Table of contents

We consider the concept of atomic pressure for atoms subjected to quantum confinement. New scaling rules are introduced which allow the compressibility to be expressed as the product of two factors. The first is a term independent of compression, which varies widely from atom to atom, but can be computed in the free atom limit. The second is a term expressed in dimensionless variables, whose dependence on compression is in general nonlinear and may exhibit discontinuities. However, it is shown not to vary much from one atom to another and to follow general rules which are easily understood. We have performed fully relativistic ab initio calculations to illustrate these general rules of atomic compressibility, and we characterize the variation of atomic compressibility for both soft and hard atoms.

In `On the quantum mechanics of particles with classically assigned trajectories', Barton and Calogeracos (1996 Proc. R. Soc. A 452 1167) find that the wavefunction surprisingly acquires an overall phase factor of the form exp(+i∫₀^tE(t') dt'), surprising in that the conjugate was expected, with E the relative kinetic energy. It is shown that, with the correct interpretation in terms of electron translation phase factors, there is no surprise and the effect is well known experimentally and theoretically in charge transfer and ionization in ion-atom collisions.

In this paper we review the correlation function quantum Monte Carlo (CFQMC) method. We describe the functional forms and the optimization of trial basis functions used to treat the vibrational and rotational motions. We discuss selected applications to di-, tri- and tetra-atomic molecules. Our main goal is to discuss the potentiality of the CFQMC method in the study of rovibrational excited states of polyatomic molecules. In particular, we focus our discussion on the generation of the trial basis functions for ground and excited states, and the guiding function used to perform the multidimensional integral sampling required by the method.

The competition of stimulated Raman scattering (SRS) between 4S-(5P)-5S and 4S-(3D)-5S channels has been observed as a laser is tuned near the 4S-5P resonance in potassium vapour. The experimental results show that SRS only occurs in the 4S-(5P)-5S channel. In this Raman scattering, suppression of the amplified spontaneous emission (ASE) (5S-4P) has been observed. The influence of the four-wave mixing (FWM) processes on the SRS is discussed. In the 4S-(5P)-3D channel, in the backward direction no detectable emission corresponding to SRS (4S-(5P)-3D) has been observed, so the forward (5P)-3D emission should be FWM, not SRS. The ASE (3D-4P) arises from the ASE (5P-3D), which can be observed in the backward direction.

This paper presents experimental studies of resonant two-photon ionization of Mg via the 3s^2 1S₀→3s3p ¹P₁ transition using 285.2 nm CW light. Dimensionless ratios of the cross section for ionization into a continuum state of S character relative to ionization into a state of D character are extracted from data obtained in two independent experiments. We obtain the values 0.102±0.003 and 0.096±0.012, respectively, and compare these to current theoretical predictions.

The state-selective double-photoionization cross sections of the Ne III 2s²2p⁴ [³P,¹D,¹S], 2s¹2p⁵ [³P,¹P] and 2s⁰2p⁶ [¹S] states in the exciting-photon energy region from 60 up to 200 eV are calculated with the use of V^(N-1) and V^(N-2) potentials. To our knowledge, the basis of wavefunctions obtained with the use of the V^(N-2) potential is employed for the first time for the calculation of the total DPI cross section of a many-electron atom. The lowest-non-vanishing-order perturbation theory V^(N-2) cross sections are compared with V^(N-1) ones and with theoretical results of other authors. The obtained results show that the V^(N-1) potential overestimates and the V^(N-2) potential underestimates the experimental total DPI cross section of the L shell in Ne. The best agreement with experiment is achieved for the sum of the 2s¹2p⁵ and 2s⁰2p⁶ state-selective V^(N-2) velocity-form cross sections. The necessity of including the higher-order correlations, especially those responsible for singlet-triplet mixing of the final doubly excited states, is demonstrated and discussed.

We extend the method introduced recently by Korol for the approximate calculation of the compound relativistic free-free matrix elements. The method is based on the accurate treatment of the diagonal singularities in the one-photon relativistic matrix elements, which appear in the compound matrix element.

For the case of relativistic projectile scattering in the field of a short-range potential we present the evaluation of the singular parts of the free-free single-photon matrix elements. The result is used to treat approximately the amplitude of the two-photon bremsstrahlung (2BrS) process for the relativistic electron. This is done for the first time.

Plasma ionization composition and level population calculations require, in particular, the cross sections of direct ionization from each quantum state into each state which may be generated by means of removal of any electron. We analysed published data and propose here an empirical formula for cross sections of direct electron-impact ionization of positive atomic ions. The cross sections given by this formula are in satisfactory agreement with those calculated in the distorted-wave (DW) approximation; therefore, we believe that for any direct state-to-state ionization channel this formula provides a reasonably accurate prediction of the DW result. Comparisons with published data and with the Lotz formula are reported as well.

A comprehensive study of absolute differential cross sections (DCSs) for electron impact excitation of the bending (010) and unresolved stretching (100 + 001) vibrational quanta of water (H₂O) is reported. Eight incident electron energies (E₀) in the range 6-20 eV were investigated, and the scattered electron angular range was 10°-135°. Integral cross sections (ICSs) were derived from the corresponding vibrational DCSs using a molecular phase shift analysis technique. The self-consistency of these vibrational ICSs was considered by summing them, at each E₀, with available elastic and ionization ICS to provide estimates for the H₂O grand total cross section (GTS), which could then be checked against the independent GTSs of Szmytkowski (1987 Chem. Phys. Lett. 136 363) and Sueoka et al (1986 J. Phys. B: At. Mol. Phys. 19 L373). Good agreement was typically found.

The energy loss in the collision of a moving charged projectile with a free electron is described in a rigorous approach. The collision is treated as stationary scattering of an electron in the projectile Coulomb field. In the laboratory frame, the picture can be represented as a spatial distribution of energy losses to the electron. It has been shown that the local rate of the energy gain can be presented as a product of the induced electron current and the projectile electric field. The analytical results and numerical calculations reveal a principal disagreement with the generally recognized condition for the classical description, η = Z₁e²/ℏv≳1 (Z₁e and v are, respectively, the charge and velocity of the projectile): for any value of η, the quantum effects appear to be significant in the close vicinity of the projectile trajectory (small impact parameters) restricted by the distance ~λ = ℏ/mv. Essentially, the problem has been cleared in the qualitative analysis of collisions with electron wavepackets. The main results of the Bloch theory are reproduced in a simpler way. The clearer basis permits us to eliminate the ambiguity in the interpretation of the origin of the Bloch correction, which reflects in fact the evolution of the classical features in the quantum mechanical picture.

We present an exact analytic investigation of the electron dynamics in the field of two linearly polarized interfering copropagating laser beams of different frequencies, arbitrary intensities, and arbitrary relative polarizations. In one part of the paper, the laser fields are modelled by plane waves and in another part the fields are allowed to have one-dimensional sin² pulse shapes which model focusing in the propagation direction. The general situation in which the electron is injected at an angle with the common direction of wave propagation is considered throughout. A cycle-by-cycle analysis of the electron motion, and its momentum and energy exchange with the laser fields is conducted. It is found that an electron may be accelerated, even from rest, to GeV energies over short distances using present-day laser field intensities. This leads, in principle, to energy gradients in the TeV m^-1 range. The trajectory calculations also show clearly that the electron gets scattered away from its initial direction of motion during interaction with the laser fields. The transverse as well as longitudinal motions may be followed exactly using our equations, and predictions could thus be made concerning where the electron should, in principle, be ejected in order for it to emerge with a particular energy gain.

The dual laser plasma photoabsorption technique has been used to measure the time-resolved vacuum-UV photoabsorption spectrum of a chromium plasma. Resonant photoabsorption cross sections, constructed with the aid of Hartree-Fock calculations, and weighted in accordance with the plasma temperature, have been used to produce the synthetic Cr²⁺ spectra. The relevant plasma temperature and ionization balance are obtained from simple analytical models for various times during the expansion phase of the plasma plume. The experimental spectra taken at delays of 32, 62 and 90 ns compare well with Cr²⁺ spectra computed for corresponding predicted temperatures. It is found that in order to produce synthetic spectra that match experiment well, it is necessary to take into account absorption from many states belonging to the Cr²⁺ ground state configuration 3p⁶3d⁴, while states from the nearest metastable configuration 3p⁶3p³4s make a negligible contribution.

In this paper we describe polarization spectroscopy measurements of O⁵⁺(1s²3p ²P_3/2), following single-electron capture from He and H₂. A novel arrangement for measurements of the polarization degree has been developed to reduce the systematic error. These measurements are shown as a function of projectile velocity, which was varied from 0.34 to 0.55 au. A simple model for the results with H₂ is presented by considering the velocity dependence of capture cross sections for each 4l state and the cascade from 4l to 3p. However, for the case of the He target, no such simple model is found to be consistent with the experimental results.

Producing Ca⁺ and Sr⁺ ions by laser ablation of pure metal samples and detecting their laser induced fluorescences, cross sections of collision induced transitions between fine-structure levels in the 4p ²P_J state of Ca⁺ and the 5p ²P_J state of Sr⁺ due to collisions with He atoms at room temperature (298 K) have been measured. The cross sections determined are σ(Ca⁺: 4p ²P_3/2→4p ²P_1/2)= 1.17±0.05 Å², σ(Ca⁺: 4p ²P_1/2→4p ²P _3/2) = (7.92±0.44)×10^-1 Å² and σ(Sr⁺: 5p ²P_3/2→5p ²P _1/2) = (1.44±0.10)×10^-2 Å².

A theoretical study of the inelastic scattering of low-energy electrons from metallic clusters is presented. We calculate the total inelastic electron scattering cross section using the standard jellium model and the methods of quantum many-body theory. Many-electron correlations for collective excitations of the cluster target are taken into account within the random-phase approximation with exchange (RPAE). The polarization interaction between the projectile and the cluster electronic system is described using the Dyson equation. We report resonance maxima in the energy dependence of the total inelastic cross section in the energy region above the surface plasmon frequency. This resonance effect is connected with the process of electron capture to quasi-discrete levels localized in the field of the target cluster and simultaneous excitation of the surface plasmon. This process can explain experimentally observed resonance behaviour of the electron attachment cross section in the projectile energy range ε<5 eV. We present a detailed comparison with experimental data.

The mobility of ³He⁺ in ³He has been calculated at 2 and 4.35 K for E/N values up to 30 Td, where E denotes the electric field strength, N is the gas number density and 1 Td is 10^-21 V m². The best available potentials and kinetic theory have been employed and full account has been taken of the nuclear spin statistics. At the same temperature and E/N value, the results differed by no more than 5% from those for ⁴He⁺ in ⁴He when scaled by the square root of the mass ratios for the two systems. For ⁴He⁺ in ⁴He, comparison with recent measurements at 4.3 K by Tanuma et al shows agreement to within 6% for E/N values up to 15 Td.

We first test our recently developed relativistic coupled-cluster-based linear response theory (RCCLRT) by computing the principal and the shake-up ionization potentials (IP) of highly stripped atoms. Comparison is made between the IP values obtained from the relativistic and non-relativistic CCLRT calculations. The comparisons for light atoms, where the relativistic contributions are negligible, provide a test of the method, while comparisons for heavy atoms quantify the relativistic effect. For one-valence problems such as ionization processes, there is a formal equivalence between the principal IP values from the CCLRT and multi-reference coupled cluster (MRCC) theory when using the 1h-0p model space. The principal IPs obtained from the CCLRT are size-extensive, but the (2h-1p) shake-up IPs are not fully size-extensive, where the size-inextensivity error scales as the number of valence excitations. The computed valence and shake-up ionization energies via the RCCLRT approach are in excellent agreement with experimental data. The IPs computed using the non-relativistic CCLRT also match favourably well with the experiment only when the atomic number and ionic charge are small.

Transition energy calculations for low-lying states of Pb and Pb²⁺ by the four-component versions of the Fock-space RCC-SD and PT2/CI methods are reported. Contributions of valence and core electron correlation are studied in all-electron calculations with the Dirac-Coulomb Hamiltonian. The accuracy of our generalized RECP and the RECP of Christiansen and co-workers is tested. The consideration of only one- and two-body amplitudes for valence electrons in the RCC method for Pb is shown not to be sufficient to reproduce valence excitations within 100-300 cm^-1. Correcting RCC-SD results by estimated contributions of triple and quadruple excitations yields an accuracy of about 200 cm^-1.

The complex absorbing potential (CAP) method has been applied to compute the complex Stark eigenvalues of low-lying excited states of the hydrogen and the lithium atoms. As a relatively new technique, the method turns out to be a simple and powerful tool for the investigation of resonance parameters in polyelectronic atoms. Results for electric-field effects on the 3s, 3p, 3d, 4s, 4p, 4d and 4f states of Li are presented.

Excitation and ionization processes in collisions of atomic hydrogen with antiprotons () are studied in the energy range of 1-500 keV. A time-dependent Schrödinger equation is solved directly by using a discrete-variable-representation technique. For the electron radial coordinate, the numerical mesh is constructed from generalized Laguerre quadrature points. The Laguerre mesh is found to be numerically efficient, and is very useful to study the problems of ionization as well as electronic excitation.

Hydrogen atom-hydrogen atom scattering is a prototype for many of the fundamental principles of atomic collisions. In this work we present the formalism and the predictions of a time-dependent self-consistent-field description of the H + H system for scattering in the intermediate energy regime of 1-100 keV. Because of the unrestricted nature of the numerical orbital description, this method includes the effects of an unlimited basis set within each orbital. Electron exchange and a limited amount of electron correlation are included as well. We solve numerically coupled three-dimensional Schrödinger equations for the two-electron orbitals in singlet and triplet symmetries. Excitation and ionization cross sections are computed and compared with other theory and experiment. The results capture many features of the problem but illustrate a need for more quantitative experimental information concerning the H + H system in this energy range.

We report four odd-parity Rydberg series in the spectrum of europium atoms in the energy region 45 000-45 735 cm^-1. These four series belong to total angular momentum quantum numbers J = 5/2,7/2,9/2 and 11/2 and converge to the first ionization limit ⁹S₄. The studies were carried out employing the multistep resonance ionization spectroscopy technique using two pulsed dye lasers. For some of the Rydberg series we could observe the members up to n = 67. Different stepwise excitation-ionization schemes helped us to assign a unique J quantum number up to n = 39 and enabled us to separate the series with different values of J. The Rydberg series belonging to J = 5/2 was found to be quite unperturbed and was therefore used to evaluate the first ionization limit of the europium atom.

The relative photoabsorption cross-section of the Li⁺ atomic ion was measured using the dual laser plasma photoabsorption technique. The measurements were carried out in the photon energy range from 62 eV (1s2p discrete resonance) up to 190 eV, i.e. about two-and-a-half times the value of the first ionization potential (I₁ = 75.64 eV). In the continuum, the relative photoabsorption data (with an estimated uncertainty of ±14%) are normalized to the theoretical photoionization cross-section, given in analytical form by Verner et al (Verner D A, Ferland G J, Korista K T and Yakovlev D G 1996 Astrophys. J.465 487). Comparisons between calculated photoionization cross-sections and with relevant experimental data are presented.

Emission cross sections for hydrogen Lyman-α, -β, Balmer-α, -β, C(3s ³P_J'^o→2p²³P_J, 165.7 nm), C(2p³³D_J'^o→2p²³P_J, 156.1 nm) and He(2p ¹P₁→1s²¹S₀, 58.4 nm) produced in He⁺ + CH₄ collisions are measured in the energy range from 4 eV (cm) to 4000 eV (cm). The emission cross sections of hydrogen Lyman and Balmer series have a plateau above 100 eV. The cross sections of helium and carbon lines decrease rapidly with decreasing collision energy. The branching ratio when an excited hydrogen with n = 2 is produced is estimated to be 2.5×10^-2 at 4000 eV by using measured emission cross sections for H_α to H_ε and by empirical relations.

The intrinsic parameters β₁ and γ₁ were determined separately for the first time by explicit measurement of the angular distribution of the transferred spin polarization of Xe N₄O_2,3O_2,3 ³P₁ Auger electrons after primary excitation with circularly polarized light from the BESSY-II helical undulator UE56/1. The feasibility of a complete experiment for the Auger decay, i.e. extraction of Coulomb matrix elements from the experimental data, is discussed and reveals a new fundamental equation connecting the intrinsic parameters of Auger decay. An analysis procedure is performed, yielding a well confined solution space for amplitude ratios and phase shift differences.

We have computed thermally averaged rate coefficients for vibrational self-relaxation v = 1→0 of ortho- and para-H₂. The quantum mechanical, coupled channels method was employed, with bases which are adequate to ensure convergence of the results at the kinetic temperatures (T = 300 and 500 K) considered. Although the inclusion of excited rotational states of the perturber molecule leads to increases in the rate coefficients for vibrational relaxation, these increases are insufficient to reconcile the theoretical results with experimental measurements.

The emission spectrum of a single atom in a two-mode Jaynes-Cummings model including any form of nonlinearity of both the two-mode fields and the intensity-dependent atom-field coupling is studied. A general expression for the emission spectrum is given as an explicit function of any nonlinear terms presented in the model. The effects of the nonlinearities on the spectrum are demonstrated for several important examples. It is shown that features of the emission spectrum are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields. It is also found in an analytic way that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium and the initial two-mode field photon statistics can be counterbalanced in some special cases.

We have discovered a phase problem in the version of the R-matrix codes that was used to calculate the final state Ψ^- with the proper boundary conditions. While there is no effect on total cross sections, the triple-differential cross section graphs presented in our paper need to be corrected. The general tendency is a reduction of the binary peak and an increase of the recoil peak. The corrected results for the `3 + 2' and `1-HF' models are shown in figure 1, in comparison with the first-order and second-order results of Byron et al (1986) and with the experimental data of Müller-Fiedler et al (1985). Note that our revised results are in significantly better agreement with those of Byron et al (1986) and also with those from other calculations (see, for example, Bray and Fursa 1996) than the earlier predictions, particularly due to the increase in the recoil peak. Finally, we point out that the general conclusions given in our paper, regarding the effects of various approximations on the theoretical results, remain valid.

Figure 1. Triple-differential cross section for electron impact ionization of He(1s²) at incident energy/ejected energy/scattering angle combinations of 256 eV, 3 eV, 4° (top) and 256 eV, 3 eV, 10° (bottom) as a function of the ejection angle. (3 + 2)-state R-matrix (second order) ————; (3 + 2)-state R-matrix (first order) – – – –; 1-HF R-matrix (second order) - - - - - -; 1-HF R-matrix (first order) - -  - -  - -; second-Born results of Byron et al (1986) - · - · - · -; first-Born results of Byron et al (1986) ········; experiment of Müller-Fiedler et al (1985) . These results replace those given in figures 1 and 2 of Reid et al (1998).