Analysis of nucleon-nucleus scattering

Abstract

The small angle scattering amplitudes of 140 MeV nucleons elastically scattered from He, Be, C, and Al have been determined by making a least squares fit to some of the available proton and neutron cross section and polarization data. The nuclear amplitudes were parameterized as in the earlier work of Cromer and (in the case of p-nucleus scattering) were combined with the Coulomb amplitudes following the work of Bethe. The analysis was restricted to the angular region from 3° to 11° and resulted in the determination of the real and imaginary parts of the spin-independent and spin-dependent amplitudes at zero degrees. All the p-nucleus data at angles <6° were corrected for multiple Coulomb scattering, following the work of Cormack. These corrections were very large (e.g., the correction was 35% for carbon at 4° lab.) and were found to be necessary in order to obtain simultaneous fits to the proton and neutron data. The high energy scattering approximation was then used to determine the central and spin-orbit optical parameters from these amplitudes. In impulse approximation these optical parameters are related directly to the nucleon-nucleon scattering amplitudes (The subscripts 1 and 0 refer to the isotopic spin states of the two-nucleon system.) In this way a and c have been determined from the scattering amplitudes for each nucleus. The results are found to be approximately independent of the particular nucleus, as they should be. Good agreement is found value. None of the basic conclusions of the paper is affected by this change in the polarization.