Inverse-kinematics proton scattering on $^{50}$Ca: Determining effective charges using complementary probes

TL;DR

This study measures excitations in neutron-rich calcium isotopes via proton scattering to determine effective charges for shell model calculations, providing insights into nuclear structure near $^{48}$Ca.

Contribution

It introduces a method combining inelastic proton scattering and lifetime measurements to extract effective charges in neutron-rich isotopes.

Findings

Determined neutron and proton matrix element ratios for $^{48,50}$Ca.

Provided effective charge ratios for shell model calculations.

Enhanced understanding of nuclear structure near $^{48}$Ca.

Abstract

We have performed measurements of the $0_\mathrm{g.s.}^+ \rightarrow 2_1^+$ excitations in the neutron-rich isotopes $^{48,50}$Ca via inelastic proton scattering on a liquid hydrogen target, using the GRETINA $\gamma$-ray tracking array. A comparison of the present results with those from previous measurements of the lifetimes of the $2_1^+$ states provides us the ratio of the neutron and proton matrix elements for the $0_\mathrm{g.s.}^+ \rightarrow 2_1^+$ transitions. These results allow the determination of the ratio of the proton and neutron effective charges to be used in shell model calculations of neutron-rich isotopes in the vicinity of $^{48}$Ca.