α+Zr92 cluster structure in Mo96

Abstract

In the evaluation of the half-life of the neutrinoless double-$\ensuremath{\beta}$ decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) of a doubly closed-subshell nucleus $^{96}\mathrm{Zr}$, the structure of the nucleus $^{96}\mathrm{Mo}$ is essentially important. The $\ensuremath{\alpha}$-clustering aspects of $^{96}\mathrm{Mo}$ are investigated for the first time. By studying the nuclear rainbows in $\ensuremath{\alpha}$ scattering from $^{92}\mathrm{Zr}$ at high energies and the characteristic structure of the excitation functions at the extreme backward angle at the low-energy region, the interaction potential between the $\ensuremath{\alpha}$ particle and the $^{92}\mathrm{Zr}$ nucleus is determined well in the double folding model. The validity of the double folding model was reinforced by studying $\ensuremath{\alpha}$ scattering from neighboring nuclei $^{90}\mathrm{Zr}, ^{91}\mathrm{Zr}$, and $^{94}\mathrm{Zr}$. The double-folding-model calculations reproduced well all the observed angular distributions over a wide range of incident energies and the characteristic excitation functions. By using the obtained potential the $\ensuremath{\alpha}+^{92}\mathrm{Zr}$ cluster structure of $^{96}\mathrm{Mo}$ is investigated in the spirit of a unified description of scattering and structure. The existence of the second-higher nodal band states with the $\ensuremath{\alpha}+^{92}\mathrm{Zr}$ cluster structure, in which two more nodes are excited in the relative motion compared with the ground band, is demonstrated. The calculation reproduces well the ground-band states of $^{96}\mathrm{Mo}$ in agreement with experiment. The experimental $B(E2)$ value of the transition in the ground band is also reproduced well. The effect of $\ensuremath{\alpha}$ clustering in $^{96}\mathrm{Mo}$ on the the half-life of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ double-$\ensuremath{\beta}$ decay of $^{96}\mathrm{Zr}$ is discussed.