Static Meson Potentials and the Deuteron Problem

Abstract

THE static potential of interaction between two nucleons predicted by meson theory¹ has the general form ϕ(r) is here the Yukawa central potential; D the dipole axial operator; J and F two constants depending on the source parameters. The r⁻³ singularity of this potential must be removed by some arbitrary cut-off procedure. We have investigated the ground-state solution of the deuteron equations for such a potential, using the ‘zero cut-off’ introduced by Bethe², for the two values 225 m and 284 m of the meson mass, and a number of numerical values of the constants J and F. In each case the value 2.24 MeV. of the binding energy of the deuteron was assumed, and the amount P of D-state, the quadrupole moment Q and the cut-off radius r_c were determined.