Distorted wave impulse approximation analysis for spin observables in nucleon quasielastic scattering and enhancement of the spin longitudinal response

Abstract

We present a formalism of distorted wave impulse approximation for analyzing spin observables in nucleon inelastic and charge-exchange reactions leading to the continuum. It utilizes response functions calculated by the continuum random-phase approximation, which include the effective mass, the spreading widths, and the $\ensuremath{\Delta}$ degrees of freedom. The Fermi motion is treated by the optimal factorization, and the nonlocality of the nucleon-nucleon t matrix by an averaged reaction plane approximation. By using the formalism we calculated the spin-longitudinal and the spin-transverse cross sections, ${\mathrm{ID}}_{q}$ and ${\mathrm{ID}}_{p},$ of ${}^{12}\mathrm{C},$ ${}^{40}\mathrm{Ca}$ $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})$ at 494 and 346 MeV. The calculation reasonably reproduced the observed ${\mathrm{ID}}_{q},$ which is consistent with the predicted enhancement of the spin-longitudinal response function ${R}_{\mathrm{L}}.$ However, the observed ${\mathrm{ID}}_{p}$ is much larger than the calculated one, which was consistent with neither the predicted quenching nor the spin-transverse response function ${R}_{\mathrm{T}}$ obtained by the ${(e,e}^{\ensuremath{'}})$ scattering. The Landau-Migdal parameter ${g}_{N\ensuremath{\Delta}}^{\ensuremath{'}}$ for the $N\ensuremath{\Delta}$ transition interaction and the effective nucleon mass at the nuclear center ${m}_{N}^{*}(r=0)$ are treated as adjustable parameters. The present analysis indicates that the smaller ${g}_{N\ensuremath{\Delta}}^{\ensuremath{'}}(\ensuremath{\approx}0.3)$ and ${m}_{N}^{*}(0)\ensuremath{\approx}0.7$ ${m}_{N}$ are preferable. We also investigate the validity of the plane-wave impulse approximation with the effective nucleon number approximation for the absorption, by means of which ${R}_{\mathrm{L}}$ and ${R}_{\mathrm{T}}$ have conventionally been extracted.