Assault frequency and preformation probability of theαemission process

Abstract

A study of the assault frequency and preformation factor of the $\ensuremath{\alpha}$-decay description is performed from the experimental $\ensuremath{\alpha}$-decay constant and the penetration probabilities calculated from the generalized liquid-drop model (GLDM) potential barriers. To determine the assault frequency a quantum-mechanical method using a harmonic oscillator is introduced and leads to values of around ${10}^{21}$ s${}^{\ensuremath{-}1}$, similar to the ones calculated within the classical method. The preformation probability is around ${10}^{\ensuremath{-}1}$--${10}^{\ensuremath{-}2}$. The results for even-even Po isotopes are discussed for illustration. While the assault frequency presents only a shallow minimum in the vicinity of the magic neutron number 126, the preformation factor and mainly the penetrability probability diminish strongly around $N=126$.