On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.