Three different approaches to the same interaction: the Yukawa model in nuclear physics

TL;DR

This paper compares three different theoretical approaches—non-relativistic, relativistic, and lattice quantum field theory—to modeling the nucleon-nucleon interaction via the Yukawa potential, highlighting their differences and insights.

Contribution

It provides a comparative analysis of the Yukawa model across three dynamical frameworks, illustrating how each approach handles the same interaction.

Findings

Consistent results across models for certain interaction features

Differences in quantitative predictions between frameworks

Insights into the applicability of each method in nuclear physics

Abstract

After a brief discussion of the meaning of the potential in quantum mechanics, we examine the results of the Yukawa model (scalar meson exchange) for the nucleon-nucleon interaction in three different dynamical frameworks: the non-relativistic dynamics of the Schrodinger equation, the relativistic quantum mechanics of the Bethe-Salpeter and Light-Front equations and the lattice solution of the Quantum Field Theory, obtained in the quenched approximation.