Correlation Between the Behavior of ${\alpha}$-Decay Half-Life Time and $\boldsymbol{Q}$ Values with Neutron Number Variation of Daughter Nuclei

Abstract

$\alpha$ decay of 2000 parent heavy and superheavy nuclei, with atomic numbers in the range $Z=80$ to $Z=122$, is considered. We calculated the half-life time, $T_{\alpha}$, of each nucleus using the density-dependent cluster model with M3Y-effective nucleon–nucleon interaction. The $Q_{\alpha}$ values needed for calculation of $T_{\alpha}$ were extracted from four different mass tables used frequently in $\alpha$-decay calculation. These tables are WS4, WS3, FRDM(2012), and DZ tables. The present study shows to what extent the behavior and value of $T_{\alpha}$, as the nucleon number varies, depends on choosing the mass table used to extract $Q_{\alpha}$ values. For this purpose, we studied the variation of log $T_{\alpha}$ and the corresponding $1/Q_{\alpha}$ with the neutron number of the daughter nucleus, $N_{d}$, using the four different mass tables. The results show that the log $T_{\alpha}$ variation follows the corresponding $1/Q_{\alpha}$ variation. The two mass tables WS3 and WS4 predict almost the same log $T_{\alpha}$ variation and agree in the magic and semi-magic numbers. For FRDM(2012) and DZ tables the variation of log $T_{\alpha}$ with $N_{d}$ follows the same $1/Q_{\alpha}$ variation but the magic numbers deduced from these two tables do not agree with each other and almost differ from those predicted from WS3 and WS4. FRDM(2012) tables predict the main deep minimum at $N_{d}=128$ instead of the magic neutron number $N_{d}=126$.