modifications in various forms to fit the most recent experimental data.…”

“…In our previous work [2], we started by Royer's formula for α-decay half-lives and derived five improved empirical formulas that can be used to calculate α-decay half-lives of heavy and superheavy nuclei. In the present work, we extend our previous study to include cluster radioactivity.…”