Three-body model comprising a diatomic homonuclear molecule and an atom, the solutions of which are necessary for modelling interactions of three-body systems with laser radiation and spectroscopy, is formulated in the collinear configuration of the adiabatic representation. The mapping of the relevant 2D boundary-value problems (BVPs) in the Jacobi coordinates and in polar (hyperspherical) coordinates is reduced to a 1D BVP for a system of coupled second-order ordinary differential equations (ODEs) by means of the Kantorovich expansion in basis functions of one of the two independent variables, depending on the other independent variable parametrically. The efficiency of the proposed approach and software is demonstrated by benchmark calculations of the discrete spectrum of Be<sub>3</sub> trimer in the collinear configuration.
We consider theoretically laser-assisted ionization of a helium atom by electron impact at large momentum transfer. Fully differential cross sections of these processes are studied as functions of the recoil-ion momentum for the cases when the residual He<sup>+</sup> ion is left both in the bound (<i>n</i> = 1 and <i>n</i> = 2) and in the continuum states in the presence of a linearly-polarized laser field with frequency <i>w</i> = 1.55 eV and intensity <i>I</i> = 5×10<sup>11</sup>W/cm<sup>2</sup>. We inspect how the orientation of the polarization influences the laser-assisted momentum profiles using different models of the helium wave function. It is found that the Kroll-Watson sum rule is well applicable in the (<i>e</i>, 3 − 1<i>e</i>) case.
Aimed at applications to the photonics of composite two-electron quantum systems like a helium atom in hyper spherical coordinates, the boundary value problem (BVP) for a system of coupled self-adjoined 3D elliptic partial differential equations of the Schrodinger type with homogeneous third-type boundary conditions is formulated in coupled-channel adiabatic approach. The Kantorovich reduction of the problem to BVPs for ordinary second-order differential equations (ODEs) with respect to functions of a single hyper-radial variable is implemented by expanding the solution over a set of surface (angular) functions that depend on the hyper-radial variable as a parameter. Benchmark calculations are presented by the example of the ground and first excited states of a Helium atom. The convergence of the results with respect to the number of the surface functions and their components is studied. The comparison with the known results is presented.
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.