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

TL;DR

This study reveals an $ ext{alpha}$ cluster structure in $^{48}$Ti, identifying a higher nodal band state and demonstrating the importance of $ ext{alpha}$ clustering in nuclear matrix element calculations for neutrinoless double-$eta$ decay.

Contribution

First demonstration of $ ext{alpha}$ clustering in $^{48}$Ti and its implications for nuclear structure and decay processes, using a unified scattering and structure approach.

Findings

Identification of a $7^-$ resonance state at 10.2 MeV as a higher nodal band with $ ext{alpha}$+$^{44}$Ca structure.

Successful reproduction of $ ext{alpha}$+$^{44}$Ca scattering and fusion data over a wide energy range.

Enhanced $B(E2)$ values indicating strong $ ext{alpha}$ clustering effects 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.