Half-lives of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decaying nuclei in the medium-mass region within the transfer matrix method

Abstract

The $\ensuremath{\alpha}$-decay half-lives of even-even nuclei from Sm to Th are systematically studied based on the transfer matrix method. For the nuclear potential, a type of cosh-parametrized form is applied to calculate the penetration probability. Through a least-squares fit to experimental half-lives, we optimize the parameters in the potential and the $\ensuremath{\alpha}$ preformation factor ${P}_{0}$. During this process, ${P}_{0}$ is treated as a constant for each parent nucleus. Eventually, the calculated half-lives are found to agree well with the experimental data, which verifies the accuracy of the present approach. Furthermore, in recent studies, ${P}_{0}$ is regulated by the shell and paring effects plus the nuclear deformation. To this end, ${P}_{0}$ is here associated with the structural quantity, i.e., the microscopic correction of nuclear mass (${E}_{\mathrm{mic}}$). In this way, the agreement between theory and experiment is greatly improved by more than 20%, validating the appropriate treatment of ${P}_{0}$ in the scheme of ${E}_{\mathrm{mic}}$.