Lukas Pichl

Complete reflection in two-state crossing and noncrossing potential systems

A semiclassical study is made for the complete transmission and the complete reflection phenomena in two coupled molecular potential systems. The conditions for these phenomena to occur are expressed analytically in terms of nonadiabatic transition probabilities and phase integrals, which can be provided by the semiclassical theory. We also introduce an exactly solvable analytical model of diabatically avoided crossing, in which two diabatic potentials coupled by a constant coupling are close together in a certain spatial region. These models and phenomena may be useful in controlling various molecular processes in laser fields, since in the dressed or Floquet state formalism molecular potentials can be shifted up and down and are made to cross or avoid crossing with other potentials.

Total, Partial, and Differential Ionization Cross Sections in Proton–Hydrogen Atom Collisions in the Energy Region of 0.1–10 keV/u

Single-differential, partial, and total ionization cross sections for the proton–hydrogen atom collision system in the energy region of 0.1–10 keV/u are determined by using the molecular-orbital close-coupling method within a semiclassical formalism. The present cross sections are in an excellent agreement with the recent experiments of Shah et al. [J. Phys. B. 31, L757 (1998)], but decrease more rapidly than the cross sections measured by Pieksma et al. [Phys. Rev. Lett. 73, 46 (1994)] with decreasing energy. The numerical data for all calculated cross sections are included in this paper. A critical evaluation of the existing data for the ionization process in the keV energy range is performed both for the experiment and theory. The recommended data are obtained from a converged close-coupling expansion, which in total includes 362 bound and continuum channels with their wave functions augmented by the electron translation factor in order to insure the correct scattering boundary condition.

Non-adiabatic transitions in a two-state exponential potential model

A general two-state exponential potential model is investigated and the corresponding two-channel scattering problem is solved by means of semiclassical theory. The analytical expression for the non-adiabatic transition matrix yields a unified expression in the repulsive and previously studied attractive case. The final formulae are expressed in terms of model-independent quantities, i.e. the contour integrals of adiabatic local momenta. Oscillations of the overall transition probability below the crossing of diabatic potentials are observed in the case of strong coupling. The theory is demonstrated to work very well even at energies lower than the diabatic crossing region. Based on our results the unified theory of non-adiabatic transitions, covering the Landau-Zener-Stueckelberg and Rozen-Zener-Demkov models in such an energy range, is possible.

Analytical treatment of singular equations in dissociative recombination

Abstract The Lippmann–Schwinger type singular integral equation, which arises in the multi-channel quantum defect theory of dissociative recombination process, is investigated. The singularity of its kernel is treated analytically by introducing an energy dependent quadrature. In many cases of physical interest the energy-dependent coupling potential, which gives the integral kernel of the equation, is quasi-separable in a way that allows to write down an analytical solution. The analytical treatment as well as the new solution are illustrated by taking the H 2 + as an example. Our method is demonstrated to be much better than the conventional ones, such as the first order perturbation theory and the grid method.

Analytical Treatment of the K Matrix Integral Equation in the Dynamics of Superexcited Molecules

Superexcited states (SES) constitute one peculiar class of electronically highly excited states of molecules whose internal energies exceed the corresponding lowest ionization potentials.1, 2, 3 They play important roles in various fields of chemistry and physics as intermediate states of dynamic processes. Fig. 1 shows a schematic view of this feature. It is crucial to understand the characteristics of the central SES M*, in order to systematically comprehend the various dynamic processes. Dissociative recombination represents one of several good examples. According to the difference in the autoionization mechanisms, the SES are classified into the following two kinds: (i) multiply or inner-shell excited states, which are called “SES of the first kind”, and (ii) rovibrationally excited Rydberg states, which is called “SES of the second kind.” The dynamics of SES are governed by the two basic interactions: the electronic coupling, V(R, e), between the first kind of SES and the electronic continuum, and the quantum defect function µ(R), where R is the internuclear distance and e is the electron energy. If these two quantities are available together with the potential curves E d(R) of the first kind of SES, then the MQDT (multi-channel quantum defect theory) presents a very powerful tool to investigate the various dynamics. These quantities should be basically evaluated by quantum chemical electronic structure theory, but it is not easy to obtain accurate absolute values, especially in the case of V(R, e).

Analytical treatment of the Green function singularity in integral equations of scattering theory

A technique for solving the Lippmann - Schwinger equation in momentum space based on Chebyshev polynomials is proposed. It is found that exact results are obtained for standard low-energy nuclear separable potentials with an extremely low number of meshpoints. The technique naturally leads to a class of analytically solvable separable potentials. The application of the Chebyshev technique to two local standard N - N potentials, Yukawa and Reid, is discussed.