TwoNucleon Potential from Pion Field Theory with Pseudoscalar Coupling
Abstract
The twonucleon potential is derived from psps pion field theory, using the TammDancoff method with the subsequent appropriate renormalization of the twonucleon amplitude, up to orders g^{2}(pκ)^{2} and g^{4}(pκ), g^{2} being the equivalent pspv coupling constant and p, κ the nucleon (relative) momentum and rest mass, respectively. Neglected are the mass and charge renormalizations and the pionpion scattering term. It is shown that the only quadratic term is V_{2}(r)(p^{2}2κ^{2})+H.c., where V_{2}(r) is the second order static potential. All remaining terms of order g^{2}(pκ)^{2} are converted by a canonical transformation to terms of order g^{4}(pκ) or a linear combination of a static and an L.S potential. In the case of psps coupling, in particular, no velocitydependent potential besides the quadratic one mentioned above follows from diagrams of one and twopion exchange without nucleon pairs; thus the nucleonpair diagrams are the only source of an L.S potential, if there is any, up to the orders considered. The nucleonpair diagrams are also estimated assuming the effective pionpair interaction Hamiltonian, the static limit of which agrees with the Swave static model of Drell et al. The L.S potential thus obtained has the right sign in the odd state and changes its sign in the even state, while its magnitude seems in both states somewhat too small. As for the static part of our potential, the new correction [g^{4}(μκ)] cancels out the conventional fourthorder term [g^{4}] appreciably; the entire static potential becomes quite close to the secondorder static potential down to distances of the order of the pion Compton wavelength, except for the central force in the triplet even state. The details are shown on graphs. The pspv coupling case is treated separately in the following paper.
 Publication:

Physical Review
 Pub Date:
 January 1960
 DOI:
 10.1103/PhysRev.117.605
 Bibcode:
 1960PhRv..117..605S