Pion Exchange Currents in Deuteron Photodisintegration. Dispersion Theory

A dispersion-theoretic treatment of the amplitudes describing photomagnetic disintegration of the deuteron at energies very near threshold has been developed. The effects of meson exchange currents in the photodisintegration or equivalent $n-p$ capture process are calculated. At threshold the photomagnetic transition is dominant. This transition is essentially the isovector ${}_{}{}^3{}_{}{}^{}S_0^{}{}_{}{}^{}\to {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ transition. A fixed-angle dispersion relation for the dipole amplitude describing this transition can be written in terms of the related covariant amplitudes. Solutions to the dispersion relation are found using several different approximations. First, one may neglect all high-order effects which serve to define the unphysical cut, and consider only the contribution from the Born poles. Next, one may condense all the higher-order effects into a single interaction pole. The single experimental cross section value for thermal neutrons may be used to relate the position and residue of this pole in a single functional relationship by recalculating the solution to the dispersion relation with this pole included. Finally one may treat the contribution of the pion exchange currents using the Mandelstam representation, and recalculate the dispersion relations once again. This latter treatment is based upon the approximation that only the anomalous tip of the spectral function is effective in providing modifications in the physical region close to threshold. It is shown that the pion exchange terms are the dominant contributors to the spectral function in the anomalous region. The solution obtained in this approximation yields a cross section which is in agreement with the experimental value.