BOSONIZATION IN THE PRESENCE OF CONFINEMENT - CALCULATION OF THE NUCLEON-NUCLEON INTERACTION

We describe an extended version of the Nambu-Jona-Lasinio (NJL) model that includes a description of confinement. It is necessary to incorpo rate some description of confinement in order to discuss the propertie s of the sigma, rho, and omega mesons in the NJL model. These mesons, in addition to the pion, are the minimum needed to describe the salien t features of the nucleon-nucleon interaction. In previous work we con sidered the relation between the bosonized NJL model and the one-boson -exchange (OBE) model of the nucleon-nucleon force. Most of our attent ion was given to pion and sigma exchange. We provide a review of that work and extend our discussion to a consideration of rho and omega exc hange. We also present a more detailed discussion of the bosonization procedure. Our results depend upon the strength of the confining inter action. Once that is fixed, we obtain good values for the omega-nucleo n coupling constant, G(omega NN), and for the tensor coupling constant f(r)ho, in the rho-nucleon interaction. (One limitation of the presen t version of the model is that the ratio f(rho)/g(rho)=3.70, instead o f the empirical value of f(rho)/g(rho)similar or equal to 6.1.) If we consider nucleon-nucleon scattering for relatively small momentum tran sfer, we obtain good results for the processes of sigma, pion, rho, an d omega exchange. Remarkably, the description of pion exchange is very accurate up to q(2) similar to-2 GeV2. That is, the microscopic model reproduces the pion-exchange amplitude of the boson-exchange model ov er a broad range of momentum transfer when we specify a single paramet er than governs the momentum-transfer dependence of the pseudoscalar-i sovector form factor of the nucleon. In the other channels (sigma,rho, omega), the nucleon form factors may be treated in the same manner. Ho wever, if we calculate the form factors in our model, we find that the y are too ''soft'' to fit the OBE amplitudes away from q(2) similar or equal to 0. Further work is needed to obtain good fits for the variou s amplitudes for large momentum transfer, although the OBE amplitudes are well reproduced in the case of scattering at small momentum transf er (\q(2)\less than or equal to 0.1 GeV2).