Shell-model interaction energies in a relativistic hamiltonian formulation (I)

Abstract

The non-covariant hamiltonian formulation of relativistic field theory is presented and solved as a secular problem in a discrete representation space. The shell-model two-nucleon interaction in the one-boson exchange picture is used to test the method before applying it to many-body systems. The results of the diagonalization treatment are convergent as a function of the discretized meson space and are close to the usual OBEP when considering the exchange of a single type of meson, thus establishing the numerical feasibility of the method. However a significant deviation between the two approaches appears for the sigma meson or for a mixture of several types of mesons with values of the coupling constants in the “physical” domain. Also, in the limited momentum space of the nucleons in the lowest shell-model state, the cut-off in the nucleon vertex form factors plays an unimportant role.