Heavy-baryon chiral perturbation theory approach to thermal neutron capture on ${}^{3}{He}$

TL;DR

This paper calculates the thermal neutron capture cross section on helium-3 using heavy-baryon chiral perturbation theory, deriving operators up to N3LO, fitting low-energy constants, and achieving results consistent with experimental data.

Contribution

It introduces a parameter-free calculation of the $hen$ reaction cross section using chiral EFT and realistic nuclear wave functions, extending previous theoretical approaches.

Findings

Calculated cross section agrees with experimental data

Derived M1 operators up to N3LO with two low-energy constants

Used Faddeev-Yakubovski equations for nuclear wave functions

Abstract

The cross section for radiative thermal neutron capture on ${}^{3}He$ ($\He3 +n \to \He4 +\gamma$; known as the $hen$ reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N${}^3$LO). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to N${}^3$LO, the M1 operators contain two low-energy constants, which appear as the coefficients of non-derivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and ${}^3 He$, we carry out a parameter-free calculation of the $hen$ cross section. The results are in good agreement with the data.