Asymptotic Approximation for Bethe-Salpeter Equation and its Applications to Deuteron

TL;DR

This paper develops an asymptotic approximation method for solving the Bethe-Salpeter equation for a two-fermion bound state, specifically applied to the deuteron, and explores related properties like binding energy and quadrupole moment.

Contribution

It introduces an asymptotic approximation approach to the Bethe-Salpeter equation and applies it to analyze the deuteron, including calculations of binding energy and quadrupole moment.

Findings

Reproduces the deuteron binding energy accurately.

Provides insights into the quadrupole moment within the asymptotic framework.

Derives a one-dimensional integral equation from the original Bethe-Salpeter equation.

Abstract

Bethe-Salpeter equation is solved for bound state composed of two fermions mediated by pion exchange force of the pseudovector coupling. Expanding the amplitude by gamma matrices the one-dimensional integral equation is derived. It reproduces the binding energy of deuteron. The relation with the quadrupole moment is also discussed in the framework of the asymptotic approximation.