Heavy-baryon chiral perturbation theory approach to thermal neutron capture onHe3

Abstract

The cross section for radiative thermal neutron capture on ${}^{3}\text{He}$ (${}^{3}\text{He}+n\ensuremath{\rightarrow}{}^{4}\text{He}+\ensuremath{\gamma}$; known as the $\mathit{hen}$ 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$^{3}\mathrm{L}$O). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to $\mathrm{N}{}^{3}$LO, the M1 operators contain two low-energy constants, which appear as the coefficients of nonderivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and ${}^{3}\text{He}$, we carry out a parameter-free calculation of the $\mathit{hen}$ cross section. The results are in good agreement with the data.