Spin-isospin response functions and the effects of the Δ-hole configurations in finite nuclei

Abstract

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