A novel discrete variable representation (DVR) is introduced for use as the L2 basis of the S‐matrix version of the Kohn variational method [Zhang, Chu, and Miller, J. Chem. Phys. 88, 6233 (1988)] for quantum reactive scattering. (It can also be readily used for quantum eigenvalue problems.) The primary novel feature is that this DVR gives an extremely simple kinetic energy matrix (the potential energy matrix is diagonal, as in all DVRs) which is in a sense ‘‘universal,’’ i.e., independent of any explicit reference to an underlying set of basis functions; it can, in fact, be derived as an infinite limit using different basis functions. An energy truncation procedure allows the DVR grid points to be adapted naturally to the shape of any given potential energy surface. Application to the benchmark collinear H+H2→H2+H reaction shows that convergence in the reaction probabilities is achieved with only about 15% more DVR grid points than the number of conventional basis functions used in previous S‐matrix Kohn...

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A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method

Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling

We review the phenonomena which occur in multiphoton physics when the electric field of the applied laser radiation becomes comparable with the Coulomb field strength seen by an electron in the ground state of atomic hydrogen. This field is reached at an irradiance of approximately . The normal perturbative photon-by-photon based picture of the interaction of individual electrons with the field is replaced by a tunnelling picture in which, in a time of the order of, or less than one optical cycle, atomic wavepackets are generated which escape the confining Coulomb potential. These wavepackets are strongly influenced by the laser, `quiver' and may be accelerated back to the parent ion in a recollision process. Phase-coherent effects locked to the laser field become important: high harmonics are generated from these recollisions. We discuss the theory of such effects, and review progress in understanding how this quiver motion can be coherently controlled. We discuss ionization dynamics and review mechanisms by which atoms may be stabilized in very strong fields. Finally, we discuss relativistic effects which occur at very high-intensities.

https://iopscience.iop.org/article/10.1088/0034-4885/60/4/001/pdf

Atomic physics with super-high intensity lasers

Engineered photonic waveguides have provided in the past decade an extremely rich laboratory tool to visualize with optical waves the classic analogues of a wide variety of coherent quantum phenomena encountered in atomic, molecular or condensed-matter physics. As compared to quantum systems, optics offers the rather unique advantage of a direct mapping of the wave function evolution in coordinate space by simple fluorescence imaging or scanning tunneling optical microscopy techniques. In this contribution recent theoretical and experimental advances in the field of quantum-optical analogies are reviewed. Special attention is devoted to some relevant optical analogies based on the use of curved photonic structures, including: coherent destruction of tunneling in driven bistable potentials; coherent population transfer and adiabatic passage in laser-driven multilevel atomic systems; quantum decay control and Zeno dynamics; electronic Bloch oscillations and Zener tunneling, Anderson localization and dynamic localization in crystalline potentials.

Quantum-optical analogies using photonic structures

The method of complex coordinate rotation and its applications to atomic collision processes

We study the behavior of atomic hydrogen in a monochromatic radiation field of high frequency $\ensuremath{\omega}$ and high intensity $I$, when its structure depends only on the parameter ${\ensuremath{\alpha}}_{0}={I}^{\frac{1}{2}}{\ensuremath{\omega}}^{\ensuremath{-}2}$ a.u., and when multiphoton ionization is quenched. At large ${\ensuremath{\alpha}}_{0}$ the ground-state binding energy undergoes a drastic reduction. This is coupled to an unprecedented stretching of the (oscillating) electron wave function, culminating in its separation into two parts (dichotomy) for ${\ensuremath{\alpha}}_{0}g50$ a.u.

Dichotomy of the hydrogen-atom in superintense, high-frequency laser fields

We consider the extension of the complex-coordinate technique to the problem of locating molecular resonances. We suggest a method which uses complex normalizable functions and which becomes equivalent to the usual dilatation transformation asymptotically, but is different for small values of the electronic coordinates. The technique is illustrated by application to the bound states of ${\mathrm{H}}_{2}^{+}$ and to a model nonspherical resonance problem.

Extension of the method of complex basis functions to molecular resonances

We demonstrate that the array of techniques employing complex basis functions, which have been broadly applied in the calculation of resonance positions and lifetimes, can also be used, with appropriate modification, in the practical computation of photoionization cross sections and nonresonant scattering amplitudes. We illustrate a procedure with which controlled complex distortions over a localized region of the energy spectrum can be realized in a finite basis-set calculation. This technique is used to directly obtain scattering amplitudes for potentials which are not exponentially bounded at large distances, in contrast to complex scaling techniques which have been shown to be divergent in such cases. Four numerical examples are presented to exhibit the utility of the local complex distortion approach in calculations of photoionization cross sections and scattering amplitudes. We also discuss this approach in the context of variational principles for continuum amplitudes and in the context of applications to many-electron systems.

Locally complex distortions of the energy spectrum in the calculation of scattering amplitudes and photoionization cross sections

The complex Kohn variational method, which is an anomaly-free algebraic variational procedure, is implemented for the case of collisions of electrons with polyatomic molecules. The complex Kohn method requires only Hamiltonian matrix elements and, in this formulation, does not require any exchange matrix elements involving continuum functions. Direct matrix elements of the scattering potential(s) which involve continuum functions are evaluated by an adaptive three-dimensional quadrature scheme. The entire procedure is applied to elastic electron-methane scattering at the static-exchange level and proves to be both efficient and accurate. No Ramsauer-Townsend minimum is found at low energies, and it is concluded that this feature of the experimental cross section cannot be described theoretically without the inclusion of target polarization.

Collisions of electrons with polyatomic molecules: Electron-methane scattering by the complex Kohn variational method

The complex Kohn method is used to study electron-methane scattering with polarized trial functions at incident energies ranging from 0.2 to 10 eV. A perturbative method, which only requires the construction of Fock operators, is used to generate a set of polarized virtual orbitals. These polarized orbitals are then used to construct a compact {ital ab} {ital initio} scattering function that produces cross sections that are in excellent agreement with experiments in the region of the Ramsauer-Townsend minimum and at higher energies, where a broad maximum is present in the integral cross section. This is the first {ital ab} {ital initio} study to accurately characterize low-energy electron-methane scattering.

C. W. McCurdy

Papers

Dichotomy of the hydrogen-atom in superintense, high-frequency laser fields

Extension of the method of complex basis functions to molecular resonances

Locally complex distortions of the energy spectrum in the calculation of scattering amplitudes and photoionization cross sections

Collisions of electrons with polyatomic molecules: Electron-methane scattering by the complex Kohn variational method

Ab initio study of low-energy electron-methane scattering.