Alpha-cluster structure in even-even nuclei around ${}^{94}$Mo

Abstract

$Background$: The $\alpha$-cluster model was successful for describing spectroscopic properties of light nuclei near the shell closures. Evidences of the $\alpha$-cluster structure in ${}^{94}$Mo were shown, motivating the search for the same structure in other intermediate mass nuclei. $Purpose$: The systematic analysis of the $\alpha$-cluster structure in ${}^{94}$Mo and four even-even neighbouring nuclei. $Method$: The $\alpha$-cluster model with the local potential approach. $Results$: A good general description of the experimental ground state bands is obtained with only one variable parameter. It is shown that the employed $\alpha +\text{core}$ potential is weakly dependent on the angular momentum $L$ and such dependence may be described satisfactorily by a simple $L$-dependent factor for the five nuclei. The radial parameter of the $\alpha +\text{core}$ potential reveals a linear trend in relation to the total nuclear radius and the sum of the $\alpha$-cluster and core radii. The calculated $B(E2)$ transition rates reproduce correctly the order of magnitude of almost all experimental data without the use of effective charges. The rms intercluster separations and reduced $\alpha$-widths obtained for the ground state bands point to a reduction of the $\alpha$-cluster intensity with the increasing spin. Negative parity bands are calculated and compared to available experimental levels. The volume integral per nucleon pair and rms radii were calculated for the studied $\alpha +\text{core}$ potentials, revealing a similarity with the real parts of the optical potentials used to describe the $\alpha {+}^{90}$Zr and $\alpha {+}^{92}$Mo elastic scattering at several energies. $Conclusions$: This work strongly indicates the presence of similar $\alpha +\text{core}$ structures for the $N=52$ even-even nuclei of the Mo region.

15 pages, 9 figures; accepted for publication in Physical Review C

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• ${}^{92}$Mo($\alpha ,\alpha$)${}^{92}$Mo scattering,the ${}^{92}$Mo--$\alpha$ optical potential, and the ${}^{96}$Ru($\gamma ,\alpha$)${}^{92}$Mo reaction rate at astrophysically relevant energies
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