We calculate the two-step contribution to (p, p ) and (p, n) reactions at intermediate energy. We describe the motion of the incident nucleon with a plane wave and compare the contribution from two-step processes with that from one-step processes. To describe the two-step processes, we extend the response functions to nondiagonal forms with respect to the momentum transfer q.We performed a numerical calculation for the cross sections of the 12 C, 40 Ca(p, p ) scattering and the spin longitudinal and spin transverse cross sections of the 12 C, 40 Ca(p, n) reactions at 346 MeV and 494 MeV. We found that the two-step contribution is appreciable in comparison with the one-step processes in the higher-energy transfer region for the spin longitudinal and the spin transverse (p, n) reactions. We also found that the two-step processes give larger contributions to the spin transverse (p, n) reaction than to the spin longitudinal reaction. This finding is very encouraging to interpret the discrepancy between the DWIA calculation and the experimental results of the spin longitudinal and the spin transverse cross sections. §1. IntroductionIn nucleon induced high energy reactions, single-step processes have often been considered as the main contribution to the cross sections. When the excitation energy is low, it is probable that the projectile nucleon collides with the nucleons in the target only once, but as the excitation energy becomes higher, the pre-equilibrium processes, in which the projectile collides with the nucleons several times, are considered to become more effective.Actually, it has been reported that the single-step process calculation underestimates the scattering cross sections, especially in the large scattering angle region, 1), 2) where the two-step and further multi-step scattering are found to have a large effect.The multi-step direct reaction (MSDR) was actively studied at the end of the 1970s. Feshbach, Kerman, and Koonin (FKK) 3), 4) developed the framework of multi-step reaction theory. Tamura, Udagawa, and Lenske (TUL), 1) who pointed out a problem in FKK theory, replaced the sum over the excited nuclear eigenstates with that over 1-particle-1-hole (1p-1h) states, introducing a weight function. Another type of formalism was presented by Smith and Wambach, 5) who applied the Glauber approximation to the motion of the projectile and analyzed the for- * )

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The two-step contribution to the spin-longitudinal and the spin-transverse cross sections of 12 C, 40 Ca(p,n) reactions at 494 MeV and 346 MeV is calculated. We use a plane-wave approximation and evaluate the relative contributions from the one-step and the two-step processes. We found that the ratios of the two-step to the one-step processes are larger in the spin-transverse cross sections than in the spin-longitudinal ones. Combining these results with the distorted-wave impulse approximation (DWIA) results we obtained considerable two-step contributions to the spin-longitudinal and the spin-transverse cross sections. The two-step processes are important in accounting for the underestimation of the DWIA results for the spin-longitudinal and the spintransverse cross sections.

A complete set of polarization transfer coefficients has been measured for the quasielastic 12 C(p, n) reaction at a bombarding energy of 345 MeV and laboratory scattering angles of 16 • , 22 • , and 27 •. The spin-longitudinal ID q and spin-transverse ID p polarized cross sections are deduced. The theoretically expected enhancement in the spin-longitudinal mode is observed. The observed ID q is consistent with the pionic enhanced ID q evaluated in a distorted wave impulse approximation (DWIA) calculation employing a random phase approximation (RPA) response function. On the contrary, the theoretically predicted quenching in the spin-transverse mode is not observed. The observed ID p is not quenched, but rather enhanced in comparison with the DWIA+RPA calculation. Two-step contributions are responsible in part for the enhancement of ID p .

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