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Register a new userA potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion
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The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrodinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.
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Although the convergent close-coupling (CCC) method has achieved unprecedented success in obtaining accurate theoretical cross sections for electron-atom scattering, it generally fails to yield converged energy distributions for ionization. Here we report converged energy distributions for ionization of H(1s) by numerically integrating Schroedingers equation subject to correct asymptotic boundary conditions for the Temkin-Poet model collision problem, which neglects angular momentum. Moreover, since the present method is complete, we obtained convergence for all transitions in a single calculation. Complete results, accurate to 1%, are presented for impact energies of 54.4 and 40.8 eV, where CCC results are available for comparison.
In order to describe few-body scattering in the case of the Coulomb interaction, an approach based on splitting the reaction potential into a finite range part and a long range tail part is presented. The solution to the Schrodinger equation for the long range tail is used as an incoming wave in an inhomogeneous Schrodinger equation with the finite range potential. The resulting equation with asymptotic outgoing waves is then solved with the exterior complex scaling. The potential splitting approach is illustrated with calculations of scattering processes in the H${}^+$ -- H${}^+_2$ system considered as the three-body system with one-state electronic potential surface.
An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schrodinger equation for the long range tail of the reaction potential is used as an incoming wave. This reformulation of the scattering problem into an inhomogeneous Schrodinger equation with asymptotic outgoing waves makes it suitable for solving with the exterior complex scaling technique. The validity of the approach is analyzed from a formal point of view and demonstrated numerically, where the calculations are performed with the finite element method. The method of splitting the potential in this way is illustrated with calculations of the electron scattering on the hydrogen atom and the positive helium ion in energy regions where resonances appear.
The electron detachment from the hydrogen negative ion in strong fields is studied using the two-electron and different single-electron models within the quasistatic approximation. A special attention is payed to over-the-barrier regime where the Stark saddle is suppressed below the lowest energy level. It is demonstrated that the single-electron description of the lowest state of ion, that is a good approximation for weak fields, fails in this and partially in the tunneling regime. The exact lowest state energies and detachment rates for the ion at different strengths of the applied field are determined by solving the eigenvalue problem of the full two-electron Hamiltonian. An accurate formula for the rate, that is valid in both regimes, is determined by fitting the exact data to the expression estimated using single-electron descriptions.
The S-wave model of electron-hydrogen scattering is evaluated using the convergent close-coupling method with an emphasis on scattering from excited states including an initial state from the target continuum. Convergence is found for discrete excitations and the elastic free-free transition. The latter is particularly interesting given the corresponding potential matrix elements are divergent.
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