The non-adiabatic method with a neutral pseudo-scalar meson field

Abstract

Dancoff's non-adiabatic procedure for the two-nucleon system interacting with a meson field is applied to the neutral pseudoscalar meson field, taking into account both types of couplings, the pseudoscalar and the pseudo-vector. The procedure is limited to the 2nd order of the coupling constants. Using the Hamiltonian containing the directinteraction term, the Schrodinger equation of motion contains interaction potentials, one of which introduces into the equation a high singularity. The reason is that the term arising from the direct-interaction Hamiltonian does not cancel completely with the so-called contact-term, which arises from the nucleon-meson interaction Hamiltonian, as it is the case in the adiabatic procedure. If the direct-interaction Hamiltonian is neglected from the beginning, the Schrodinger equation contains a singular potential, which corresponds to the contact-term of the adiabatic approximation. This potential behaves, however, as the corresponding potential in the previous case, and not as a δ-function, as is the case in the diabatic procedure. The remaining interaction potentials, which are the same in the two cases, are less singular than the potentials in the adiabatic procedure. In the non-relativistic limit, the interaction functions lead to the same functions given by the conventional perturbation procedure.