We present a unified study of the role of the $\rho$-exchange interaction in spin-isospin strength distribution effects in a finite nuclear system. We study both the longitudinal ($\overrightarrow{\sigma }·\hat{q}{\tau }_{\lambda }$, where $\overrightarrow{\mathrm{q}}$ is the momentum transfer to the nucleus) and the transverse ($\overrightarrow{\sigma }\times \hat{q}{\tau }_{\lambda }$) spin channels for a large range of momentum transfer ($q\sim 0-600$ MeV/c). We examine a number of effective $\rho$-coupling schemes used in the literature. Using the finite-nucleus formalism of Toki and Weise, we examine in detail the response function in the presence of the $\rho$-meson exchange term. The renormalization of matrix elements of spin-isospin sensitive probes is given for the $J^P=1^{+}$, $T=1\mathrm{}$ level of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. We analyze the results, gaining some insight into the nature of the longitudinal versus transverse channels and into approximations suggested in the past for handling finite-nucleus calculations. A comparison with local density approximation and infinite nuclear matter with a constant density results is presented for a variety of cases.

• Received 9 April 1984

DOI:https://doi.org/10.1103/PhysRevC.30.1573