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In recent years, novel techniques have been developed to achieve high laser field intensities by shortening the duration of the pulses after several stages of amplification (by first stretching and subsequently compressing mode-locked laser pulses). A laser system built according to these principles at Imperial College is described. It is capable of reaching powers of ~ 1018 W cm−2 in pulse lengths of about 1 ps. The availability of field strengths 10 to 100 times as strong as the field experienced by the electron of the hydrogen atom in the first Bohr orbit opens up a new regime in the study of the interaction between light and matter. In particular, several effects, characteristic of very strong AC fields such as "above threshold ionisation" (ATI) high harmonic generation, etc are observed. Examples are given and their implications for atomic physics are discussed. Although such effects are novel and interesting in their own right, an important question which arises is the extent to which they may reveal new characteristics specific to the atom under study. Alternative possibilities are that most of the atomic features (correlations, shell structure, etc) are swamped by the effects of the strong field, or else that the atom is ionised before the strong field regime can even be reached. Some account of the controversies surrounding this question is given, and the importance of the dynamics is stressed. A theory is described which accounts for multiphoton excitation and ionisation by pulses of intense laser light in a generalised Landau-Zener model within a dressed atom basis of Floquet states. Different regimes of the interaction are classified, and a semi-classical limit is illustrated using action-angle plots of the Poincare section. These reveal how excitation takes place across a separatrix between two modes of motion, and how the growth of chaotic trajectories near such a separatrix provides new paths leading to ionization. Our approach stresses the significance of the match between pulse rise time and the magnitude of the avoided crossings between dressed atom states for the atom or molecule concerned.

We present a theory of harmonic generation by a strongly driven atom within the framework of non-relativistic QED. The atom is assumed to possess a finite number N of levels and ionization is neglected. This atom is dressed by the driving field using a unitary time-dependent transformation. Within the quasistatic approximation this transformation is shown to lead from the bare to the Floquet atom. The interaction of the Floquet atom with the vacuum modes is derived and it is shown to give rise both to the high-order harmonic and to the hyper-Raman spectrum. In the case N=2 the spectrum of the light scattered into the vacuum modes can be evaluated analytically and it is shown to consist of two parts. Neglecting interference between these two parts, the first of them is the high-order harmonic spectrum displaying peaks at the odd harmonics of the driving field. The second part is the hyper-Raman spectrum which has finite bandwidth and which displays peaks at the even harmonics of the laser frequency, centred at the Stark-shifted natural atomic frequency. These two spectra partially overlap and they are discussed in various ranges of intensity of the driving field, both in the minimal coupling and in the multipolar scheme. The results support recent suggestions that the presence of the plateau is related to interference between the two spectra. The dependence of the high-order harmonic spectrum from the driving field intensity is found to be related to that of the hyper-Raman spectrum in such a way that when the former increases the latter decreases and vice versa. It is argued that this might help to explain the non-visibility of the hyper-Raman lines when the high-order harmonics are visible.

For pt.II see ibid., vol.26, no.13, p.1885-96 (1993). The authors employ the method developed in a previous paper for small systems-Be, LiH, H2-where full CI calculations are available for monitoring convergence of many-body perturbation theory. It is shown that divergent series, in particular for excited states, can be transformed into fast converging ones. In essence their method consists in performing infinite subsummations of perturbation series in order to improve convergence: coupling constants are redefined such that singularities are incorporated in a non-perturbative manner and remaining correlations can be expanded in a larger domain of the complex coupling constant plane. It is in this way that the notion of 'improved convergence' has a well defined meaning.

The theoretical background of schemes for accelerating convergence of Moller-Plesset-Goldstone perturbation theory is discussed. Aiming at practical applications the authors consider approximate formulations of the many-body theory of atoms and molecules in finite-dimensional Hilbert spaces. A key role is played by nearby singularities of energy levels and eigenfunctions considered as functions of a suitably chosen coupling parameter. Infinite subsummations in the perturbation series are performed such that the influence of these singularities is eliminated or, at least, sufficiently attenuated. The danger of double counting of diagrammatic contributions already included in these infinite subsummations is avoided by the very construction of the authors' scheme.

A non-perturbative scheme for the interaction of strong laser pulses with atoms and molecules is discussed and model calculations are presented. A semiclassical analysis leads to a clear-cut distinction of four categories of reactions. Separatrix crossing mechanisms, the dissolution of initial tori and classical adiabatic motion are seen to play a central role in a non-perturbative picture of interactions with strong laser fields.

Many-body perturbation theory (MBPT) based on Hartree-Fock and non-standard mean fields is employed to calculate the energy, the first and the second moments of Be and LiH. The results are compared with the 'exact' energy, etc obtained in a finite-dimensional model Hilbert space (full configuration interaction taken into account). The authors test the idea that part of the correlations calculated in a Hartree-Fock MBPT scheme can be simulated as mean field or low-order effects when non-standard mean fields derived in non-relativistic or relativistic quantum electrodynamics with non-standard gauges are employed to set up a systematic perturbation theory.

A basic mean-field theory for the interaction between several bound electrons of an atom and an intense electromagnetic field is presented. From it, the authors infer that simultaneous ejection of several electrons is to be seen as a zero-order process, i.e. as an independent quasi-particle reaction of dressed single-electron states and that the shell structure of the atom does not dominate the process. Indeed, even inner shell electrons can be ejected in this way, with comparable probability. Their conclusions contrast with those of other authors who have argued that complete shells tend to be blown off or that, as is the case in very low electromagnetic fields where single photon processes dominate, multiple ionization depends for its existence on the magnitude of electron-electron correlations. The authors estimate the turn-on time of the laser pulse required to observe simultaneous, multiple ionization.

Employing a (1+1)-dimensional model, we discuss non-perturbative methods for the description of the ionization of highly excited hydrogen atoms by a pulsed strong microwave field. We restrict our attention to high scaled frequenciesn3ω≧1 and show that the recently developed picture of Landau-Zener dynamics leads to a transparent explanation of prominent structures in the 10% ionization curve measured by Koch et al. in experiments using microwave cavities; these structures are predicted to depend on fringe field parameters in a systematic manner. Waveguide experiments are expected to yield qualitatively different results.

Relativistic mean-field equations are obtained by minimizing the effective energy obtained from the gauge-invariant energy density by eliminating electromagnetic degrees of freedom in certain characteristic nonlinear gauges. It is shown that by an appropriate choice of gauge many-body correlations, e.g. screening and three-body 'forces', can be included at the mean-field level. The many-body perturbation theory built on the latter is then expected to show improved 'convergence'.

The authors develop a mechanism for the selective excitation of molecular vibrational states by short strong laser pulses. This mechanism is based on constructive interference of Floquet states. A phase functional is constructed which allows the theoretical prediction of the parameters of optimal pulses. The role of anharmonicities of the molecular binding potential and their effect on the structure of the instantaneous Floquet states is clarified.

It is pointed out that quantum optics provides examples where the origin of geometrical phase factors can be investigated in two different ways. The first possibility relies on a line bundle in which the fibers over each base point in parameter space consist of Stark states, whereas fibers of Floquet states yield a second possibility. Both constructions are compared in some detail, and the Floquet bundle is found to offer distinct advantages.

Etude de la convergence de series de perturbation a n corps basees sur les champs moyens de Hartree g de Hartree Fock et de Hartree-Fock a echelons pour les modeles quantiques de l'atome de beryllium et de la molecule LiH

Etablissement d'une approche perturbative pour le calcul d'observables de systemes a n electrons inhomogenes qui incorpore un algorithme pour le choix d'une approximation optimisee d'ordre zero dans le sens que des perturbations d'ordre superieur convergent rapidement et d'une maniere controlee

The Schrodinger picture of Quantum Field Theory is taken as the general framework for the formulation of a relativistic many-body theory. The main emphasis is put on many-electron systems within the scope of Quantum Electrodynamics. Relativistic mean-field theories are discussed and a perturbative scheme is introduced. Hamilton's principle is proposed as a criterion for the construction of mean-fields which allow for optimisation. Criteria for the choice of the latter are discussed.

The authors calculated oscillator strengths for the principal series of the alkali atoms Li, Na and K from the g-Hartree equation. A mean field optimised by the procedure described in earlier publications is shown to yield a rapidly convergent expansion of the remaining correlation effects: the zero order already yields a substantial improvement over HF and DHF calculations and gives good agreement with experiment. It is noteworthy that the optimised g-Hartree single-particle potential for the excited states interpolates between purely V(N) and V(N-1) potentials.

Relativistic and non-relativistic mean-field theories are discussed in the framework of quantum electrodynamics. g-Hartree mean-fields are derived using methods of the steepest descent which yields semi-classical expansions as a generalisation of asymptotic expansions of classical analysis. Our applications of the g-Hartree theory of atoms show that, in the examples considered, correlations are efficiently suppressed.

We discuss general notions of the regularisation and renormalisation of ground-state observables in quantum field theory. We evoke a theorem by Ramanujan to introduce the concept of the cut-off independent parts of vacuum observables and discuss their measurement and methods for their calculation. The role of Atiyah-Patodi-Singer spectral invariants in determining the vacuum structure of relativistic matter fields is illustrated.

We discuss non-perturbative aspects of the Floquet picture for the interaction of single mode strong laser fields with electrons. In numerical studies we show that this system stays adiabatic to a surprising degree: for smooth pulses, adiabaticity holds even for very short pulse-length (down to the order of 10 cycles) except for transitions at avoided crossings sharply located in time. The latter are seen to act as interferometers, a non-adiabatic pumping mechanism is proposed. Non-perturbative aspects of multi-photon transitions are clarified.

The authors analyse the atomic many-body effects associated with single-electron excitations within the g-Hartree framework: g values are determined which exactly reproduce inner- and outer-shell ionisation energies for the whole periodic table. Average g values are then used to compute physical observables for several channels within a mean-field analysis. The results obtained, particularly for large-Z atoms, give excellent agreement with experiment.

The general significance of adiabatic motion on quasi-energy surfaces for microwave ionisation of excited hydrogen atoms is investigated. It is shown that non-monotonic structures in the ionisation signal can be traced to near-degeneracies of coarse-grained quasi-energy surfaces of a few effective states. Further experimental implications are discussed.

Brillouin-Wigner perturbation theory, formulated in the Schrodinger picture of quantum field theory, is employed to derive a perturbative scheme for the scattering matrix for photoionisation and electron scattering reactions on atoms. It is important to note that the intermediate states appearing in this series are physical, i.e. fully correlated, eigenstates of the total Hamiltonian. The scheme is amenable to numerical analysis: The key point is the use of an “energy-optimised”g-Hartree basis which yields an efficient treatment of atomic correlations and makes Brillouin-Wigner and Rayleigh-Schrodinger perturbation theories coincide.

It is pointed out that generalized Atiyah-Patodi-Singer η-invariants naturally appear in the thermodynamic potential describing the equilibrium properties of a localized system of relativistic interacting fermions. Under circumstances to be specified, externalU(1) gauge fields induce oscillating charge distributions which should be experimentally detectable for strong Coulomb fields produced by highly stripped large-Z atoms. Casimir energy shifts result be the same mechanism.

By explicitly introducing degrees of freedom for the electromagnetic field into the Hamiltonian for an N-electron system, we propose a variational procedure leading to mean fields different from the Hartree-Fock field. We show that g-Hartree equations result if the electromagnetic field is assumed to be in a coherent state. Since the solutions of these equations, the g-Hartree orbitals, are derived from a variational ansatz more general than the Hartree-Fock functional, we expect them to be particularly suitable to furnish a single-particle basis set for fast converging configuration interaction (CI) calculations. We report configuration interaction studies on the water molecule in a double zeta basis set employing various single-particle basis set transformations for the construction of the configuration state functions and investigate the convergence behaviour of the CI expansion explicitly. We find that the expansion in terms of g-Hartree orbitals receives substantially larger fractions of the total correlation energy in the case considered, if single excitations with respect to the mean field configuration are retained in the CI procedure.

A novel many-body approach, developed recently for atoms (the g-Hartree method), has been applied to the critical double-well problem in Ba+. A significant improvement over earlier ab initio approaches is demonstrated and correlations are shown to have a large effect. A correct choice of g leads to simultaneous agreement between theory and experiment for three different classes of data, namely, quantum defects, intensity variation and the spin-orbit splitting.

For pt.II see ibid., vol.15, p.4315 (1982). Relativistic and non-relativistic g-Hartree calculations of correlation energies for first-row atoms are presented. A discussion of the connection of various mean-field approaches is given.

For pt.I see ibid., vol.15, no.23, p.4293 (1982). The one-parameter non-uniqueness of stationary electron configurations in atoms can be used to single out a mean-field equation yielding the exact total energy. This equation is Hartree-like and contains exchange terms with a strength parametrising electron correlations, radiative corrections and further perturbative contributions. A numerical study of this equation is presented for the relativistic case.

For pt.IV see Physica, vol.131, A, p.363 (1985). The g-Hartree method is adapted to the direct ab initio calculation of transition energies in atoms. For the elements He (Z=2), Li (Z=3), Be (Z=4), Ne (Z=10), Mg (Z=12) and Ar (Z=18) all ionisation energies have been computed and found to agree with available experimental data within the computational errors. The systematic aspect (which is a truly second-order determination of the optimal mean field and contains no semi-phenomenological partial-summation prescriptions such as the self-energy summations in the Schwinger-Dyson approach) is emphasised and is shown to match experimental data significantly better than second-order (in the same strict sense) Brueckner-Hartree-Fock calculations. A detailed comparison of the method with other published approximation schemes shows a systematic improvement over the results obtained in conventional many body theories.

Relativistic g-Hartree equations are derived. Negative energy (Dirac sea) states enter. Their renormalised contributions can be interpreted as Casimir-like energy shifts in the total energy of atoms. The use of optimised g parameters leads to their unambiguous determination. The effect should be particularly important for large Z (Ze2 to 1) and relatively small N, the number of electrons, if transitions between distant configurations, e.g. transitions from the ground state to Rydberg states, are considered. For simplified numerical computations approximate g-Hartree equations are proposed in which Dirac sea contributions are treated in a Thomas-Fermi version.

Siegert's representation (1960) for the grand canonical partition function of a fermion system with two-particle interactions serves as a starting point for a perturbation expansion around stationary points. It is shown that, in general, the latter are given by solutions of the time-independent Hartree equation. Introducing more general random fields, exchange terms are obtained in the stationarity equation. The procedure is extended to relativistic systems. A perturbative expansion for e.g. the ground-state energy of the N-particle relativistic bound-state problem is obtained which allows, contrary to 'Hamiltonian methods', a straightforward application of standard regularisation and renormalisation procedures.

In the present paper we start from the Mandelstam representation for πN scattering and give equations for the partial-wave amplitudes which differ from similar relations by CGLN in the following ways:a) the projection on the partial-wave amplitudes is carried out excatly;b) the dependence on the nucleon mass is also taken into account excactly;c) CGLN consider only the contribution of the first πN resonance to the dispersion integral. We avoid a large part of this approximation by subtracting the (J=T=1) π+π→N+N amplitude which can be computed approximately from the ϱ-resonance data and the total πN cross-sections. The accuracy of the method is tested quantitatively by comparison with the forward scattering dispersion relation.S, P, D πN partial waves are calculated.S-waves up to about 100 MeV can be predicted practically without fitting free parameters. The predictions should hold fairly well up to about 200 MeV.

In the photoproduction of pions (neutral and positive), there are large differences between the calculated Born cross sections and the experimental data which cannot be accounted for only by the resonance terms. It is known that there exists a large non-resonant effect of the final state interaction which partially compensates the magnetic Born term in the case of the neutral pion. It is not definite that the effect is small compared with the second order multipole transition because of the magnetic term. In order to demonstrate that the same term is responsible for the compensation, the angular distribution for the neutral pion is calculated. It is shown that the magnetic Born term is essential to the production amplitade. In the case of positive pion production the magnetic Born term is smaller, but there seems to exist a similar compensating effect, because the electric Born term alone represents the general behavior of the non-resonant part of the amplitude. (N.W.R.)

Using a previously introducedK-matrix model, differential cross-sections and decay distributions are calculated and compared to the experimental results for 3 GeV/c K+p reactions. Good agreement is found for all measured quantities of two-body inelastic reactions and for the cross-section of three- and more-particle production. The calculated elastic cross-section agrees in shape, but is too big by a factor of eight.

The structure of quasi-energy surfaces, i.e. of quasi-energies as functions of external parameters like the laser frequency, laser intensity, atomic distances etc., is discussed and avoided crossings are traced to the existence of diabolical points at the origin of doublecone structures. The notion of non-contractable closed loops produces non-trivial Berry-phases. We then consider the interaction of atomic or molecular systems with relatively short smooth pulses and find that avoided crossings and, hence, diabolical points essentially, dominate non-adiabatic effects; away from avoided crossings the system evolves adiabatically in Floquet states, phases picked up during this motion lead to a new interference phenomenon which we study numerically in an appropriately simplified model. A scenario for the measurement of Berry phases is proposed which is linked to this interference in an essential manner; its eventual feasibility stems from the fact that at least two external parameters can be freely tuned in laser-atom (molecule) systems.