Applications of the Covariant Spectator Theory

Abstract

In this talk I provide a short overview of applications of the so-called Covariant Spectator Theory to two-and three-nucleon systems. It is a quasi-potential formalism based on relativistic quantum field theory, and can be derived from a reorganization of the complete Bethe-Salpeter series. In this framework, we constructed two one-boson-exchange models, called WJC-1 and WJC-2, for the neutron-proton interaction that fit the 2007 world data base, containing several thousands of neutron-proton scattering data below 350 MeV, with a χ 2 /N data close to 1. The close fit to the observables implies that the phase shifts derived from these models can be interpreted as new phase-shift analyses, which can be used also in nonrelativistic frameworks. Both models have a considerably smaller number of adjustable parameters than are present in realistic nonrelativistic potentials, which shows that the inclusion of relativity actually helps to achieve a realistic description of the interaction between nucleons. This became also evident in calculations of the three-nucleon bound state, where the correct binding energy is obtained without additional irreducible three-body forces which are needed in nonrelativistic calculations. In addition, calculations of the electromagnetic form factors of helium-3 and of the triton in complete impulse approximation also give very reasonable results, demonstrating the Covariant Spectator Theory's ability to describe the structure of the three-nucleon bound states realistically. Keywords Relativistic few-body systems · Nuclear interaction Covariant Spectator Theory of Two-and Three-Nucleon SystemsThe purpose of this talk is to give a brief overview of recent results we obtained in relativistic calculations of two-nucleon (2N) and three-nucleon (3N) systems in the framework of the covariant spectator theory (CST). As will be demonstrated, we found simple one-boson-exchange (OBE) models of the nucleon-nucleon (NN) interaction that provide a more efficient description of the NN observables than nonrelativistic models. This efficiency applies also to the 3N bound state, which can be well described without 3N forces. The obtained simplification depends crucially on relativity.One way of introducing the two-body CST is to start from the manifestly covariant Bethe-Salpeter (BS) equation for the scattering amplitude M of two particles with masses m 1 and m 2 , which can be written in the general form M = V BS + V BS G BS M, where V BS is a complete kernel consisting of an infinite number of twobody-irreducible boson-exchange diagrams. The propagator G BS is the product of the propagators of the two particles. This equation can then be recast into another equivalent form, M = V CST +V CST G CST M, in which a different propagator G CST and an accordingly modified kernel V CST is used. For the case of spin-1/2 particles,