Onset of η-meson binding in the He isotopes

The onset of binding η(548) mesons in nuclei is studied in the He isotopes by doing precise ηNNN and ηNNNN few-body stochastic variational method calculations for two semi-realistic NN potentials and two energy dependent ηN potentials derived from coupled-channel models of the N^⁎(1535) nucleon resonance. The energy dependence of the ηN subthreshold input is treated self consistently. It is found that a minimal value of the real part of the ηN scattering length a_ηN close to 1 fm is required to bind η mesons in ³He, yielding then a few MeV η binding in ⁴He. The onset of η-meson binding in ⁴He requires that Rea_ηN exceeds 0.7 fm approximately. These results compare well with results of recent ηNNN and ηNNNN pionless effective field theory calculations. Related optical-model calculations are also discussed.