Table of contents

The energies and the widths of the Stark resonances for the hydrogen atom are calculated using a new approach. It is based on the operator form of the perturbation theory of the Schrodinger equation. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact quantum-mechanical procedure. The zero-order Hamiltonian possessing only stationary states is determined only by its spectrum without specifying its explicit form. The method of calculation of the perturbation theory matrix elements is described.

The authors have dealt with the problem of the effect of an external DC field on the prototypical He2s^{2 1}S and 2s2p ³P⁰ (M_L=0, M_L=+or-1) doubly excited autoionizing states, by computing the complex eigenvalues of appropriately constructed small non-Hermitian matrices. The major correlation effects and the mixing of autoionizing and of bound states with the open channels 1s epsilon l, 2s epsilon 'l and 2p epsilon 'l are taken into account to all orders. The smooth decrease of the widths as a function of field strength shows the influence of the nearby strongly coupled narrower states, 2s2p ¹P⁰ and 2p^{2 3}P. The polarizabilities, alpha , and hyperpolarizabilities, gamma , are: alpha (¹S) = 75.4 au, gamma (¹S) = 2.9 * 10⁵ au alpha (³P⁰, M_L = 0) = 41.2 au, gamma (³P⁰,M_L = 0) = 1.2 x 10⁵ au, alpha (³P⁰, M_L = +or-1) = 130.8 au, gamma (³P⁰, M_L = +or-1) = -7.0 x 10⁵ au.

A unique autoionization decay dynamic is encountered in Cr. It embraces several correlated processes. First, the 3p to 3d and the rest of the 3p to nd resonant excited orbitals are subject to dramatic orbital anti-collapse. Second, the giant 3p to 3d resonance and the rest of the 3p to nd Rydberg series are essentially configurationally mixed with one another. Thirdly what is particularly unusual is that the giant 3p to 3d resonance decays while the orbital anti-collapse is in full progress. This dramatically affects not only the final parameters of the 3p to 3d resonance itself, but through the configuration mixing this critically reflects on those for the rest of the 3p to nd Rydberg series. All this finally results in the unique resonance structure in the 3p absorption spectrum of Cr, which has been a puzzle for many years. A way to introduce what are called the 'relaxed transition states' for the 3p to 3d autoionizing decay and thus to describe correctly the whole resonance structure in Cr is proposed. Good agreement between the calculated and experimental data for the Cr 3p absorption is achieved.

For P⁰ states of helium the authors formulate a Schrodinger equation in perimetric coordinates in which the rotational coupling is already pre-diagonalized. Expansions in near-complete basis sets and complex scaling techniques allows the determination of highly accurate ab initio parameters for doubly excited resonant states and photo cross sections. The results are in excellent agreement with recent high-quality experimental data.

Laser-induced fluorescence was observed in the BaCl molecule using various Ar⁺ and Kr⁺ ion laser radiations. The spectra were recorded by high resolution Fourier transform spectroscopy. The following electronic transitions were rotationally analysed for vibrational levels up to nu = 10: C ² Pi to X ² Sigma ⁺, C ² Pi to A' ² Delta , C ² Pi to A ² Pi , C ² Pi to B ² Sigma ⁺, B ² Sigma ⁺ to X ² Sigma ⁺, E ² Sigma ⁺ to C ² Pi , E ² Sigma ⁺ to B ² Sigma ⁺, F ² Sigma ⁺ to C ² Pi , F ² Sigma ⁺ to A ² Pi , F ² Sigma ⁺ to B ² Sigma ⁺. A global fit was performed, including simultaneously all the data for these transitions. Accurate molecular constants are derived for the X ² Sigma ⁺, A' ² Delta , A ² Pi , B ² Sigma ⁺, C ² Pi , E ² Sigma ⁺ and F ² Sigma ⁺ electronic states.

The authors have determined absolute cross sections for ionization-excitation of He by energetic electron and proton projectiles. Using a semi-empirical analytic formula the authors have been able to decompose their He⁺ (np) cross section data in leading order terms which are proportional to Z_pⁿ for n = 2, 3 and 4. In particular the authors have found a strong Z_p³ dependence which appears to represent quantum interference effects. The set of amplitude coefficients obtained here is universal for both their electron and proton cross section results from He⁺ (np) states with principal quantum numbers n = 2 to 5.

The authors report a coupled pseudostate calculation of integrated cross sections for electron impact excitation of hydrogen atoms from the ground state to the n = 3 states for incident energies from 13.6 to 100 eV. The results are compared with experiment.

The non-adiabatic treatment of vibrational motion in e^--molecule scattering typically involves a sum or integral over a complete set of vibrational functions, in general including a continuum. If all functions of the vibrational coordinate are defined by interpolation on a finite point set they can be represented as linear combinations of basis functions that are Kronecker-delta functions on this point set. The authors introduce 'spline-delta' basis functions with this property, providing a discrete complete set for which intermediate sums in matrix products can be closed without truncation.

Higgins and Burke using the R-matrix method indicated the existence of a resonance in the s-wave ground-state capture cross section in positron-hydrogen scattering. Hewitt et al. have confirmed this resonance using the coupled static method. The calculations using the close-coupling approximation (CCA) with six basis sets have been carried out and a resonance is located for each basis. With enlargement of the basis in the expansion scheme, the location of the resonance is shifted towards higher energy. The authors' six-state (H(1s,2s,2p)+Ps(1s,2s,2p)) CCA calculation predicts resonance around 50.0 eV instead of around 20.0 eV as obtained by Hewitt et al using the same basis set.

The pseudo-potential Dirac equation is solved numerically. The authors closely follow the semi-empirical method proposed by Bottcher for the Schrodinger equation that can be applied without modifications to the Dirac equation. Besides a compilation of the main contributions to the pseudo-potential of a valence electron in an alkali atom, the differences between the two alternative ways to include the exclusion principle into the pseudo-potential are discussed in the context of the Dirac equation. The energies, calculated by the application of that version which was found to be most appropriate for the reproduction of the spectra of the alkali atoms, Li, Na, K, Rb and Cs, are tabulated together with the experimental data and the parameters specified by the developed semi-empirical method. It is found that, for each alkali atom, the complete spectrum can be reproduced by a single pseudo-potential with an accuracy better than 99%.

The non-relativistic spin polarized version of the random phase approximation with exchange has been used to calculate the positions and intensities of the resonances seen experimentally in the photoionization spectrum of Ca⁺, in the range 27-43 eV. Values for the oscillator strengths and energy positions for the main one-electron transitions have been obtained, and this information has been used to identify the most prominent features in the experimental spectrum. Tentative assignments are made for the remaining structure, probably due to two-electron excitations, extending the previous work in this respect by earlier authors.

A non-perturbative theory which is based on the three-dimensional gauge-invariant quasistationary state decay approach is developed to describe the non-resonant multiphoton ionization of real atoms. Using this approach, we are able to (a) solve a time-dependent Schrodinger equation for an atom-field system in a controllable approximation. Thus this leads us to (b) the possibility of describing non-resonant multiphoton processes which are straightforwardly treated in our formalism with none of the gauge difficulties sometimes encountered in previous approaches. Low-order low-frequency moderate-field approximations of the theory eventually reduce to results of earlier efforts, namely, the pioneering non-perturbative description of multiphoton ionization by Keldysh and refinements to it through partial consideration of atom-field interaction in initial state (Faisal, Reiss). Besides, (c) we can analyse the exceptional stabilization effect in a high-frequency superintense laser field. Our analytic high-frequency results provide a simple yet instructive extension to the weak-bound regime of ionization processes.

The Coulomb-Born approximation has been formulated for the capture of a single electron, initially bound to a two-electron atomic or ionic target of nuclear charge Z_T, by a fully stripped ion of nuclear charge Z_p. This approximation is applied in the post and prior forms to calculate total cross sections for electron capture by a proton from the ground state of the negative hydrogen ion. The obtained results are found to be in good agreement with experimental data for the inverse reaction H(1s) + H(1s) to H⁺+H^- in the energy region from 25 to 60 keV.

State-selective single electron capture in slow (0.5-3 keV amu^-1) collisions of He²⁺ with laser-excited Na*(3p) atoms has been studied by means of translational energy spectroscopy and the results compared with 64-state atomic orbital (AO) close coupling calculations, considering cross sections for electron capture into He⁺(n=3,4,5) final states for different impact energies. In addition, alignment effects have been studied by controlling the polarization of the exciting laser light. The experimentally observed dependence on Na*(3p Sigma ) and Na*(3P Pi ) initial state preparation is quantitatively reproduced by the AO calculations.

For pt. I, see ibid., vol. 26, p. 2137-51 (1993b). Single electron capture in collisions of slow (keV amu^-1) He²⁺ ions with aligned Li*(2p) atoms has been investigated by means of translational energy spectroscopy. A single mode cw dye laser beam has been modified by using an electro-optical modulator in order to pump both hyperfine ground states of Li simultaneously, thus maximizing the fraction of excited target atoms. Cross sections for electron capture from Li(2s), Li*(2p Sigma ) and Li*(2p Pi ) initial states into He⁺(n = 3 4, 5) final states have been determined for different impact energies and compared with 68-state atomic orbital (AO) close coupling calculations.

The theory of the circular polarization from the 3²D state is analysed and angular correlation formulae are derived for the scattered n = 3 electron and the cascade Lyman-alpha radiation. The formulae include allowance for the polarization of the intermediate-state 2p electron from the LS coupling in the time evolution of the decay of the collisionally excited n = 3²D states. The effect of a finite coincidence time window is also examined. The predictions of the model are compared with the model which assumes that the intermediate-state 2p electron is unpolarized. New experimental data at an incident electron kinetic energy of 54.4 eV are reported and indicate the circular polarization of the Lyman-alpha radiation has small negative values from 10 degrees to 120 degrees . The theoretical predictions of the correlation are illustrated in a six-state close-coupling model which gives a minimum at forward angles but does not agree quantitatively with the experimental data.

The second-order Born approximation (SBA) has been used to calculate the differential cross sections (DCS) and some electron-photon angular correlation parameters for electron impact excitation of the 2¹P state of the helium atom (He). Incident electron energies of 80, 100, 200 and 500 eV have been chosen. Our calculated values of the differential cross sections are in good agreement with the available experimental data and other approximations. In general the electron-photon angular correlation parameters are in poor agreement with the existing experimental data and other theoretical results.

An experimental study of the depopulation of Na 30s Rydberg atoms under electron bombardment has been carried out. Electron energies E ranged from 105 to 660 eV corresponding to collision velocities 80 to 200 times the mean orbital speed of the excited 30s electron. The collision-induced final states were identified by means of selective field ionization (SFI). 30p, 29p and a small trace of 28p were clearly observed in the adiabatic SFI distributions. Collision-induced diabatic SFI signals were absent, in contrast with a previous study that used slow ionic projectiles. 30s-30p and 30s-29p absolute cross sections were obtained from measurements of the collisional depopulation of the 30s state and measurements of the electron beam current-density-profiles. The cross sections ranged from 0.33 to 1.69 * l0^-10 cm². The results agreed with calculations based on the dipole approximation with first-order perturbation theory and the Born approximation. Cross sections were also measured in external electric fields up to 15.75 V cm^-1 for the higher collision energies (422 to 660 eV), but unlike the previous study no field dependence of cross sections for final-state distributions was apparent.

Calculations of intermediate energy electron scattering from the ground state of the potassium atom are performed using the unitarized distorted wave Born approximation. The target states (4s, 4p, 5s, 3d, 5p, 4d) of the potassium atom are calculated with a semi-empirical polarization potential added to the Hartree-Fock potential of the fixed core. Differential cross sections for elastic scattering and the 4s.

From the existing calculations of the hyperpolarizability, gamma , of Li 1s²2s ²S, it is evident that this quantity is very difficult to obtain reliably. The authors present a state-specific approach for the computation of linear and non-linear polarizability of polyelectronic ground or excited states and apply it to the prototypical He ¹S and Li ²S states. The problem is formulated as one of searching for the complex eigenvalue of a non-Hermitian matrix, H, constructed from multidimensional function spaces, Q and P, which are chosen according to the spectral features and electronic structure of the system under investigation. For example, in the present case, singly and selected doubly excited states are included, representing valence and core-valence electron correlation and field-induced excitations. On the other hand, for reasons of economy the pair correlation of the K-shell electrons in Li is neglected. The results, alpha (He) = 1.389 au, gamma (He) = 42.78 au and alpha (Li) = 164.9 au, gamma (Li) = 3.7 x 10⁴ au are compared with previous ones, obtained from methods using fixed basis sets or r_ij-dependent expansions. For gamma (Li), the observed discrepancy suggests that additional theoretical and certainly experimental information would be very useful.

For original paper, see Paquet et al., ibid., vol. 25, p. L95-100 (1992). It is shown that negative correlations between products of competing processes are always absent provided that the number of the parent particles fluctuates according to the Poisson distribution and the rest of the experimental conditions are kept constant. In particular no negative regions can be expected on covariance maps built from time-of-flight spectra of ions or electrons produced in multiphoton multiple ionization of atoms or molecules.

A response to the comment of Frasinski on the authors' previous work (J. Phys. B: At. Mol. Opt. Phys.25 L95) is presented.