Two-Nucleon Potential from the Cut-Off Yukawa Theory

Abstract

Using the Yukawa theory with cutoff, the two-nucleon interaction is calculated up to fourth order in the coupling constant. The resulting potential at large distances (≳${10}^{-13\mathrm{}}$ cm) is similar to the well-known potential with no cutoff. At small distances, however, the tensor potential approaches zero, and the central potential is strongly repulsive. The details are essentially determined by two parameters, the coupling constant and curoff. The Schrödinger equation for the two-nucleon problem at low energies is solved numerically, and values are obtained for the binding energy, the quadrupole moment, and the four $n-p$ scattering parameters. It is found that the triplet experimental values are reproduced quite well, and the singlet parameters reasonably well by the same coupling constant and cutoff required to explain pion-nucleon scattering and photoproduction.