Quasi-Elastic Proton-Proton Scattering at 158 Mev

The cross section in impulse approximation for a quasi-elastic proton-proton scattering reaction with a bound target proton depends on the probability of finding inside the nucleus a proton with a momentum equal to the momentum transfer required by kinematics. This momentum transfer is determined if the incident energy and the energies and angles of the two outgoing partners of a proton pair are measured. Events involving $s$ and $p$ protons can be experimentally distinguished by noting that more energy is required to remove an $s$ proton from the nucleus than a $p$ proton. Thus the momentum eigenfunctions of each state can be explored experimentally by varying the momentum transfer, keeping constant the energy sum of a proton pair. Two methods of doing this to bring out the difference between scattering from $s$ and $p$ protons are discussed. They are (1) examination of the distribution of events as a function of the energy sharing between the two out-going protons, at fixed scattering angles, and (2) examination of the angular distribution of events having fixed sharing. Born approximation calculations are presented for predicting the regions of maximum sensitivity to differences between $s$ and $p$ protons. These predictions are used in the design of two experiments on the reaction ${\mathrm{C}}^{12}(p, 2p){\mathrm{B}}^{11}$ whose results are reported. They show good qualitative agreement with the predictions for $p$ protons, namely that the sharing will tend to be unequal if the scattering angle of each proton is near 45° [type (1) experiment] and that the angular distribution of events of equal sharing will have a minimum at 45° [type (2) experiment]. The predicted behavior (opposite to that for $p$ protons) for events involving $s$ protons is not observed, and this fact is discussed in the light of possible inadequacies of the theory or of the experiment.