The possibility of quasi-bound state formation of $\eta$-meson with helium isotopes

Abstract

The necessary conditions of quasi-bound state formation of $\eta$-meson with isotopes $^{3}$He, $^{4}$He have been found within the framework of optical potential model. These conditions have been compared with the findings about helium nucleus densities and with the available information about $\eta$N-scattering length. Thus, we have conclude that within the framework of discussed model $\eta-^{3}$He quasi-bound state formation is not possible, but $\eta-^{4}$He quasi-bound state formation is possible with the great probability.