Three-dimensional approach applied to quasistationary states of deformed α emitters

Abstract

We apply a three-dimensional (3D) approach to investigate the quasistationary states of well-deformed $\ensuremath{\alpha}$ emitters. With a splitting of the anisotropic 3D potential into internal and external parts at a separation surface, the 3D $\ensuremath{\alpha}$-cluster decay width is determined by the initial wave function of a true bound state of an anisotropic harmonic oscillator potential and a nonresonance scattering wave function of Coulomb potential. Substantial difference between the one-dimensional (1D) and 3D decay width is found for typical $\ensuremath{\alpha}$ emitters with large quadrupole and hexadecapole deformations.