Asymptotic Form of Parametric Basis Functions for the Model of Quantum Tunnelling of Diatomic Molecules

The mathematical model of quantum tunnelling of diatomic molecules through repulsive barriers is formulated in the s-wave approximation. The 2D boundary-value problem in polar coordinates is reduced to a 1D one by means of Kantorovich expansion over the set of parametric basis functions. The algorithm for calculating the asymptotic form of the parametric basis functions at large values of the parameter (radial variable) is presented. The solution is sought by matching the numerical solution in one of the subintervals with the analytical solution in the adjacent one. The efficiency of the algorithm is shown by comparison of the calculated solutions with those of the parametric eigenvalue problem obtained by applying the finite element method in the entire domain of definition at large values of the parameter.