Title: The field-theoretical definition of nuclear potential — II
Abstract: The results of Part I are extended to include the exchange forces introduced by charged pions. It is shown that the scattering amplitude for a proton and neutron between which acts a potential with an exchange part, is related by symmetrization to that for the scattering of non-identical particles through an isotopic spin dependent potential. This enables the amplitude to be split into two parts, each of which obeys a Khuri-type dispersion relation if the appropriate momentum transfer is kept fixed. The method allows also the generalization of the Mandelstam represntation to the case where exchange forces are present. A similar separation of the field-theoretic amplitude is possible into parts which satisfy one-dimensional dispersion relations without the pion singularities for negative energies. A comparison of the dispersion relations and the unitarity condition for the field theoretic amplitudes with those of the potential theory lead to a definition of the potential (which is partly direct, partly exchange) which is capable of simulating the field-theoretic amplitude for energies sufficiently below meson production threshold.