  We present a formalism of distorted wave impulse approximation (DWIA) 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 (RPA), 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 non-locality 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, ID_q and ID_p, of 12C, 40Ca (\vec{p},\vec{n}) at 494 and 346 MeV. The
calculation reasonably reproduced the observed ID_q, which is consistent with
the predicted enhancement of the spin-longitudinal response function R_L.
However, the observed ID_p is much larger than the calculated one, which was
consistent with neither the predicted quenching nor the spin-transverse
response function R_T obtained by the (e,e') scattering. The Landau-Migdal
parameter g'_N\Delta for the N\Delta transition interaction and the effective
mass at the nuclear center m^*(r=0) are treated as adjustable parameters. The
present analysis indicates that the smaller g'_{N\Delta}(\approx 0.3) and
m^*(0) \approx 0.7 m are preferable. We also investigate the validity of the
plane wave impulse approximation (PWIA) with the effective nucleon number
approximation for the absorption, by means of which R_L and R_T have
conventionally been extracted.
