Local chiral interactions and magnetic structure of few-nucleon systems

TL;DR

This paper calculates magnetic form factors and electrodisintegration cross sections of light nuclei using chiral two- and three-nucleon interactions with $\Delta$ intermediate states, achieving good agreement with experiments for some observables.

Contribution

It introduces a comprehensive calculation framework incorporating $\Delta$ states and consistent current operators for few-nucleon systems, improving theoretical predictions.

Findings

Predicted form factors agree with experiments up to 2-3 fm$^{-1}$.

Deuteron electrodisintegration cross sections match data well.

Photodisintegration cross sections are underestimated unless using the Siegert operator.

Abstract

The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $\Delta$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schr\"odinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with $\Delta$ intermediate states are only retained at the OPE level, and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2--3 fm$^{-1}$. However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. A complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.