Onset of $\hat{I}\cdot$-meson binding in the He isotopes

Abstract

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

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