Evidence of a higher nodal band $\alpha$+${}^{44}$Ca cluster state in fusion reactions and $\alpha$ clustering in ${}^{48}$Ti

Abstract

In the nucleus ${}^{48}$Ti, whose structure is essential in evaluating the half-life of the neutrinoless double-$\beta$ decay ($0\nu \beta \beta$) of ${}^{48}$Ca, the existence of the $\alpha$ cluster structure is shown for the first time. A unified description of scattering and structure is performed for the $\alpha$+${}^{44}$Ca system. By using a global potential, which reproduces experimental $\alpha$+${}^{44}$Ca scattering over a wide range of incident energies, $E_{\alpha }$=18 - 100 MeV, it is shown that the observed $\alpha$+${}^{44}$Ca fusion excitation function at $E_{\alpha }$=9 -18 MeV is described well. The bump at $E_{\alpha }$=10.2 MeV is found to be due to a resonance which is a $7^{-}$ state of the higher nodal band with the $\alpha$+${}^{44}$Ca cluster structure in ${}^{48}$Ti. The local potential $\alpha$+${}^{44}$Ca cluster model locates the ground band of ${}^{48}$Ti in agreement with experiment and reproduces the enhanced $B(E2)$ values in the ground band well. This shows that collectivity due to $\alpha$ clustering in ${}^{48}$Ti should be taken into account in the evaluation of the nuclear matrix element in the $0\nu \beta \beta$ double-$\beta$ decay of ${}^{48}$Ca.

6 pages, 6 figures

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