Onset of $\eta$-meson binding in the He isotopes

Abstract

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

Comments: v3 -- 18 pages, 6 figures, 4 tables, and matching the published version