Relativistic treatment of the few body system

Abstract

Some specific examples of effects of mesonic degrees of freedom and special relativity in the two- and three-nucleon system are reviewed. For the twonucleon system a relativistic covariant formulation of the one boson exchange and isobar model is described based on the Bethe-Salpeter equation. Its extension to dynamical equations satisfying three-particle unitarity above one pion production threshold is presented. Moreover, the meson theoretical basis of the Dirac approach for elastic proton-nucleus scattering is discussed using the above mentioned relativistic one boson exchange model. In the past two decades strong evidence has been presented that a nonrelativistic description of the few nucleon system in terms of pair-wise interaction is not in accordance with the various experimental results. Well known examples are radiative neutron capture and the electro disintegration of the deuteron'. We review briefly two other cases in view of some recent interesting experimental and theoretical work. NN interactions which are believed to describe the nuclear force in an accurate way at least up to the one pion production threshold, leads to the underbinding of the triton typically by l-11 MeV whereas the secondary maximum in the elastic charge form factor of 3 He is much too low in the theoretical predictions. In table I some recent results are summarized for the case of the Paris and Reid-soft-core (RSC) potentials. The 5-channel calculations contain only the 'so, 3s1-3 D1 two-nucleon partial waves potentials while the complete 18-channel analysis has all the components up to angular momentum a=2 included. The results of the triton binding calculations of refs. 2 and 3 agree very well for the RSC potential. A puzzling point however is that in the Paris case they differ by 0.2 MeV which is greater than the suggested numerical inaccuracy. Possible explanations for the failure of the nonrelativistic description are the presence of the non-nucleonic degrees of freedom such as mesons and quarks and effects of special relativity. Attempts to explain the differences by the presence of mesonic degrees of freedom have been rather successful. They give rise to effective three-nucleon (3N) forces and so-called mesonic exchange