Relativistic Structure of the Deuteron: 1.Electro-disintegration and y-scaling

TL;DR

This paper investigates relativistic effects in electron-deuteron scattering using Bethe-Salpeter solutions, demonstrating covariant y-scaling and the importance of negative energy states in describing the deuteron structure.

Contribution

It introduces a fully covariant approach to y-scaling in deuteron scattering, including negative energy states, and shows the agreement of simplified models with exact calculations at moderate momenta.

Findings

Relativistic y-scaling occurs with the usual relativistic variable.

Covariant momentum distributions can approximate exact calculations.

Asymptotic relativistic scaling matches longitudinal covariant momentum distribution.

Abstract

Realistic solutions of the spinor-spinor Bethe-Salpeter equation for the deuteron with realistic interaction kernel including the exchange of pi, sigma, omega, rho, eta and delta mesons, are used to systematically investigate relativistic effects in inclusive quasi-elastic electron-deuteron scattering within the relativistic impulse approximation. Relativistic y-scaling is considered by generalising the non relativistic scaling function to the relativistic case, and it is shown that y-scaling does occur in the usual relativistic scaling variable resulting from the energy conservation in the instant form of dynamics. The present approach of y-scaling is fully covariant, with the deuteron being described by eight components, viz. the 3S_1^{++}, 3S_1^{--}, 3D_1^{++}, 3D_1^{--}, 3P_1^{+-}, 3P_1^{-+}, 1P_1^{+-}, 1P_1^{-+} waves. It is demonstrated that if the negative relative energy states 1P_1, 3P_1 are disregarded, the concept of covariant momentum distributions N(p_0,p), with p_0=M_D/2-\sqrt{p^2+m^2}, can be introduced, and that calculations of lectro-disintegration cross section in terms of these distributions agree within few percents with the exact calculations which include the 1P_1, 3P_1 states, provided the nucleon three momentum |p|\<= 1 GeV/c; in this momentum range, the asymptotic relativistic scaling function is shown to coincide with the longitudinal covariant momentum distribution.