Vacuum Polarization Effects in Proton-Proton Scattering

The problem of vacuum polarization scattering of protons by protons is treated to first order in the vacuum polarization interaction. The phase shifts caused by the interaction are calculated, and the corresponding addition to the $p-p$ scattering matrix is constructed. The phase shifts are calculated using Coulomb wave functions as the unperturbed wave functions. The corresponding addition to the $p-p$ scattering matrix is then constructed, including exactly the Coulomb phase shift factors $\exp \left[2i\right({\sigma }_L-{\sigma }_0\left)\right]$ appearing in the series representation of the scattering amplitudes. Other electromagnetic and relativistic modifications of the Coulomb scattering amplitudes are also examined in the limit of low energies. Numerical results are given for the vacuum polarization contributions to the $p-p$ scattering cross section over the energy range 1.4-4.2 Mev. It is found that vacuum polarization scattering may easily be confused with nuclear $P$-wave scattering.