One-pion exchange potential in a strong magnetic field

TL;DR

This paper derives the one-pion exchange potential in strong magnetic fields using chiral perturbation theory, revealing that the potential's range decreases and the deuteron energy shifts significantly under such conditions.

Contribution

It extends the understanding of nuclear forces by deriving the OPEP in strong magnetic fields and quantifying its effects on nuclear binding energies.

Findings

The range of the OPEP decreases with increasing magnetic field strength.

The deuteron energy shift can reach about 1 MeV at strong magnetic fields.

The modified OPEP affects nuclear interactions in magnetized environments.

Abstract

We derive the one-pion exchange potential (OPEP) in the presence of a homogeneous magnetic field using chiral perturbation theory with nonrelativistic nucleons. Our approach is applicable not only to weak magnetic fields but also to strong ones up to around the pion-mass scale. The Green's function of charged pions is modified by the magnetic field, leading to changes in the nuclear force. By numerically evaluating the modified OPEP incorporating its spin and isospin dependencies, we show that the range of the potential decreases in both directions parallel and perpendicular to the magnetic field as the field strength increases. We also compute the resulting energy shift of the deuteron due to the modified OPEP, which can reach the order of 1 MeV around $|eB| = m_\pi^2$, which is comparable to the deuteron binding energy.