  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.
