Proton-Proton Effective-Range Theory with Vacuum Polarization

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The effect of vacuum polarization upon $p\ensuremath{-}p$ scattering is considered by first solving the problem in the Coulomb plus vacuum polarization potentials (called "electric" potential) without the nuclear potential. The nuclear phase shifts are then defined with respect to the electric wave functions, and the scattering cross section is written in terms of these phase shifts. The connection with other nuclear phase shifts (in the presence of vacuum polarization) which appear in the literature is established.The effective-range expansion for the nuclear $s$-wave phase shift is derived. An analysis of three low-energy $p\ensuremath{-}p$ scattering experiments indicates that the omission of vacuum polarization from the analysis results in a value for the shape-dependent parameter which is 0.02 smaller than the value obtained when vacuum polarization is included in the analysis. A discussion of the accuracy required to usefully delimit this parameter is included.