The Nuclear Yukawa Model on a Lattice

TL;DR

This paper investigates the nuclear Yukawa model using lattice quantum field theory techniques, focusing on two fermions interacting via scalar meson exchange, and explores critical coupling and scattering properties.

Contribution

It applies lattice methods to the Yukawa model with Wilson fermions in the quenched approximation, identifying a critical coupling and calculating scattering lengths.

Findings

Existence of a critical coupling constant limiting numerical solutions

Range of coupling constants below bound state formation threshold

Computed two-body scattering lengths consistent with non-relativistic results

Abstract

We present the results of the quantum field theory approach to nuclear Yukawa model obtained by standard lattice techniques. We have considered the simplest case of two identical fermions interacting via a scalar meson exchange. Calculations have been performed using Wilson fermions in the quenched approximation. We found the existence of a critical coupling constant above which the model cannot be numerically solved. The range of the accessible coupling constants is below the threshold value for producing two-body bound states. Two-body scattering lengths have been obtained and compared to the non relativistic results.