Effective theory of3H and3He

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order (LO) the spin-singlet nucleon–nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron–deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse scattering lengths converges rapidly. Using a new systematic treatment of the proton–proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the – binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the LO is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting .