Models of quantum tunneling of a diatomic molecule affected by laser pulses through repulsive barriers

The model for quantum tunneling of a diatomic homonuclear molecule is formulated as a 2D boundary-value problem (2D BVP) for the Schrodinger equation with homogeneous boundary conditions of the third type. The molecule is considered as a pair of identical particles coupled via the effective potential. For short-range barrier potentials the Galerkin reduction to BVP for a set of closed-channel second-order ordinary differential equations (ODEs) is obtained by expanding the solution in a basis of transverse variable functions. Benchmark calculations of quantum tunneling through Gaussian barriers are presented for a pair of identical nuclei coupled by Morse potential. The results are compared with the direct numerical solution of the original2D BVP obtained using the Numerov scheme. The effect of quantum transparency, i.e., the resonance behavior of the transmission coefficient versus the energy of the molecule, is shown to be a manifestation of the barrier metastable states, embedded in the continuum below the dissociation threshold, as well as quantum diffusion. The possibility of controlling the dynamics of atom-ion collisions by laser pulses is analyzed using a lD BVP two-center model with Poschl-Teller potentials.