Field-Theoretical Calculation of the One-Pion-Exchange and Two-Pion-Exchange Contributions to the Phase-Shifts with Higher Angular Momenta for Nucleon-Nucleon Scattering
The one-pion-exchange and two-pion-exchange parts of the S matrix for nucleon-nucleon scattering are calculated field-theoretically. The rescattering of virtual pions by nucleons and the pion-pion interaction between virtual pions are taken into account. The S matrix is then decomposed into the partial-wave amplitudes, and the phase shifts are calculated. Numerical evaluations are carried out for the 310-MeV proton-proton scattering, and the results are compared with the phase shifts obtained by analyzing the experimental data. It is found that, without contribution of the pion-pion interaction, the results are far from agreement with experiment because of too strong attraction arising from the contributions of the two-pion-exchange part, but the contribution of the pion-pion resonance in the I=J=1 state improves the results considerably by largely cancelling the attraction. It is, however, also found that definite discrepancies still remain between the theory and the experiments, and this suggests that some unknown effects must play important roles in determining the nuclear force in the region of the internucleon distance around the Compton wavelength of the pion.