Model-independent analysis on the regular behavior of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> preformation probability in heavy nuclei
Shulin Tang, Yibin Qian, Zhongzhou Ren
Abstract
The formation process of the $\ensuremath{\alpha}$ cluster at the surface of nuclei is believed to unravel the structural properties of heavy nuclei, while the fully microscopic understanding of the formation probability is still extremely difficult. In this study, the $\ensuremath{\alpha}$ decay width is obtained within the cluster model plus the identical $\ensuremath{\alpha}$-core interaction potential for our previous $\ensuremath{\alpha}$-cluster structure investigation. Given that the $\ensuremath{\alpha}$ decay half-life is determined by the decay width (penetration probability) and the $\ensuremath{\alpha}$ preformation probability (${P}_{\ensuremath{\alpha}}$), the relative-varying trend of ${P}_{\ensuremath{\alpha}}$ can be then systematically analyzed via the comparison of the ratio of experimental $\ensuremath{\alpha}$ decay half-lives in isotopic chains with that of calculated decay widths to avoid exploring the model-dependent values of preformation probabilities. The ratio of extracted ${P}_{\ensuremath{\alpha}}$ values, for neighboring $\ensuremath{\alpha}$ emitters, is further presented to clearly reveal the smooth pattern of the formation probabilities of the $\ensuremath{\alpha}$ cluster off the shell closure. As a comparative study, the ratio of the ${P}_{\ensuremath{\alpha}}$ value from the cluster formation model is listed in the valence nucleon scheme as well, showing a similar pattern to the present results.