Nuclear Potential with Two Pion Exchange

TL;DR

This paper provides a detailed numerical calculation of the nucleon-nucleon interaction via two pion exchange, revealing an attractive potential with specific scalar meson characteristics and notable isospin dependence.

Contribution

It offers a precise, approximation-free numerical evaluation of the two pion exchange potential, highlighting features not captured by simpler models.

Findings

Two pion exchange produces an attractive force with scalar meson characteristics.

The potential exhibits strong isospin dependence not replicable by one boson exchange models.

Numerical integration of Feynman diagrams confirms the scalar meson parameters.

Abstract

We carefully calculate the nucleon-nucleon interaction due to two pion exchange processes by properly evaluating the corresponding Feynman diagrams. In the estimation, we have made no approximation, and instead, we carry out the numerical integrations of three Feynman parameters. It is found that the two pion exchange potential gives rise to the attractive force which corresponds to the effective scalar meson with its mass of $m_s\simeq 4.7 m_\pi$ and its strength of ${g_s^2\over 4\pi}\simeq 1.45 $. There is a strong isospin dependence of $(\bm{\tau}_1\cdot \bm{\tau}_2)^2 $ which cannot be simulated by the one boson exchange model calculations.