Simple relation for alpha decay half-lives

Abstract

The experimental values of ${\mathrm{log}}_{10}$${\mathit{T}}_{1/2}$(sec) plotted vs ${\mathit{Z}}_{\mathit{d}}^{0.6}$/ \ensuremath{\surd}${\mathit{Q}}_{\mathrm{\ensuremath{\alpha}}}$ are shown to fall on a nearly universal straight line with ${\mathrm{log}}_{10}$${\mathit{T}}_{1/2}$(sec)=(9.54${\mathit{Z}}_{\mathit{d}}^{0.6}$/ \ensuremath{\surd}${\mathit{Q}}_{\mathrm{\ensuremath{\alpha}}}$)-51.37, where ${\mathit{Z}}_{\mathit{d}}$ is the charge number of the daughter nucleus and ${\mathit{Q}}_{\mathrm{\ensuremath{\alpha}}}$ is expressed in units of MeV. This behavior also numerically comes out of the semiclassical WKB calculation of the barrier penetration factor. The fine structure in the ratio of experiment over theory is briefly discussed.