A new method for solving the inverse scattering problem in a single-channel approximation of the coupled channels method of an optical model (OM), described by a second-order ODE with a complex potential and with regular boundary conditions, is presented. The complex potential consists of two parts. The known real part is the sum of the nuclear, Coulomb and centrifugal potentials. The imaginary part is the product of the unknown coupling constant g(E) depending on the collision energy E and the derivative of the real part of the nuclear potential with respect to the independent variable ODE. The method implements the solution to the inverse problem: it calculates the unknown coupling constant g(E) and the scattering matrix S(g(E), E) from the equation |S(g(E), E)|² = 1 – |T(E)|² by the secant method, using at each step of the method the solution of the direct scattering problem for OM calculated with the KANTBP 5M program. The transmission amplitude T(E) and reflection amplitude R(E), subject to the condition |R(E)|² = 1 – |T(E)|² of the incoming wave boundary condition (IWBC) model, are also calculated by the KANTBP 5M program. The effectiveness of the method is demonstrated by solving the OM scattering problem and calculating the reference cross section for capture and metastable states of a heavy ion pair ^16O + ¹⁴⁴Sm in the single-channel approximation.