Table of contents

The hydrogenic energy level shifts of a Dirac lepton due to the finite size of the nucleus are developed as a double power series in nuclear/atomic size ratio R and (squared) fine structure constant α². The method relies on matching small and large radius solutions and is much simpler than the perturbation approach of Friar (1979 Ann. Phys.122 151). Seven terms are obtained for nS_1/2, six for nP_1/2 and four for nP_3/2. Analytic expressions are given for the standard uniform, Gaussian and exponential models; also numerical values for various toy proton models that approximate the proton electric form factor reasonably well.

High resolution x-ray spectroscopy has revealed a complex structure in the spectrum of core-ionized elements. To date, theoretical reproductions must be fitted to experimental results using fitting parameters to account for transition widths, energy corrections, spectator intensities and spectator broadening—up to 12 or more parameters depending on complexity. We provide here the first accurate reconstruction of the Kα spectra in titanium using only instrumental broadening widths as free parameters. We also determine structural systematics in observed shake processes in transition metals for the first time.

Anion production cross sections in collisions between C_n⁺, C_n carbon clusters (n ≤ 5) and helium atoms have been measured in high-velocity collisions (v = 2.25 and 2.6 au). This paper focuses on two of the three processes responsible for the C_n⁻ production, namely double electron capture (DEC) onto C_n⁺ cations and single electron capture onto neutral (SECN) C_n. They were experimentally distinguished from a gaseous thickness dependence study. Dissociative and non-dissociative cross sections were measured and, in the case of DEC, all dissociative branching ratios measured; for these small systems, the C₂⁻ fragment was found magical. Data concerning electron capture in neutral–neutral collisions are extremely rare, especially at high velocity. Introduction of this measured process in the independent atom and electron (IAE) model allowed us to revisit and satisfactorily reproduce the so-far unexplained size evolution of single electron capture (SEC) cross sections in 2.6 au C_n⁺–He (n ≤ 10) collisions (Chabot et al 2006 J. Phys. B: At. Mol. Opt. Phys.39 2593–603). IAE calculations for DEC cross sections and their comparison with experiment suggest a loss of electron in anionic C_n⁻ species after the collision, competing with fragmentation and depending on the size.

A hyperspherical Sturmian approach recently developed for three-body break-up processes is tested through an analytically solvable S-wave model. The scattering process is represented by a non-homogeneous Schrödinger equation in which the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wavefunction and a bound state in the particles' coordinates. The model contains most of the difficulties encountered in a real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behaviour, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed so as to include the correct asymptotic behaviour, a very fast convergence of the scattering wavefunction is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This holds true down to very low energies, a domain which is usually challenging as it involves huge spatial extensions. Within our method, such calculations can be performed without increasing significantly the computational requirements.

Electron impact excitation of the (4p⁵5s²)²P_3/2,1/2 and (4p⁵4d5s)⁴P_1/2,3/2,5/2 autoionizing states in rubidium atoms was studied experimentally by measuring the ejected-electron excitation functions and theoretically by employing a fully relativistic Dirac B-spline R-matrix (close-coupling) model. The experimental data were collected in an impact energy range from the respective excitation thresholds up to 50 eV with an incident electron energy resolution of 0.2 eV and an observation angle of 54.7°. Absolute values of the excitation cross sections were obtained by normalizing to the theoretical predictions. The observed near-threshold resonance structures were also analysed by comparison with theory. For the ²P_3/2,1/2 doublet states, a detailed analysis of the R-matrix results reveals that the most intense resonances are related to odd-parity negative-ion states with dominant configurations 4p⁵5s5p² and 4p⁵4d5s6s. The measured excitation functions for the ²P_1/2 and ⁴P_J states indicate a noticeable cascade population due to the radiative decay from high-lying autoionizing states. A comparative analysis with similar data for other alkali atoms is also presented.

We review and critically evaluate our proposal of a pulse amplification scheme based on two Bose–Einstein condensates inside the resonator of a mode-locked laser. Two condensates are used for compensating the group velocity dispersion. Ultraslow light propagation through the condensate leads to a considerable increase in the cavity round-trip delay time, lowers the effective repetition rate of the laser, and hence scales up the output pulse energy. It has been argued recently that atom–atom interactions would make our proposal even more efficient. However, neither in our original proposal nor in the case of interactions, were limitations due to heating of the condensates by optical energy absorption taken into account. Our results show that there is a critical time of operation, 0.3 ms, for the optimal amplification factor, which is of the order of ∼10² at effective condensate lengths of the order of ∼50 μm. The bandwidth limitation of the amplifier on the minimum temporal width of the pulse that can be amplified with this technique is also discussed.

In this paper, we propose an efficient scheme to drive three atoms in an optical cavity into a singlet state via adiabatic passage. Appropriate Rabi frequencies of the classical fields are selected to realize the present scheme. The scheme is robust against deviations in the pulse delay and laser intensity through some simple analysis of the adiabatic condition. It is notable that the estimated range of the effective adiabaticity condition coincides with the numerical results. When taking dissipation into account, we show that the process is immune to atomic spontaneous emission as the atomic excited states are never populated in adiabatic evolution. Moreover, under certain conditions, the cavity decay can also be efficiently suppressed.

Recently, geometric phases of nonlinear coherent and squeezed states have been investigated by Yang et al (2011 J. Phys. B: At. Mol. Opt. Phys.44 075502). In this paper, after a modification of Yang et al's derivation procedure, we deduced the non-cyclic and non-unitary geometric phases of nonlinear coherent and nonlinear squeezed states with a new approach which is consistent with the nonlinear coherent states theory. Indeed, the most important distinguishable feature of our presentation lies in the fact that we employed the (nonlinear) Hamiltonian which appropriately generates the time evolution of nonlinear coherent and squeezed states. It is established that this modification directly affects the resultant geometric phases of the states under consideration. As a physical realization, we applied our formalism to a particular nonlinear physical system corresponding to the centre-of-mass motion of a trapped ion coherent state. Then, the variation of the geometric phases of the considered nonlinear states in terms of time, intensity of radiation field, squeezing and Lamb–Dicke parameters are investigated. Finally, we discuss our numerical results.

The new mechanism of x-ray generation by clusters at their irradiation by femtosecond laser pulses has been suggested. We develop photo-recombination theory for electrons which first leave atomic clusters due to the outer ionization and then go into the ground quantum state of the neighbouring charged cluster. The charged cluster field is considered as a quantum potential well. The conclusion has been made that non-dipole x-ray photons at the photo-recombination into charged clusters have an energy which is larger than that for the well-known photo-recombination on separate atomic ions inside the cluster.

Time-resolved spectroscopy was used to study the plasma emission induced by a 1064 nm, 10 ns pulsed laser ablation titanium during the early phase of between 60–200 ns in an atmospheric environment. The line intensity evolution of Ti III and Ti II was analysed in terms of the delay time, as well as the plasma temperature and electron density, based on the observed spectra. The Stark broadening for two Ti III lines at 237.4986 and 241.3989 nm was measured. Since the self-absorption of the lines was not observed in our experiment, its influence on the lines was assumed to be negligible. Moreover, a modified semi-empirical approach was used to calculate the Stark broadening for the two lines and generally good agreement was obtained between the theoretical results and experimental data.