Cecil Laughlin

A highly accurate study of a helium atom under pressure

Basis sets incorporating the interelectronic distance r12 are employed in variational calculations of the non-relativistic ground-state energies and pressures of a helium atom confined at the centre of an impenetrable spherical cavity and results are presented for a series of cavity radii Rc. The calculated values asymptotically approach the correct values in the limits Rc → 0 and Rc →∞ , and a simple analytical expression is obtained which makes accurate predictions for small cavities. The same method is also used to study two penetrable cavities modelled by Gaussian and harmonic potential wells. It is concluded that the present results are the most accurate currently available for a confined helium atom. The calculation method employs Gaussian quadrature to evaluate integrals and can very easily be adapted to any spherical confining potential.

Two-valence-electron model-potential studies of the Be I isoelectronic sequence

Calculations of the radiative properties of the Be I isoelectronic sequence, through Ne VII, have been carried out using a semi-empirical model-potential method. Bound-bound oscillator strengths among the lowest few states of the 1S, 3S, 1P0, 1P, 3P0, 3P, 1D and 3D symmetries are tabulated. Where accurate theoretical or experimental data are available, the agreement is excellent. Results are given for the 1S0-3P10 intercombination oscillator strengths for fine-structure splittings in the term 2s2p 3P0 and 2p2 3P, and for the dipole polarisability of the ground-state ions.

Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field

Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored. Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of caesium (Cs) atoms in an intense 3,600-nm mid-infrared laser field. Combining with a synchrosqueezing transform of the quantum time-frequency spectrum and an extended semiclassical analysis, the roles of multiphoton and multiple rescattering trajectories on the near- and below-threshold harmonic generation processes are clarified. We find that the multiphoton-dominated trajectories only involve the electrons scattered off the higher part of the combined atom-field potential followed by the absorption of many photons in near- and below-threshold regime. Furthermore, only the near-resonant below-threshold harmonic is exclusive to exhibit phase locked features. Our results shed light on the dynamic origin of the near- and below-threshold harmonic generation.

Energy levels, wavefunction compositions and electric dipole transitions in neutral Ca

A configuration-interaction approach, based on the use of B-spline basis sets combined with a model potential including monoelectronic and dielectronic core polarization effects, is employed to calculate term energies and wavefunctions for neutral Ca. Results are reported for singlet and triplet bound states, and some quasi-bound states above the lowest ionization limit, with angular momentum up to L = 4. Comparison with experiment and with other theoretical results shows that this method yields the most accurate energy values for neutral Ca obtained to date. Wavefunction compositions, necessary for labelling the levels, and the effects of semi-empirical polarization potentials on the wavefunctions are discussed, as are some recent identifications of doubly-excited states. It is shown that taking into account dielectronic core polarization changes the energies of the lowest terms in Ca significantly, in general by a few hundred cm-1, the effect decreasing rapidly for the higher bound states. For Rydberg states with n7 the accuracy of the results is often better than a few cm-1. For series members (or perturbers) with a pronounced 3d character the error can reach 150 cm-1. The wavefunctions are used to calculate oscillator strengths and lifetimes for a number of terms and these are compared with existing measurements. The agreement is good but points to a need for improved measurements.

Perturbation Theory for a Hydrogen-like Atom Confined Within an Impenetrable Spherical Cavity

Abstract Perturbation expansions for a hydrogen-like atom confined at the centre of an impenetrable spherical cavity, of finite radius R , are discussed in a non-relativistic approximation. Properties considered include: energy, oscillator strength, dipole polarisability and nuclear shielding factor. The appropriate form of perturbation theory to employ depends on the cavity size and three different regimes are considered: small, intermediate and large. For large cavity radii, perturbation of the unconfined atom boundary condition at r = R to satisfy a Dirichlet condition results in exponentially small deviations from the unconfined atom values which are predicted to high accuracy in first order. For small R , Rayleigh–Schrodinger perturbation theory can be used, with the electron-nucleus Coulomb interaction treated as a perturbation, to generate expansions in powers of R . These expansions, whose radii of convergence are explored, provide highly accurate results even for moderately large R (depending on the state considered). The difficult intermediate range of R values is finally investigated using Rayleigh–Schrodinger perturbation theory based on known exact solutions obtained from lobes of free-atom solutions.

Wavelengths, transition probabilities and lifetimes in the quartet spectra of O VI and F VII

A model-potential method is employed to describe core-excited 1s2snl4L and 1s2pnl4L levels of the ions O VI and F VII. Wavelength, transition probability and lifetime data are predicted. The calculated wavelengths and lifetimes are compared with the available experimental measurements.

An accurate model-potential description of the valence spectrum of Ca

A modified effective potential for an valence-electron - -core interaction is shown to substantially improve the accuracy of calculated energies for Ca terms containing significant components, while maintaining high accuracy for other terms. In fact, we obtain near spectroscopic precision for those series which have little 3d character. Our calculations support the assignments of some 4s ng levels recently identified in the solar spectrum and, in particular, we confirm that lies below . The energy of the unidentified calcium term is predicted.

Core polarisation corrections to multipole operators for valence-electron wavefunctions

Corrections to valence-electron transition operators are needed when matrix elements are calculated with wavefunctions obtained from a valence-electron model Schrodinger equation. Electric multipole operators are analysed and correction terms of O(r-6) are derived for the dipole operator. It is shown that the new O(r-6) terms involve dipole-quadrupole interactions of the form (1/r).(1/r).

Theoretical studies of 1s2snl and 1s2pnl quartet levels of Li I

Radiative properties of 1s2snl and 1s2pnl quartet levels of the neutral lithium atom are studied with the framework of a model-potential method, in which the K-shell electron is represented by a non-local effective potential. Convergence of configuration-interaction expansions for the wavefunctions is examined and it is found that continuum configurations often make important contributions. Two practical approaches to including such configurations are investigated. Transition wavelengths and probabilities, and radiative lifetimes, are calculated and compared with recent experimental values. Fine-structure-induced autoionisation of 4P and 4D0 levels above the 2s 3S ionisation limit of Li II is briefly discussed.

Model-potential calculations of wavelengths, transition probabilities and lifetimes for core-excited quartet levels of Be II

A non-local model potential nu M, which approximates the interaction of the 1s and nl electrons in 1snl 3L levels of Be III to high accuracy, is used to construct an effective two-electron Schrodinger equation for 1s2snl 4L and 1s2pnl 4L core-excited levels of Be II. Wavefunctions for quartet levels of Be II are found by a configuration-interaction expansion in terms of anti-symmetrised products of eigenfunctions of nu M and wavelengths, transition probabilities and radiative lifetimes are calculated. Some outstanding lines in the beam-foil spectrum of beryllium are discussed.