H. Bachau

Applications of B-splines in atomic and molecular physics

One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.

Evidence for highly correlated electron dynamics in two-photon double ionization of helium

Experiments using new sources of XUV pulses now tackle the difficult problem of few-photon direct double ionization of atoms. Despite its apparent simplicity, the fundamental process of two-photon direct double ionization of helium is far from being understood. Here, we use a time-dependent approach to study the process. Our results for the electron angular and energy distributions demonstrate that the dominant mechanism for double-electron escape involves a highly correlated electron motion. Angular correlations strongly favour back-to-back electron emission along the polarization axis, while dynamical screening leads to an equipartition of the electron energy for a broad range of field frequencies. These features are reflected in the recoil-ion-momentum distributions that are presently accessible to experiments.

Attosecond timescale analysis of the dynamics of two-photon double ionization of helium

We consider the two-photon double ionization (DI) of helium and analyze electron dynamics on the attosecond timescale. We first re-examine the interaction of helium with an ultrashort XUV pulse and study how the electronic correlations affect the electron angular and energy distributions in the direct, sequential and transient regimes of frequency and time duration. We then consider pump-probe processes with the aim of extracting indirect information on the pump pulse. In addition, our calculations show clear evidence for the existence under certain conditions of direct two-color DI processes.

Reproducibility of observables and coherent control in molecular photoionization: from continuous wave to ultrashort pulsed radiation.

One-photon single ionization of molecules has been at the focus of several discussions concerning the reconstruction of observables obtained with ultrashort pulses from those obtained from continuous wave radiation (and vice versa). A related controversy on the conditions and observables that allow for coherent control in one-photon processes has been recently revisited (Science 2006, 313, 1257; J. Chem. Phys. 2010, 133, 151101). Our benchmark to investigate these issues is photoionization of the hydrogen molecule, where the autoionization events are the time-dependent processes in field-free evolution that could serve as a target for coherent control. We show that the variation of one-photon ionization probabilities with pulse duration are solely due to spectral effects and thus cannot be coherently controlled. We then discuss for which observables and under which conditions phase control of autoionization dynamics is possible.

Ionization of H- by a strong ultrashort laser pulse

We compare the outcome of two different numerical methods aimed at solving the time-dependent Schrodinger equation associated with the interaction of H- with an ultrashort laser pulse. These methods of spectral and configuration interaction type are based on an expansion of the total wavefunction on eigenstates of H- built as products of either B-spline or complex Sturmian functions. A careful analysis of our results together with a comparison with other existing theoretical data sheds some light on subtle aspects of the theoretical treatments of H- in a strong laser field. A particular emphasis is put on the crucial role played by the density of states in the continua.

Resonant and non-resonant ionization of helium by XUV ultrashort and intense laser pulses

We study the multiphoton ionization of He by a strong ultrashort laser pulse. We solve the time-dependent Schrodinger equation numerically by means of a spectral method of configuration-interaction type (CI). Our method is based on an expansion on B-spline functions, more precisely each two-electron configuration is built as an antisymmetrized B-spline product for the (two-dimensional) radial part and dipolar spherical harmonics for the (four-dimensional) angular part. We focus on both the atomic structure calculations and the laser-atom dynamics. We show that our approach allows one to properly treat the electron-electron correlations so as to provide an accurate description of many eigenstates simultaneously. The method is applied in two different situations: (a) the multiphoton excitation and ionization of helium with photon energies ranging from 5.4 to 32.6 eV and (b) the two-photon ionization of helium below the He+(2l) threshold and three-photon ionization above the He2+ threshold with photon energies ranging from 25.8 to 34 eV. The results are compared with other CI calculations (where a comparison is possible) and, in case (a), to Hartree-Fock calculations. In case (b) we particularly focus on the dynamics of the production of doubly-excited structure by laser pulses with a duration which is shorter than the autoionization lifetime.

Resonance parameters and properties of beryllium-like doubly excited states: 4 ≤ Z ≤ 10

The authors report and tabulate theoretical values for the energy positions and total and partial widths of singlet and triplet (even and odd) resonances of beryllium-like (Z = 4-10) systems lying above the 1s{sup 2}2p threshold. To complete the data and help with classification, the authors also include a table indicating the character of the closed-channel wave functions, as well as figures describing the variation of the resonance energies with (fractional) nuclear charge.

Electronic correlation effects in a model of endohedral Mg (Mg@C60)

We have studied theoretically the atomic structure and ground-state photoionization cross-section in a model of endohedral Mg (Mg@C60) with particular emphasis on doubly excited bound and autoionizing (AI) states. We modelled Mg@C60 as a system of two active electrons outside a frozen, doubly charged ionic core, confined to a spherically symmetric potential well of finite depth. We employed a suitable B-spline basis set within a CI approach to describe the two-electron states of the confined system. In addition, we have calculated the ground-state photoionization cross-section in a limited energy range above the first ionization threshold. We found that doubly excited perturbers appear in each regular singly excited Rydberg series of bound states. They are composed of two-electron configurations built with those one-electron orbitals mostly affected by the confining potential. Moreover, the low-lying part of the AI spectrum for each symmetry analysed is perturbed by states novel to the confined system, whose configuration expansion is again dominated by the one-electron orbitals mostly affected by the confining potential and whose AI widths vary over a wide range of values. Finally, the ground-state photoionization cross-section in a limited energy range (a few eV) above the first ionization threshold is structured by the AI resonances in a way markedly different from the corresponding Mg atom cross-section.

The role of autoionizing states in two-photon dissociative ionization of H2 by xuv ultrashort laser pulses

A theoretical study of two-photon ionization of H2 by low-intensity ultrashort xuv laser pulses is reported. The method is based on the solution of the time-dependent Schrodinger equation in a basis of stationary molecular vibronic states which include all electronic and vibrational degrees of freedom. In contrast with previous work, the doubly excited states, which also contribute to the ionization probabilities through autoionization, are explicitly included. We have found that, just below the one-photon ionization threshold, molecular autoionization leads to an enhancement of dissociative ionization, whose corresponding probability can be an order of magnitude larger than that of the nondissociative ionization process, and even larger than the corresponding dissociative probability in the one-photon absorption region. This result suggests that multicoincidence experiments, in which the orientation of the molecule with respect to the polarization axis is determined, might be easier to perform in the two-photon absorption regime than in the one-photon absorption regime. Electron angular distributions in the same range of photon energies are also reported.

Transfer and excitation in ion-atom collisions at high impact velocities: a unified continuum distorted wave treatment of resonant and non-resonant modes in a four-body approach. II. Application to the collision S15+(1s)+H(1s)

For pt.I see ibid., vol.25, no.4, p.825-37 (1992). Resonant (RTE) and non-resonant (NTE) transfer and excitation processes which occur in collisions of fast S15+ (1s) with H atomic targets, are investigated through a four-body continuum distorted wave approximation (CDW-4B) derived by Gayet and Hanssen (1992). The present application is a test of this new theoretical unified approach. Results are compared with previous theoretical and experimental data obtained with molecular targets for impact energies close to resonances. A first quantitative study of the interference between the two coherent processes is made using a model in which both the projectile and the target are hydrogen-like ions. For inner-shell capture from targets whose nuclear charge is comparable with the charge of the projectile, it is shown that interference effects might be significant, even at impact energies close to resonances.