M. Chrysos

Quantum description of high-frequency Raman scattering from pairs of argon atoms

The quantum theory is applied for the accurate computation of high-frequency (up to ) spectral intensities in Ar - Ar collision-induced light scattering (CILS) processes at room temperature. Numerically, this becomes possible by means of the two-point Fox - Goodwin integrator, propagating on a grid the ratio of the wavefunction at adjacent points. Wavefunctions are normalized in a handy way which is based on the notion of the local wavenumber. Various potentials and anisotropy models are tested and compared. For frequencies exceeding our results show significant deviations as compared to the theoretical predictions of the classical theory. When the self-consistent field (SCF) anisotropy is applied, a clear tendency of the quantum calculation to approach recent experimental data is observed.

Stability and physicochemical reactions of light dications

The authors present theoretical results on the stability of Be22+, BeH2+, BH2+, BeHe2+ and BeLi+. The wavefunctions and potential energy curves have been obtained with large basis sets to account properly for the ionic structures and the correct shape of the curves. The ground-state potential curve of the first three molecules is dissociative with a local minimum. However, the previously predicted BH2+ does not seem to exist since its potential is found not to support any vibrational levels. BeHe2+ and BeLi+ are thermodynamically stable. The tunnelling widths of the BeH2+ and Be22+ lowest rovibrational resonances are negligible at room temperatures. Using the stable light dications as reactants, highly exothermic physicochemical reactions are possible.

Resonance quantization with persistent effects

Resonance energies and widths are calculated for non-standard situations where the potential matrix does not assume a constant diagonal form for infinite interparticle separation. Two cases are examined. The first (persistent potential effects) is illustrated by the calculation of the Rayleigh scattering amplitude by a diatomic molecule, where a linear open channel potential is coupled to a harmonic closed channel. In the second case (persistent coupling effects) the channel potentials remain coupled at infinity because the channel functions do not describe the separated atoms. In both cases the introduction of complex-energy resonance boundary conditions requires special treatments. Partial widths can be accurately extracted either by explicitly considering the correct asymptotic form of the channel functions or through a suitable asymptotic analysis of the complex-energy probability flux.

Resonances and exterior complex scaling

Abstract We have implemented the technique of exterior complex scaling via inward numerical integration of the complex-eigenvalue Schrodinger equation for resonances. The method has been tested successfully on three physically meaningful model potentials, the (12, 6) Lennard-Jones, the cubic anharmonic oscillator and the exponential, and on the vibrational resonances of He 2 2+ , 1 Σ g + , whose potential goes asymptotically as 1/ R . Widths as small as 10 −15 au have been computed.

On the self-generation of asymptotic boundary conditions in energy quantization

The calculation of bound and resonance energies and wavefunctions of the Schrodinger equation requires the introduction of appropriate boundary conditions in the asymptotic region. The authors determine under which conditions these constraints can be spontaneously built up, in a step-by-step inward propagation of the wavefunction by means of the Fox-Goodwin method. These conditions also apply to the renormalized Numerov method of Johnson (1978). This analysis gives a new insight into the role of complex rotation in resonance calculations.

EXTERIOR COMPLEX SCALING AND THE COMPUTATION OF CONTINUUM-CONTINUUM TRANSITION MATRIX ELEMENTS INVOLVING CONVERGING OR DIVERGING OPERATORS

A general methodology and a numerical procedure are presented for the accurate computation of continuum-continuum transition matrix elements E´,l´||E,l, where couples any two scattering states of a single-variable Hamiltonian. The procedure makes use of the exterior complex scaling of the r-coordinate [r r0+(r-r0)exp(i)], widely known for its precious properties in resonance quantization. It is applicable whatever the potential interaction, provided its functional form is globally analytic asymptotically. As coupling , any holomorphic function of the coordinate can be considered for which the matrix element is meaningful. This methodology enables one to handle systematically not only converging operators, but also diverging ones (such as the electric dipole moment in length form) for which standard real-coordinate integration fails. Graphical representation of the imaginary part of the -dependent complex matrix element against its real part shows that the exact value of the integral is clearly marked by a cusp, loop or inflection on a well defined -trajectory, analogously with resonance quantization.

The two-electron ionisation ladder for He- 2S and H- 1S

The authors have identified and computed the two-electron ionisation ladder (TEIL) of He- 2S with one electron in the 1s shell (up to n=10), and of the coreless but similar system H- 1S. Conditional probability plots show the expected localisation of the valence electrons on the Wannier ridge. For He-, these calculations verify the assignment of the electron-helium resonance spectrum given by Buckman et al. (1983).

Partial widths of the resonances of the H- 1P0 two-electron ionization ladder

The resonance wavefunctions of two-electron ionization ladder (TEIL) states can be identified a priori and computed to a high degree of accuracy from the solution of the complex eigenvalue Schrodinger equation. Depending on the form of the trial functions and on the concomitant non-Hermitian matrices, energies, energy shifts and partial widths can be obtained. The authors present the first predictions for the partial widths of the 1P0 TEIL states in H-, for n=3, 4 and 5, from calculations which include interchannel coupling. As before for the 1S symmetry, their analysis of the decay distribution shows that most of the width goes to the nearest hydrogenic threshold, while within each threshold there is strong mixing of the angular momentum channels. As n increases, the lifetime increases while it is given with increasing accuracy by the decoupled width (i.e. golden rule) to the nearest hydrogenic threshold.

Properties of Multiply Excited States

Intense laser light or the combination of more than one laser beams can send an atom into highly excited states whose electronic structure can be characterised as multiply or inner shell excited. The role of such states on the multiphoton ionization process has been of interest during the past few years. In this article, we outline the theoretical framework for the multielectron analysis of some of their properties which are relevant to current developments of laser spectroscopy.

The geometry of the Wannier two-electron ionisation ladder and the corresponding spectrum

Numerical results of a variety of atoms, using the theory of those doubly excited states (DES) which define the two-electron ionisation ladder (TEIL), demonstrate that the degree of localisation on the Wannier ridge is already high for n>or=5. These results are used to interpret the behaviour of the TEIL as an effective rigid rotor system, whose energy spectrum is deduced to be En=An(n-1)/r2n, where A is a constant, characteristic of the system, and rn is the average value of the radii of the pair of valence electrons, calculated from first principles. The prediction is made that the TEIL states can be distinguished from the other DES in complex photoabsorption spectra according to the spectral characteristics of the rigid rotor in external static fields.