On the Theory of a Mixed Pseudoscalar and a Vector Meson Field

Abstract

Schwinger's modification of the M\o{}ller-Rosenfeld theory of nuclear forces based on a mixture of pseudoscalar and vector meson field is investigated in the strong coupling theory. The isobar separation turns out to be $\frac{1}{3}$ of its value in the pseudoscalar theory. The interaction energy between two nucleons is calculated, and in the most interesting case of the symmetrical theory, it is the same as the corresponding expression in the weak coupling theory with the spin and isotopic spin vectors replaced by the ${\mathrm{e}}^{\ensuremath{\alpha}}$ vectors of Pauli and Dancoff. A classification of the states of the two-nucleon system is made, and the lowest state for the deuteron is found to be the triplet state. An estimate is made for the values of the constants involved, and we find that a suitable choice of the coupling constant and the masses of the mesons can be made in such a way that the binding energy and the quadrupole moment of the deuteron agree with the observed values, and such that the conditions for small source (compared to the Compton wavelengths of the mesons) and for small effect of the higher spin states on the ground state are fulfilled. However the theory gives for the magnetic moment of the deuteron a value only a few percent of the observed value, and according to this theory highly charged nuclei would be unstable. We therefore conclude that the strong coupling theory, based on the assumption of an extended source, should be abandoned in favor of a weak coupling theory, based on a point source with the singularities of its field eliminated by means of a subtraction formalism.