Charge dependent effects of the photon-pion exchange process in the n-n interaction

Considerable effort has been made to explain the observed charge dependence of the low-energy parameters of the 1S nucleon-nucleon scattering, as due to various electromagnetic corrections. Noyes has pointed out that the difference between the p-p effective ranges, rpp–rpn ≈ 0.4 fm, indicated by the experiment of Engelke et al., would imply that the p-p potential is more than 30% more attractive than the p-n potential in the region between 2 and 4 fm and correspondingly less attractive by the same amount at shorter distances. None of the electromagnetic effects so far considered can produce such a long-ranged correction with that strength. However, there is one process which has not been examined and seemed to us to be the only candidate that might result in anything like Noyes' phenomenological correction. This is the photon-pion exchange process, which gives rise to a charge-dependent potential of one-pion range. This photon-pion exchange potential (γπEP) is evaluated by means of essentially the same technique as that for the two-pion-exchange potential. It turns out that the charge-dependent part of the γπEP cannot produce the strong charge-dependent correction at large distances required by Noyes' phenomenological analysis. Including the γπEP, a semi-phenomenological analysis of the charge dependence of the scattering parameters is done. It is emphasized that it is futile to attempt to explain the charge-dependent splitting of the scattering length because it is too sensitive to the potential at short distances. Rather, we phenomenologically fix the short-range part of the potential so that the observed splitting of the scattering length is fitted, and then we examine the splitting of the effective range. For the various long-range charge-dependent effects considered, the splitting is found to be ifrpp – rpn ≈ 0.1 fm.