FieldTheoretical NucleonNucleon Potential
Abstract
A formulation is presented for the derivation of a Schrödingerequation potential from a fieldtheoretical model. The relativistic twobody equation of Bethe and Salpeter is reduced using a generalization of the BlankenbeclerSugar method. The resulting equation is shown to be identical with the nonrelativistic LippmannSchwinger equation upon a unitaritypreserving identification of the amplitudes. An equivalent potential is thereby defined and expressed as a solution of an integral equation. The second and fourthorder potentials are calculated, and their energy dependence and nonlocality are studied. An approximation scheme is developed for expanding the configurationspace potentials in the powers of the momentum operator. Terms up to and including the first power are retained, giving rise to a potential composed of central, spinorbit, tensor, and spinspin parts. The contributions of the meson resonances η, ρ, and ω are included to second order. The complete potential is numerically calculated using masses and coupling parameters taken from meson experiments; no parameter of the potential is searched upon. The resulting potential is remarkably similar to that of Hamada and Johnston (outside half a pion Compton wavelength), particularly for the parts that are relatively well determined by nucleonnucleon scattering data. Further extensions of the program, including the treatment of the nucleon resonances and pair suppression, are discussed, and an outline of such extensions is given.
 Publication:

Physical Review D
 Pub Date:
 November 1970
 DOI:
 10.1103/PhysRevD.2.1999
 Bibcode:
 1970PhRvD...2.1999P