A Relativistic Theory of Few-Nucleon Systems

Abstract

This talk provides an overview of recent results for two-and three-nucleon systems obtained within the framework of the covariant spectator theory (CST). The main features of two recently published models for the neutron-proton interaction, that fit the 2007 world data base containing several thousands of neutron-proton scattering data below 350 MeV with χ 2 /N data ≈ 1, are presented. These one-boson-exchange models, called WJC-1 and WJC-2, have a considerably smaller number of adjustable parameters than are present in realistic nonrelativistic potentials. When applied to the three-nucleon bound state, the correct binding energy is obtained without additional three-body forces. First calculations of the electromagnetic form factors of helium-3 and the triton in complete impulse approximation also give very reasonable results. One can conclude that the CST yields a very efficient description of few-nucleon systems, in which the relativistic formulation of the dynamics is an essential element. The Fundamental Ideas of the Covariant Spectator TheoryIn low-energy few-body nuclear physics, relativity is often considered an unwelcome complication that gives rise to only small effects, which can be either neglected or included perturbatively. The argument is usually based on the observation that typical kinetic energies of nucleons in light nuclear systems are small compared to their rest mass. However, a relativistic description of such systems becomes unavoidable when they are investigated with hadronic or electromagnetic probes at high momentum transfer and the final nuclear states reach relativistic velocities.This talk intends to show that relativity can also lead to a significant simplification of the description of fewnucleon systems. This will be demonstrated for the case of the covariant spectator theory (CST), where simple one-boson-exchange (OBE) models of the nucleon-nucleon (N N) interaction can be derived that provide a more efficient description of the N N 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.The basic idea of the CST is to reorganize the manifestly covariant Bethe-Salpeter (BS) equation with its complete kernel to another equivalent form, in which a different propagator and an accordingly modified kernel is used. The specific propagator of the CST places all particles but one in intermediate states on their mass shells [1][2][3]. This reduces the dimension of the integration over intermediate momenta from four to