Spin-Isospin Response Functions and the Effects of the $\Delta$-Hole Configurations in Finite Nuclei

Abstract

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, $g_{N\Delta }^{\prime }$ and $g_{\Delta \Delta }^{\prime }$, and the nucleon parameter $g_{NN}^{\prime }$, independently, so that the universality ansatz, $g_{NN}^{\prime }=g_{N\Delta }^{\prime }=g_{\Delta \Delta }^{\prime }$, 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 $g_{NN}^{\prime }$ and $g_{N\Delta }^{\prime }$ 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 $g_{N\Delta }^{\prime }$. The isovector spin-transverse response function $R_T^{(e,e^{\prime })}$ obtained by $(e,e^{\prime })$ is calculated by various effective interactions and compared to each other as well as experimental data.

Comments: 26 pages (LaTeX + RevTeX), 15 figures available via Fax upon request