The Jost function treated by the F-matrix phase integral method

Exact as well as approximate expressions for the Jost function of a radial barrier transmission problem are derived by the phase-integral method developed by Froman and Froman (1974). The resulting formulae are used for calculating the positions and the widths of the quasi-stationary states. To demonstrate the essential features as simply as possible, an s-state in a potential, regular at the origin, is considered, and only the first-order phase-integral formulae are given explicitly, but the generalisation to l not=0 and arbitrary-order phase-integral approximations is indicated.