Cumulative reaction probabilities using Padé analytical continuation procedures

Abstract

New computational techniques for calculation of cumulative reaction probabilities, N(E), are suggested. They are based on the expression of N(E) through the imaginary part of the Green function G [Seideman and Miller, J. Chem. Phys. 96, 4412 (1992)]. We use three methods to overcome numerical problems arising from branch cuts of G located along the real positive energy axes, addition of constant imaginary part iε to the Hamiltonian, addition of unoptimized optical potentials of the form iλ‖s‖ or iλ‖s‖2, and complex rotation of the reaction coordinate s→s⋅exp(iϑ). When N(E,u) is calculated on a grid of values of the numerical parameter u (u being ε, λ, or ϑ), Padé analytical continuation to their zero values gives correct energy dependence of N(E). The method makes it possible to save computer time by using unoptimized parameters of the optical potential or of the complex scaling when calculating N(E,u). Test calculations on a one dimensional Eckart barrier and a model H+H2(ν=1) potential which supports a quasibound state have shown high accuracy and convergence of the method with respect to Padé input parameters.