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.
Categories: nucl-ex