Nuclear density dependence of polarization transfer in quasi-elastic A(e,e′) reactions

The ratio of the transverse and longitudinal components of polarization transfer to protons in the quasielastic (e - ,e′p - ) reaction, Px′/Pz′, is sensitive to the proton's electromagnetic form factor ratio, GE/GM. To explore density-dependent in-medium modifications, a comparison of polarization transfer ratios involving protons from distinct nuclear shells, each with different local nuclear densities, has been proposed. In this study, we present such comparisons between four shells, 1s1/2,1p3/2 in C12 and 1d3/2,2s1/2 in Ca40. In an effort to account for other many-body effects that may differ between shells, we use a state-of-the-art relativistic distorted-wave impulse-approximation (RDWIA) calculation and present the double ratios (Px′/Pz′)Data/(Px′/Pz′)RDWIA as well as the super-ratios [(Px′/Pz′)A/(Px′/Pz′)B]Data/[(Px′/Pz′)A/(Px′/Pz′)B]RDWIA, for chosen shells A and B, as a function of effective local nuclear densities. We find that double ratios for individual shells show a dependence on the probed effective nuclear densities. Studying the super-ratios, we observed a systematic variation between pairs of higher- and lower-density shells.