$\alpha$ + ${}^{92}$Zr cluster structure in ${}^{96}$Mo

Abstract

In the evaluation of the half-life of the neutrinoless double-$\beta$ decay ($0\nu \beta \beta$) of a doubly closed-subshell nucleus ${}^{96}$Zr, the structure of the nucleus ${}^{96}$Mo is essentially important. The $\alpha$-clustering aspects of ${}^{96}$Mo are investigated for the first time. By studying the nuclear rainbows in $\alpha$ scattering from ${}^{92}$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 $\alpha$ particle and the ${}^{92}$Zr nucleus is determined well in the double folding model. The validity of the double folding model was reinforced by studying $\alpha$ scattering from neighboring nuclei ${}^{90}$Zr, ${}^{91}$Zr, and ${}^{94}$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 $\alpha$ +${}^{92}$Zr cluster structure of ${}^{96}$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 $\alpha$+ ${}^{92}$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 ${}^{96}$Mo in agreement with experiment. The experimental $B(E2)$ value of the transition in the ground band is also reproduced well. The effect of $\alpha$ clustering in ${}^{96}$Mo on the the half-life of the $0\nu \beta \beta$ double-$\beta$ decay of ${}^{96}$Zr is discussed.

arXiv comment11 pages, 9 figures

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