Microscopic description of α-like resonances

Abstract

A description of $\ensuremath{\alpha}$-like resonances is given in terms of single-particle states including narrow Gamow resonances in continuum. The equations of motion are derived within the multistep shell-model approach; the lowest collective two-particle eigenmodes are used as building blocks for the four-particle states. A good agreement with the low-lying states in ${}^{212}\mathrm{Po}$ is obtained. A new technique to estimate the $\ensuremath{\alpha}$-particle formation amplitude for any multipolarity is proposed. The spectroscopic factor of the $\ensuremath{\alpha}$-decay between ground states is reproduced, but the total width is by two orders of magnitude less than the experimental total width, due to the absence of the background components. The $\ensuremath{\alpha}$-like structure of the lowest states in ${}^{212}\mathrm{Po}$ is analyzed and strong high-lying resonances are predicted. The derived equivalent local potential for the $\ensuremath{\alpha}$-particle scattering has a molecular shape.