Search for $\alpha$-cluster states in even-even Cr isotopes

Abstract

The $\alpha +\mathrm{core}$ structure is investigated in even-even Cr isotopes from the viewpoint of the local potential model. The comparison of $Q_{\alpha }/A$ values for even-even Cr isotopes and even-even $A=46,54,56,58$ isobars indicates that ${}^{46}$Cr and ${}^{54}$Cr are the most favorable even-even Cr isotopes for $\alpha$-clustering. The ground state bands of the two Cr isotopes are calculated through a local $\alpha +\mathrm{core}$ potential with two variable parameters. The calculated spectra give a very good description of most experimental ${}^{46}$Cr and ${}^{54}$Cr levels. The reduced $\alpha$-widths, rms intercluster separations and $B(E2)$ transition rates are determined for the ground state bands. The calculations reproduce the order of magnitude of the available experimental $B(E2)$ values without using effective charges and indicate that the first members of the ground state bands present a stronger $\alpha$-cluster character. The volume integral per nucleon pair and rms radius obtained for the $\alpha {+}^{50}$Ti potential are consistent with those reported previously in the analysis of $\alpha$ elastic scattering on ${}^{50}$Ti.