Construction of the Adiabatic Nuclear Potential: Formalism

Abstract

A new formalism is presented for the construction of the two-nucleon potential, whose salient characteristic is that it involves an expansion only in the number of mesons exchanged, the self-mesonic field of each nucleon being treated, in principle, exactly. Access to the potential is achieved through the intermediary of the scattering matrix. With the assumption that nonlinear meson propagation may be neglected, alternative versions of this matrix are derived, only one of which is exploited in this paper. The connection between the scattering matrix and the potential is discussed, and it is emphasized again that the transition between the two requires a knowledge of non-energy-conserving matrix elements of the potential, which can be obtained only if the underlying Schr\odinger equation is known. The potential involving the exchange of at most two $P$-wave mesons is computed and shown to depend on the renormalized coupling constant, the single-nucleon source function, and the total cross sections for pion-nucleon interaction. The numerical evaluation of these formulas is not here attempted.