Application of discrete-basis-set methods to the Dirac equation

Variational solutions to the Dirac equation in a discrete L2 basis set are investigated. Numerical calculations indicate that for a Coulomb potential, the basis set can be chosen in such a way that the variational eigenvalues satisfy a generalized Hylleraas-Undheim theorem. A number of relativistic sum rules are calculated to demonstrate that the variational solutions form a discrete representation of the complete Dirac spectrum including both positive-and negative-energy states. The results suggest that widely used methods for constructing L2 representations of the nonrelativistic electron Green\u27s function can be extended to the Dirac equation. As an example, the relativistic basis sets are used to calculate electric dipole oscillator strength sums from the ground state, and dipole polarizabilities. © 1981 The American Physical Society

Relativistic two-photon decay rates of 2s12 hydrogenic ions

Rates are calculated for the decay of metastable 2s12 ions to the ground state by the simultaneous emission of two photons. The calculation includes all relativistic and retardation effects, and all combinations of photon multipoles which make significant contributions up to Z=100. Summations over intermediate states are performed by constructing a finite-basis-set representation of the Dirac Green\u27s function. The estimated accuracy of the results is 10 ppm for all Z up to 100. The decay rates are about 20 (Z)2% larger than an earlier calculation by Johnson owing to the inclusion of higher-order retardation effects. The general question of gauge invariance in two-photon transitions is discussed. © 1981 The American Physical Society

Relativistic sum rules and integral properties of the Dirac equation

Relativistic generalizations are derived for the well-known nonrelativistic electric-dipole oscillator-strength sum rules. The relativistic sum rules include both positive- and negative-energy states. The derivations are valid for a Dirac electron in an arbitrary local potential. We also present a number of simple integral properties related to the relativistic virial theorem which are useful in the calculation of matrix elements. © 1982 The American Physical Society

Two-electron lamb shifts and 1s2s 3S1-1s2p 3PJ transition frequencies in helium-like ions [1]

The leading terms in the 1/Z expansion of the two-electron Bethe logarithm are calculated for the states 1s2 1S0, 1s2s 1S1, 1s2s 3S1, 1s2p 1P1 and 1s2p 3PJ by the use of a novel finite basis set method. The resulting QED terms are combined with other relativistic and mass polarisation corrections to obtain total transition frequencies. The results are compared with recent measurements in helium-like ions from Li+ to Fe24+

1/Z expansion calculation of the Bethe logarithm for the ground state Lamb shift of two-electron ions

The leading two terms in the 1/Z expansion of the two-electron Bethe logarithm are calculated by the application of a new finite basis set method. The results can be expressed in the form ln epsilon (1s 2 1S)=ln(19.77(Z-0.0063) 2). The high-Z behaviour appears to differ from that of a previous variational calculation by Aashamar and Austvik (1976)

Characterizing the Hofstadter butterfly's outline with Chern numbers

In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known Hofstadter butterfly's outline, is associated to a specific sequence of Chern numbers that correspond to the quantized transverse conductivity. Indeed the topological invariant that characterizes the fundamental energy band depicts successive stairways as the magnetic flux varies. Moreover each stairway is shown to be labeled by another Chern number which measures the charge transported under displacement of the periodic potential. We put forward the universal character of these properties by comparing the results obtained for the square and the honeycomb geometries.Comment: Accepted for publication in J. Phys. B (Jan 2009

1995 atmospheric trace molecule spectroscopy (ATMOS) linelist

The Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment uses a Fourier-transform spectrometer on board the Space Shuttle to record infrared solar occultation spectra of the atmosphere at 0.01-cm^(-1) resolution. The current version of the molecular spectroscopic database used for the analysis of the data obtained during three Space Shuttle missions between 1992 and 1994 is described. It is an extension of the effort first described by Brown et al. [Appl. Opt. 26, 5154 (1987)] to maintain an up-to-date database for the ATMOS experiment. The three-part ATMOS compilation contains Line parameters of 49 molecular species between 0 and 10000 cm^(-1), The main list, with nearly 700,000 entries, is an updated version of the HITRAN 1992 database. The second compilation contains supplemental line parameters, and the third set consists of absorption cross sections to represent the unresolvable features of heavy molecules. The differences between the ATMOS database and other public compilations are discussed