Relativistic treatments of the nucleon-nucleon system

Abstract

<p>The relativistically minimalist Breit equation is used to study the two-nucleon system. Generally, the equation is noncovariant and its realm of applicability is limited. It is not a field-theoretical equation but, at low energy, it was thought to be a promising candidate to explore the scheme of repulsive vector and attractive scalar interactions as the dominant ingredient of the two-nucleon interaction. In the ¹S₀ singlet case, the equation does indeed seem viable. Dynamically sound interactions and a reasonable fit of the scattering data arise. In a specific application, the discrepancy between the ¹S₀ isovector scattering lengths of the p-p and n-n interactions is explored. This novel charge-symmetry-breaking (CSB) mechanism enlarges the discrepancy between the two lengths, implying a still larger correction is required by other documented (CSB) mechanisms. An all-encompassing model of the ³S₁-³D₁ state is, on the other hand, not achieved. Models which best fit the experimental deuteron and elastic scattering data, are unphysical. The vector coupling is driven strongly negative and a dominant interference mechanism arises involving the entirely phenomenological short range OPEP. It was hoped that this parametrized short range OPEP would remain benign while the scalar/vector interference scheme took a lead role. Instead the constraint of avoiding Klein paradox difficulties defeats this picture and achieves the short-range repulsion in the N-N force by ramping up the phenomenological OPEP. It is finally argued that the Breit framework almost certainly does not lend itself to an adequate description of the N-N system. It does, however, point to novel relativistic elements which may ultimately resolve celebrated outstanding problems such as the a_t-r_m discrepancy. The triplet scattering length a_t and deuteron matter-radius r_m are tightly correlated and resistant to simultaneous fitting in conventional models. The p-wave amplitudes of the lower components of a relativistic framework offer a potential means of resolution.</p>