Method of determination of the most probable coordinate of formation of $\alpha$-particle in $\alpha$-decay

Abstract

Method of multiple internal reflections (method MIR) in description of $\alpha$-decay of nucleus in the spherically symmetric approximation is presented in paper. In approach MIR the formalism of calculation of amplitudes of wave function, described moving of $\alpha$-particle from the internal region outside with its tunneling through a realistic radial $\alpha$-nucleus barrier of arbitrary shape, has been constructed at first time. The method MIR gives convergent values for the amplitudes of transmission and reflection, coefficients of penetrability and reflection, obtained in description of leaving of the $\alpha$-particle relatively a potential with barrier in form of a number of rectangular steps (multi-steps potential), with tending this potential to the realistic $\alpha$-nucleus one, and limit values of the amplitudes and coefficients are considered as exact concerning the realistic $\alpha$-nucleus potential (without application of WKB approximation). In approach MIR a dependence of the penetrability coefficient and half-live on the location of the starting point, from where $\alpha$-particle begins to move outside, is opened. From here, we define a radial coordinate of the most probable formation of the $\alpha$-particle inside nucleus before its $\alpha$-decay as such starting point, at moving of the $\alpha$-particle from which outside the half-live, calculated by approach MIR, is maximally closed to its experimental value. For isotopes ${\rm Po}$ with different mass number $A$ we have obtained essentially closer values for half-live, calculated by such approach, to their experimental values in a comparison with half-lives obtained by approach WKB. This result is stable for all studied nuclei.