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 $\Delta$ 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 ${}^{12}\mathrm{C},$ ${}^{40}\mathrm{Ca}$ $(\overrightarrow{p},\overrightarrow{n})$ 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 ${(e,e}^{\prime })$ scattering. The Landau-Migdal parameter $g_{N\Delta }^{\prime }$ for the $N\Delta$ transition interaction and the effective nucleon mass at the nuclear center $m_N^{*}\mathrm{}(r=0\mathrm{})\mathrm{}$ are treated as adjustable parameters. The present analysis indicates that the smaller $g_{N\Delta }^{\prime }(\approx 0.3)$ and $m_N^{*}\mathrm{}\left(0\right)\mathrm{}\approx 0.7$ $m_N$ 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.

• Received 27 July 2000

DOI:https://doi.org/10.1103/PhysRevC.63.044609