Table of contents

A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electron-impact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schrödinger equation, for L ⩽ 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources.

Recent experiments (Jia et al 2003 J. Phys. B: At. Mol. Opt. Phys.36 L17 and 35 1103) have measured the relative double ionization cross sections of argon at an incident energy of 561.4 eV and the measurements do not agree with first-order plane-wave Born approximation (PWBA) calculations. A new approach to this problem has been developed which uses distorted waves (DWBA) in a first-order approach rather than the plane waves inherent in first-order PWBA. The calculations based on this approach provide better agreement with the experiments.

Based on the quantum defect theory, the broad enhancement phenomena above threshold with one-electron character in the photoabsorption and photoionization cross sections of small molecules are divided into two types: shape resonances and non-resonance enhancements. Using the multi-scattering self-consistent-field method, both of them are assigned in the partial photoionization cross section of CO.

We calculate analytically the error introduced by the rotating-wave approximation (RWA) to the description of a two-level-atom response to a resonant sufficiently intense femtosecond optical pulse of a few-cycle duration and any envelope. The analytically calculated non-RWA refinements to the RWA response are of the lowest order, i.e., linear in the small ratio of the Rabi to optical frequencies. One type of such refinements is small-amplitude rapid oscillations at nearly twice the optical frequency superimposed on the standard RWA population-inversion evolution. The other refinement is an extension of the spectrum of the induced atomic dipole moment in which the third harmonic of the transition frequency appears. The spectrum of this harmonic has an internal structure dependent on both strength and duration of the pulse. The analytically found non-RWA corrections are in qualitative agreement with the recent results of different numerical approaches by other authors and a recent experiment.

The dynamic process of laser-induced alignment in Coulomb explosion of N₂ has been studied using linearly and circularly polarized, 800 nm, 40 fs Ti:sapphire laser pulses at intensities of 10¹⁴ to 10¹⁶ W cm⁻². The fragment ions produced were observed for the different polarizations with an equal E-field along the detection axis. The intensity-dependent ratio of fragment ion signals has shown that the 40 fs pulses can never align the molecules during the ultrafast interaction at an intensity less than ∼10¹⁵ W cm⁻², and the dissociative molecular ions start to be aligned at higher intensity. The degree of alignment is increased with an increase in the charge of the dissociative molecular ions.

We test the multi-configuration time-dependent Hartree–Fock method as a new approach towards the numerical calculation of dynamical processes in multi-electron systems using the harmonic quantum dot and one-dimensional helium in strong laser pulses as models. We find rapid convergence for quantities such as ground-state population, correlation coefficient and single ionization towards the exact results. The method converges, where the time-dependent Hartree–Fock method fails qualitatively.

In the present paper we consider a nonlinear interaction between two electromagnetic field modes and a two-level atom. A new Hamiltonian model is introduced to represent such an interaction, where three coupling parameters are involved. We assume that the two-level atom interacts with each mode separately as well as with the two modes nonlinearly. Thus degenerate and non-degenerate processes are considered. Using a suitable canonical transformation and integrability condition the system is reduced to a single mode case. The density matrix is calculated and used to study the photon distribution, the atomic occupation probabilities, the von Neumann entropy and the entropy squeezing.

We present a thought experiment, based on recent experimental achievements, to manipulate the preparation of two Gaussian wave packets in collision at a specified relative speed. We establish the equations describing the collision dynamics in terms of centre-of-mass and relative coordinates. We show that, for cold collisions, there is always an effective classical time evolution giving the same asymptotic Wigner function as that obtained from the quantum scattered wave packet.

Differential, integral and momentum transfer cross sections for the vibrationally elastic and rotationally inelastic scattering of electrons from water at low collision energies (E < 7 eV) are reported. The R-matrix method is used to compute the body-fixed T-matrices while the scattering calculations are performed within the fixed-nuclei approximation corrected with the standard Born-closure formula. Our calculations are compared with the very recent experimental results of Cho et al (2003 Radiat. Phys. Chem.68 115). The differential and momentum transfer cross sections are in good agreement with the experimental results. The relative contribution of the rotationally inelastic processes is investigated in some detail. In particular, the importance of the pure elastic process at very low energy is emphasized.

We have measured the scaled-energy absorption spectra of argon Rydberg states in a uniform electric field. The experiment utilized laser spectroscopy from the metastable 4s[3/2]₂ state in a fast atom beam. The scaled absorption spectra are Fourier transformed to obtain recurrence spectra that allow semiclassical analysis. Argon recurrence spectra reveal bias towards populating downhill-oriented classical trajectories and show large-scale modulations. A quantum calculation indicates that the asymmetric trajectory distribution is caused by the large p-quantum defect and that d–f excitation from the initial metastable state is influential in shaping the observed oscillations in the recurrence maps. The analysis serves to highlight the correspondence between quantum oscillator strengths and classical orbits.

A generalization of the continuum distorted wave eikonal initial state (CDW-EIS) approximation, for the description of single-electron capture in ion–atom collisions involving multielectronic targets is presented. This approximation is developed within the framework of the independent electron model taking particular care of the representation of the bound and continuum target states. Total cross sections for single-electron capture from the K-shell of He, Ne and Ar noble gases by impact of bare ions are calculated. Present results are compared to previous CDW-EIS ones and to experimental data.

The closed form of the second-order energy shift for the discrete spectrum of atomic hydrogen is obtained, which allows us to evaluate the level shift in both cases, when the intermediate states are in continuum and in the discrete spectrum, except the resonances. The values of the second-order shift of the energy of the ground state calculated by us are in good agreement with those obtained by us and other authors using the nonperturbative Floquet method in average up to a radiation intensity of 10¹⁵ W cm⁻².

The lowest-order interelectron interaction corrections to the hyperfine structure intervals for the 2p_3/2 state in Li-like, B-like and N-like ²⁰⁹₈₃Bi ions are calculated. The contributions of the magnetic dipole, electric quadrupole and magnetic octupole moments are included. The 'dynamical' model of hyperfine interaction is employed, where the electron is assumed to interact with the valence proton in the ²⁰⁹₈₃Bi nucleus via the exchange of a virtual photon. Within this model the magnetic and electric moment distributions inside the nucleus are taken into account simultaneously.

The photodetachment of the ^∞H⁻, T⁻, D⁻, ¹H⁻, Mu⁻ and Ps⁻ ions by low-energy photons is considered in terms of the two-body cluster approximation. For all considered systems the constant C in the asymptotic form of the actual three-body wavefunction is determined from highly accurate, completely non-adiabatic wavefunctions. This constant plays a central role in this method, since it allows one to determine the photodetachment cross-sections for each of the considered ions. The computed photodetachment cross-section for the ^∞H⁻ and Ps⁻ ions agree quite well with the results of earlier studies. The photodetachment of the T⁻, D⁻, ¹H⁻ and Mu⁻ ions with finite nuclear masses is also considered. The photodetachment of the H⁻ ions is of great interest in astrophysics, since it determines the continuous spectra of our Sun and, in general, of all K-, G- and late F-type stars.

The study of the isotope shift in the electron affinity is interesting for probing correlation effects. Experiments that allow this property to be measured are rare, being difficult to realize, while accurate calculations remain a challenge for atomic theory. The present work focuses on the theoretical estimation of the isotope shift in the electron affinity of Be (2s2p ³P^o), using correlated electronic wavefunctions obtained from multiconfiguration Hartree–Fock and configuration interaction variational calculations. The reliability of the correlation models is assessed from a comparison between the observed and theoretical electron affinities, and between theoretical isotope shift values for the 2s2p ³P^o 2s²¹S transition of neutral beryllium. The sign and the magnitude of the difference between the mass polarization term expectation values obtained for the neutral atom and the negative ion are such that the resulting isotope shift in the electron affinity is 'anomalous', corresponding to a smaller electron affinity for the heavier isotope.

A detailed treatment is introduced to measure the dynamic stability of the relativistic electrons in a self-amplified spontaneous emission free-electron laser (FEL) system, which includes the numerical approach of the Kolmogorov entropy (entropy-like quantity), the general equations of motion for a charged particle and the method of monitoring the simulation accuracy. Numerical experiments reveal a new phenomenon that there exists the possibility of the transition from chaotic to non-chaotic phase-space trajectories of the strongly relativistic electrons due to the effect of their self-fields. The adiabatic magnetic field of a one-dimensional wiggler may have a slight influence on the electron transportation in the absence of the FEL fields, but substantially affects the dynamic stability of the electrons in the process of the FEL interaction. Moreover, the laser fields diminish the dynamic stability of the electrons as the FEL interaction grows exponentially.

We have previously published a non-relativistic generalization of the non-perturbative polarized-orbital method which can be used to calculate long range polarization potentials for electron and positron scattering from atomic systems. Here we present a relativistic version of this method which is designed for heavy atomic systems with large polarizabilities such as caesium or the excited states of xenon. The detailed formulae are based upon the representation of atomic states by Dirac–Fock wavefunctions.

The one-electron relativistic diatomic systems H⁺₂ and Th¹⁷⁹⁺₂ are solved in a two-spinor linear combination of atomic orbitals (LCAO) approach using a minimax principle equivalent to a constraint minimization. The values are in agreement with those of the finite element method (FEM) and of other approaches as far as results are available in the literature. No spurious or contaminated states are found. The complete spectrum for Th¹⁷⁹⁺₂ up to n = 6 correlating s_1/2 to h_11/2 states is given.

B-spline methods are now well established as widely applicable tools for the evaluation of atomic and molecular continuum states. The mathematical technique of exterior complex scaling has been shown, in a variety of other implementations, to be a powerful method with which to solve atomic and molecular scattering problems, because it allows the correct imposition of continuum boundary conditions without their explicit analytic application. In this paper, an implementation of exterior complex scaling in B-splines is described that can bring the well-developed technology of B-splines to bear on new problems, including multiple ionization and breakup problems, in a straightforward way. The approach is demonstrated for examples involving the continuum motion of nuclei in diatomic molecules as well as electronic continua. For problems involving electrons, a method based on Poisson's equation is presented for computing two-electron integrals over B-splines under exterior complex scaling.

The effects of spin–orbit induced interchannel coupling on the dipole photoelectron angular asymmetry parameter β_3d for Xe, Cs and Ba are explored using a modified version of the spin-polarized random phase approximation with exchange (SPRPAE) methodology. For Xe, is modified somewhat by the interchannel coupling in the vicinity of the 3d_3/2 → f shape resonance, and this effect is significantly more pronounced in Cs where the resonance is larger. In Ba, however, where f-wave orbital collapse has occurred, the shape resonance has moved below threshold and the effect of interchannel coupling on above the 3d_3/2 threshold is negligible. But below the 3d_3/2 threshold, is dominated by the huge broad 3d_3/2 → 4f resonance.

Rates of the electric-dipole forbidden transition in the ground configuration of Cl-like ions of Co, Ni and Cu have been measured optically at a heavy-ion storage ring. Besides testing theory and providing benchmark data for these ions, the data by isoelectronic extrapolation pertain to the Fe X spectrum of high solar interest, for which so far theory and experiment have disagreed.

The authors have detected a mistake in one of the printed figures in the above paper. Please see the PDF file for more details.

Some errors have been detected in the above paper. In particular, in table 2 the headers of the first three columns should be K, L, M, while the headers of the next three columns should be n₁, n₂, n₃, respectively. In the hypergeometric function shown in equation (20) the third argument must contain +4, rather than +3. In table 3 the used values of real parameters were a = 2.5, b = 2, c = 1.5 and d = 1. Furthermore, to evaluate the four-body (or three-electron) integrals of lowest order we have developed an alternative approach. In the lowest order three-electron integrals at least one of the n₁, n₂ and n₃ parameters equals -1 (and all of them are odd). The approach is based on the Remiddi formula [1] and allows one to produce closed analytical expressions for all such integrals. The numerical values obtained with these formulae for the first and second integrals in table 2 differ slightly from the presented result values. For instance, the new value for the first integral is '...282 100 113 999 4...' (all 19 digits before '100' coincide with the result shown in table 2). Analogously, in the second integral in table 2 the first 32 digits coincide exactly with the new (i.e. Remiddi-based) value. Starting from the 33rd decimal digit the Remiddi-based value is '25 221 389 892 711 866'. The reason for such deviations is not quite clear and is currently under investigation. We are probably dealing with some unknown instability of the Perkins formula for lowest order four-body (or three-electron) integrals. It was also found that this instability disappears rapidly when the n₁, n₂, n₃ parameters grow.

References

[1] Remiddi E 1991 Phys. Rev. A 44 5492