Bound states in a noncentral potential: $\varepsilon$ expansion and Riemannian geometry

A new approach to the problem of the critical coupling constant $\lambda_c$ (critical binding) is proposed. The case of noncentral potentials is investigated. The critical coupling constant for the ground state is calculated by means of the $\varepsilon$ expansion ($\varepsilon=(d-2)/2$, where $d$ is the dimension of space), and the corrections to the semiclassical asymptotic behavior of the number of bound states are found.