$\alpha$ + ${}^{92}$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.

11 pages, 9 figures

References in corpus (16)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Nuclear matrix elements for double-β decay
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements, QRPA, and isospin symmetry restoration
• Limits on the neutrino mass from neutrinoless double-$\beta$ decay
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Nuclear matrix element of neutrinoless double-$\beta$ decay: Relativity and short-range correlations
• Proton-Neutron Pairing Amplitude as a Generator Coordinate for Double-Beta Decay
• Nuclear deformation and neutrinoless double-$\beta$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd nuclei in mass mechanism
• Super-allowed alpha-decay above doubly-magic 100Sn and properties of 104Te = 100Sn otimes alpha
• Alpha-cluster structure in even-even nuclei around ${}^{94}$Mo
• $\alpha$ cluster states in ${}^{44,46,52}$Ti
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• $\alpha$-cluster states in ${}^{46,54}$Cr from double-folding potentials
• Existence of higher nodal band states with $\alpha$+${}^{48}$Ca cluster structure in ${}^{52}$Ti