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We have performed measurements of the $0_\mathrm{g.s.}^+ \rightarrow 2_1^+$excitations in the neutron-rich isotopes $^{48,50}$Ca via inelastic protonscattering on a liquid hydrogen target, using the GRETINA $\gamma$-ray trackingarray. A comparison of the present results with those from previousmeasurements of the lifetimes of the $2_1^+$ states provides us the ratio ofthe neutron and proton matrix elements for the $0_\mathrm{g.s.}^+ \rightarrow2_1^+$ transitions. These results allow the determination of the ratio of theproton and neutron effective charges to be used in shell model calculations ofneutron-rich isotopes in the vicinity of $^{48}$Ca.

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