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Excited states of the neutron-rich isotopes $^{42,44}$S and $^{41,43}$P havebeen studied via inverse-kinematics proton scattering from a liquid hydrogentarget, using the GRETINA $\gamma$-ray tracking array to extract inelasticscattering cross sections. Deformation lengths of the $2^+_1$ excitations in$^{42,44}$S have been determined and, when combined with deformation lengthsdetermined with electromagnetic probes, yield the ratio of neutron-to-protonmatrix elements $M_n/M_p$ for the $2^+_1$ excitations in these nuclei. Thepresent results for $^{41,43}$P$(p,p')$ are used to compare two shell modelinteractions, SDPF-U and SDPF-MU. As in a recent study of $^{42}$Si, thepresent results on $^{41,43}$P favor the SDPF-MU interaction.

Inverse-kinematics proton scattering from $^{42,44}$S, $^{41,43}$P and the collapse of the $N=28$ major shell closure