Table of contents

The role of shake-off for double ionization of atoms by a single photon with finite energy has become the subject of debate. In this letter, we attempt to clarify the meaning of shake-off at low photon energies by comparing different formulations appearing in the literature and by suggesting a working definition. Moreover, we elaborate on the foundation and justification of a mixed quantum-classical ansatz for the calculation of single-photon double ionization.

The theory of angular distributions and angular correlations of photoelectrons and recoil ions in molecular photoionization is reformulated in terms of the density matrix and statistical tensor formalism, which incorporates a full multipole expansion of the radiation field. The dynamical parameters of the angular distributions are expressed in terms of the multipole photoionization amplitudes. Photoionization of linear molecules is analysed in more detail. New possible nondipole effects in the molecular photoionization are outlined.

Using a local effective potential to account for electron exchange, Drachman and Houston (1970 J. Phys. B: At. Mol. Phys.3 1657) analysed the zero-energy scattering of ortho-positronium by helium atoms in 1970. The idea was to use the existing static-exchange results to fit the parameters of the local potential and then to use the potential in a variational target-elastic calculation. The results were remarkably good, both for the scattering length and the annihilation parameter. Recently, however, a rigorous target-elastic calculation by Blackwood et al (1999 Phys. Rev. A 60 4454) disagreed so strongly with these old results that we have undertaken a re-examination. We find that the assumption made in the earlier work, that the direct potential is negligible compared with the exchange potential, is not quantitatively correct.

The R-matrix method is used to treat electron collisions with the diatomic radical CF as a function of internuclear separation, R. These calculations concentrate on obtaining low-energy (< 10 eV) elastic and excitation cross sections of the five lowest-lying electronically excited states of the symmetries X² Π, ⁴ Σ⁻, ² Σ⁺, ²Δ, ² Σ⁻ and ⁴ Π, with vertical excitation energies in the range of 2.86–10 eV. Special measures are required to treat ² Σ⁺, which is Rydberg-like for R < 2.6 a₀. Three shape resonances of ³Σ⁻,¹ Δ and ¹ Σ⁺ symmetries are fitted. The ¹ Δ and ¹ Σ⁺ resonances have a position of 0.91 and 2.19 eV respectively at the equilibrium bond length of CF. The position of the ³ Σ⁻ resonance is close to zero at R_e = 2.44 a₀ and the resonance becomes bound at larger R. Two weakly bound states of symmetries ³Π and ¹ Π were also detected at the equilibrium geometry. Calculations which stretch the C–F bond show that the ¹Δ resonance becomes bound at R = 3.3 a₀ and ¹ Σ⁺ at larger R.

The Compton scattering of a high energy photon by a helium-like ion, followed by the ionization of two electrons, is considered outside of the Bethe surface of Compton scattering with the knock-out of a single electron. The role of shake-off (SO), of final state interactions (FSI) and of the quasi-free mechanism (QFM) is analysed. The triple and double differential distributions are calculated. It is demonstrated for the first time that in certain kinematical regions the process is dominated by the FSI and by the QFM, while the SO contribution is much smaller.

Second-order non-linear optical properties and the ground state dipole moment of 2-, 6-, and 8-substituted dipyrromethene–BF₂ complexes were evaluated using ab initio quantum mechanical methods and compared with those of a standard push–pull chromophore. The theoretical values obtained are discussed in terms of the different contributions of each spatial region using the electron density derivatives with respect to an applied electric field. As results, an origin for the second hyperpolarizability and a methodology for improving the performance of these compounds are proposed. The two-level model has been use to study the electro-optic properties of the substituted dipyrromethene–BF₂ complexes, and the applicability of this method has been discussed in terms of the electron density derivatives.

We study the free expansion of a pancake-shaped Bose-condensed gas, which is initially trapped under harmonic confinement and containing a vortex at its centre. In the case of a radial expansion holding the axial confinement fixed we consider various models for the interactions, depending on the thickness of the condensate relative to the value of the scattering length. We are thus able to evaluate different scattering regimes ranging from quasi-three-dimensional (Q3D) to strictly two-dimensional (2D). We find that as the system goes from Q3D to 2D the expansion rate of the condensate increases whereas that of the vortex core decreases. In the Q3D scattering regime we also examine a fully free expansion in 3D and find oscillatory behaviour for the vortex core radius: an initial fast expansion of the vortex core is followed by a slowing down. Such a nonuniform expansion rate of the vortex core implies that the timing of its observation should be chosen appropriately.

An effective frozen core approximation has been developed and applied to the calculation of energy levels and ionization energies of the beryllium atom in magnetic field strengths up to 2.35 × 10⁵ T. Systematic improvement over the existing results for the beryllium ground and low-lying states has been accomplished by taking into account most of the correlation effects in the four-electron system. To our knowledge, this is the first calculation of the electronic properties of the beryllium atom in a strong magnetic field carried out using a configuration interaction approximation and thus allowing a treatment beyond that of Hartree–Fock. Differing roles played by strong magnetic fields in intrashell correlation within different states are observed. In addition, possible ways to gain further improvement in the energies of the states of interest are proposed and discussed briefly.

The paper gives three main results as follows. (1) An accurate quantum expression of the radial matrix element for radiative dipole transition between nearby Rydberg states. Its remarkable numerical accuracy is demonstrated over a very wide range of principal and orbital angular momentum quantum numbers covering low-lying states to very high Rydberg states. (2) A simple but accurate approximation to a class of terminating hypergeometric functions whose three arguments are large. This result essentially solves the problem of extracting analytic properties and performing numerical computations of such hypergeometric functions over a large range of values of the arguments which were earlier regarded to pose difficulties. (3) A derivation of the formula of the radial dipole matrix element of the correspondence principle method starting from the corresponding quantum expression, which, to the best of our knowledge, was not previously available in the literature.

Elastic, vibrationally inelastic and superelastic cross sections were measured for electron impact on CS₂ at 135°, with emphasis on the threshold region. The elastic cross section rises dramatically at low energies. The cross sections for the excitation of all three fundamental vibrations (010), (100) and (001) have very strong threshold peaks, more than ten times higher than those observed for CO₂. The elastic and the (010) and (100) inelastic cross sections have deep narrow structures at energies up to about 0.3 eV. The structures are weak for the (001) vibration. Substantial excitation of overtone vibrations is observed even near threshold. The threshold structures appear to be caused primarily by the ² Π_u valence state of CS₂⁻. Various broad resonant peaks are observed in the cross sections in the 1–12 eV range.

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross–Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose–Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge–Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank–Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

A new analytical method is presented here, offering a physical view of driven cavities where the external field cannot be neglected. We introduce a new dimensionless complex parameter, intrinsically linked to the cooperativity parameter of optical bistability, and analogous to the scaled Rabbi frequency for driven systems where the field is classical. Classes of steady states are iteratively constructed and expressions for the diffusion and friction coefficients at lowest order also derived. They have in most cases the same mathematical form as their free-space analogue. The method offers a semiclassical explanation for two recent experiments of one atom trapping in a high cavity where the excited state is significantly saturated. Our results refute both claims of atom trapping by a quantized cavity mode, single or not. Finally, it is argued that the newly constructed parameter as well as the groundwork of this method are at least companions of the cooperativity parameter and its mother theory. In particular, we lay the stress on the apparently more fundamental role of our structure parameter.

We report an electron momentum spectroscopy study of the two outermost orbitals of the dicarbonyls, glyoxal and biacetyl. The experiments were performed at impact energies of 800, 1200 and 1600 eV using a recently developed multichannel (e, 2e) spectrometer. The experimental momentum profiles clearly show remarkable variations in the low-momentum region with increasing impact energy. Furthermore, it has been found that the two molecules reach their high-energy limits at different impact energies, indicating that the range of validity of the plane-wave impulse approximation (PWIA) largely depends on the target in question. The results at 1600 eV are employed for comparisons with PWIA calculations using Hartree–Fock and density functional theory (DFT). While the DFT calculations reproduce well the observations for glyoxal, considerable discrepancies between experiment and theory exist for biacetyl.

We investigate degenerate quantum gases in one dimension, trapped in a harmonic potential which is split centrally by a point-like potential. Since the single-particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi–Bose mapping theorem. We calculate the exact many-particle ground state wavefunctions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well known physics of Bose gases described by the Gross–Pitaevskii equation. We also address the experimentally important questions of the creation and detection of such states.

Dielectronic recombination resonances of Ni¹⁷⁺ that form doubly excited states in Mg-like Ni were studied in the energy range up to 6.5 eV. We observed 3sεl → 3pnl, 3dnl (Δn = 0) resonances and a single 3sεl → 4s4p (Δn = 1) resonance in this energy region. A relativistic many-body perturbation theory calculation was performed to predict the positions and strengths of the resonances in this region. A comparison of the experimental data with the calculation yields an overall good agreement as regards the resonance positions and strengths. The discrepancies are predominantly theoretical underestimations of the rate coefficient. The 3s_1/2–3p_1/2 and the 3s_1/2–3p_3/2 energy splittings have been determined from the experiment.

We report evidence for the electron-impact excitation of doubly excited states in helium and H₂ which are stable against autoionization. By detecting only long-lived (metastable) excited neutral states created by near-threshold electron scattering our technique discriminates against directly excited metastable states and is highly sensitive.

We consider hydrogen and helium ionization with emission of soft electrons in high-velocity collisions with bare ions in the perturbative regime |Z_p|/v_p ≲ 0.1, where Z_p is the projectile charge and v_p the collision velocity. For such collisions it is usually assumed that the first-order approximation in the projectile–target interaction yields good results for single ionization. However, by performing calculations in the first and second Born, Glauber and CDW–EIS approximations, we show that higher-order effects can considerably influence electron emission already in the collision plane where the main part of the emission occurs. Moreover, the deviations from the first-order results become even stronger if the electron emission is analysed in the plane perpendicular to the momentum transfer. In this plane a pronounced structure appears in the fully differential cross section. This structure is different for collisions with Z_p > 0 and Z_p < 0 and the difference remains noticeable even for collisions with protons and anti-protons moving at velocities approaching the speed of light. It is also found that, on average, the higher-order effects are relatively more important for collisions with negatively charged projectiles. The deviations from first-order results for emission from hydrogen in the perturbative regime are attributed mainly to the projectile interaction with the hydrogen nucleus. In case of helium single ionization, our calculations suggest that a proper description of electron emission in the perpendicular plane may be very demanding with respect to the quality of the approximations for the initial and final helium states.

The 4p-subshell spectrum of Mo⁺ has been recorded, for the first time, in the wavelength range 500–200 Å. The spectrum is dominated by a 4p → 4d 'giant resonance' on which extensive discrete structure is superposed. With only one exception the discrete lines can be ordered into six Rydberg series, 4p⁶4d⁵⁶S _5/2 → 4p⁵(4d⁵⁶S)(⁷P)ns,nd (J = 3/2, 5/2, 7/2), converging on three limits, the Mo III levels 4p⁵(4d⁵⁶S)⁷P _4,3,2. The observed spectrum is analysed by comparison with both Hartree plus exchange with relativistic corrections and relativistic time-dependent local density approximation calculations. The evolution of the discrete structure line shapes interacting with the giant resonance is found to be in qualitative agreement with the theory of Connerade and Lane (1987 J. Phys. B: At. Mol. Phys.20 L181–6).

Electron-impact emission cross-sections of Kr were measured from the threshold to 1000 eV for the 5p → 5s transition in visible to near infrared regions and for the 5s → 4p resonance lines (116.49 and 123.58 nm) in the VUV region. The experiment was carried out at sufficiently low target pressure to ensure a single collision between an electron and an atom since previously published works show rather large scattering not only in the magnitude, but also in the energy dependence of emission cross-sections, probably because of high target pressures. Absolute emission cross-sections for resonance lines were obtained by normalizing relative cross-sections at effectively zero target pressure to that of hydrogen Lyman-α produced in electron impact of H₂. Level excitation cross-sections of the 1s₂ and 1s₄ states (Paschen notation) were obtained by subtracting the total cascade 5p → 5s cross-sections from corresponding emission cross-sections of the 116.49 and 123.58 nm resonance lines. Obtained results are compared with other experimental and theoretical data.

A quantitative theory of multiphoton detachment with excitation of the residual atom, A⁻ + Nω → A* + e, is developed. A fully quantum treatment explicitly casts the amplitude as a result of rescattering (or a three-step process), where the above-threshold detachment (ATD) is followed by continuum electron propagation in the laser field and subsequent excitation of the residual atom by laser-dressed electron impact. The contributions of all intermediate ATD channels add up coherently. All three stages of the process are described by simple expressions. The theoretical scheme is similar to that employed previously for the calculation of high harmonic generation and high-channel ATD by an intensive laser field. To illustrate the general approach, H⁻ detachment with excitation of the residual H atom into 2s and 2p states is calculated for various numbers of absorbed photons, N. The oscillations in the angle-differential rates are qualitatively similar to those already known for the conventional ATD process without atom excitation. The rates summed over photoelectron emission angles exhibit non-monotonous dependence on the number of absorbed photons and are also qualitatively similar to known ATD patterns.

A natural approach to measure the time of arrival of an atom in a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actual physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.

We report experimental results on slowing a light pulse in a system for amplification without inversion (AWI). We were able to control a subluminal group velocity continuously from V_g = c/2850 to c/7260 by just changing an incoherent pumping beam power from 0 to 12 mW in the AWI system. And several advantages, such as the controllable delay time and the pulse amplification, for slowing of the light in the AWI system compared to in an electromagnetically induced transparency system were found.

The available electron-impact ionization cross sections for Ti and Cr ions are reviewed, and calculations of the ionization balance for the ions under coronal equilibrium are presented. The calculated ionic abundance fractions are compared with those of previous works. The effects of modelling uncertainty in dielectronic recombination on isoelectronic line ratios, which are formed using the same spectral line from two elements of slightly different atomic numbers, are discussed concentrating on high temperature ranges. Also discussed are the effects of modelling uncertainty on inter-ionization stage line ratios formed from adjacent ionization stages. It is demonstrated that the modelling uncertainty in dielectronic recombination tends to cancel out only when the isoelectronic line ratio of He-like ions is considered, and that the sensitivity of the isoelectronic line ratios to the modelling uncertainty tends to increase for less ionized stages. It is also found that the interstage line ratios are less sensitive to the typical ∼20% uncertainties of dielectronic rates than the isoelectronic line ratios, and that the interstage line ratio of He-to Li-like ions in Ti and Cr plasmas is a better choice for a temperature diagnostic in the temperature ranges from ∼0.6 to ∼1.5 keV in which Li-like ions have maximum ionic abundances.