Effect of the Knockout-Exchange Mechanism in Nucleon-Nucleus Scattering

We have studied the contribution of the knockout-exchange mechanism to inelastic proton scattering the distorted-wave Born approximation (DWBA) as a function of two-body force range, orbital-angular-momentum transfer, incident-particle energy, and bound-particle energy and configuration. Several important features are revealed: (1) The exchange mechanism is found to be important for reasonable ranges (≈ 1 F) and for energies as high as 150 MeV; (2) the exchange-to-direct ratio is quite sensitive to the orbital-angular-momentum transfer $L$, and the exchange amplitude can exceed the direct for large $L$; (3) non-normal transfers [${\mathrm{}(-1\mathrm{})\mathrm{}}^L\ne {\mathrm{}(-1\mathrm{})\mathrm{}}^{\Delta \pi }$] are usually negligible but may become significant for high $L$, especially if no spin flip is involved; (4) both the magnitude and phase of the exchange amplitude relative to the direct are sensitive to the initial and final single-particle configurations, particularly to the radial quantum numbers; (5) in collective excitations constructive interference occurs among exchange amplitudes to a sufficient extent that the inclusion of exchange can double the cross section for $2^{+}$ states. Expressions for direct and exchange amplitudes are obtained in the zero-range limit of the PWBA which qualitatively explain the behavior observed in the numerical results. A new method is presented for estimating collective enhancement due to core polarization by using empirical $B\left(E2\mathrm{}\right)\mathrm{}$ values. Calculation of the absolute cross section for the $2^{+}$ excitation in ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}(p, p^{\prime })$, including exchange and core polarization, yields a two-body effective interaction strength which agrees both with strengths derived from charge-exchange reactions and with those obtained from a semirealistic two-nucleon interaction.