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Abstract

Differential cross sections and analyzing powers have been measured for the excitation by 318 MeV protons of states of $^{40}\mathrm{Ca}$ below 7.2 MeV. The data for those normal-parity excitations for which transition densities are available from electroexcitation measurements are analyzed in terms of medium modifications to the nucleon-nucleon interaction. We find that the empirical effective interaction previously fitted to $^{16}\mathrm{O}$(p,p') data at the same energy predicts $^{40}\mathrm{Ca}$(p,p') very well. Density-dependent modifications of the effective interaction fitted to data for $^{40}\mathrm{Ca}$ or $^{16}\mathrm{O}$, either independently or simultaneously, are virtually identical. The density dependence of the empirical interaction is considerably stronger than that of interactions based upon nonrelativistic nuclear matter theory and persists to lower density. The most significant differences are that the empirical interaction has a stronger repulsive core and that absorption is enhanced at high density, contrary to expectations based upon Pauli blocking. We also find substantial suppression of the spin-orbit interaction at low density and enhancement at high density. Nevertheless, the independence of the effective interaction from the target supports the concept of local nuclear matter density. We also find that optical potentials based upon the empirical effective interaction are very similar to Schr\"odinger-equivalent potentials based upon a relativistic impulse approximation model, suggesting that the empirical density dependence is similar to the equivalent density dependence that arises from elimination of lower components from Dirac wave functions. Finally, the results are compared with global optical potentials from Dirac phenomenology.

Effective interaction forCa40(p,p’) atEp=318 MeV

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