Effects of the delta-isobar $(\Delta)$ mixing on the spin-isospin response functions in finite nuclei are studied in the quasi-elastic region. A method to calculate the response function for a finite system composed of nucleon $(N)$ and $\Delta$ is formulated in a ring approximation. It is designed to treat the $\Delta$-related Landau-Migdal parameters, $g'_{ N\Delta}$ and $g'_{ \Delta\Delta}$, and the nucleon parameter $g'_{ NN}$, independently, so that the universality ansatz, $g'_{ NN}=g'_{ N\Delta}=g'_{ \Delta\Delta}$, is removed. We calculated the isovector spin-longitudinal and -transverse response functions, $R_{ L}$ and $R_{ T}$, with and without the $\Delta$-mixing. Inclusion of $\Delta$ enhances $R_{ L}$ but reduces $R_{ T}$ for ordinary interactions. Dependence of $R_{ L,T}$ on $g'_{ NN}$ and $g'_{ N\Delta}$ is investigated. Decomposition into the process-decomposed response functions, $R^{ [NN]}$, $R^{ [N\Delta]}$ and $R^{ [\Delta\Delta]}$, is very elucidative to see the $\Delta$ effects, which are found to be mainly governed by $R^{ [N\Delta]}$ and sensitive to $g'_{ N\Delta}$. The isovector spin-transverse response function $R^{ (e,e')}_{ T}$ obtained by $(e,e')$ is calculated by various effective interactions and compared to each other as well as experimental data.
Categories: nucl-th