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

The cross section for radiative thermal neutron capture on ${}^{3}He$ ($\He3 +n \to \He4 +\gamma$;knownasthe$hen$ 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.