The Deuteron-Pickup Reaction in an Optical-Model Approximation

in which the nuclear interactions of the incoming and outgoing particles are considered. Two different formal expressions that give the transition amplitude are derived, and the wave functions in this amplitude are approximated by an optical-model procedure in which it is assumed that the initial- and final- state particles scatter elastically in the nucleus. The inelasticscattering effects are shown to be small. Several closed forms for these optical-model wave functions are derived on the hsis of a WKB approximation for a complex square- well scattering potential. The use of these wave functions, along with an approximation that gives the form of the transition amplitude in terms of Gaussian functions, allows a closed-form solution for the differential cross section. lt is found tht the elastic scattering processes are not negligible, since they affect considerably the magnitude and the shape of the differential cross section. By comparing the theory with recent pickup experiments on C/sup 12/ at 95 and 145 Mev, one obtains a nuclear-momentum distribution that, unlike the Born approximation analysis, is in good agreement with the results of other determinations of momentum distributions. It is found tht a neutron number of from 4 to 7 neutrons and a momentum distribution of exp(-- E/20) are required to fit the data. The polarization effects in the pickup process are investigated by using spin-orbit potentials in addition to the central potentials to describe the initial- and finnl-state scatterings. Simple forms for the spin orbit, elastic scattcring wave functions are developed, so tht the transition matrix can be obtained without difficulty in closed form. The usual polarization formalism is applied to obtain the asymmetry of deuterons produced by initially polarized protons, and the results compare favorably with recent experimental data. (auth