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

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

6 pages, 6 figures