Simple analytical expressions are derived for the bound-state energy as well as for the resonance energy and width in the case of the Gaussian potential. These accurate formulas may find applications in nuclear physics, in studies of low-energy electron–atom collisions, and in simulations of few-body properties in Bose–Einstein condensates and Fermi gases. An important feature of the present approach is that the formulas rely solely on the knowledge of a set of real bound-state energies. In addition, an analogous expression is obtained for the s -wave scattering length. This formula is constructed so as to yield highly accurate values of the scattering length in the ground-state region, where the scattering length becomes large.
Horáček et al. (Mon,) studied this question.