W. E. Baylis

Unified Franck-Condon treatment of pressure broadening of spectral lines

Abstract The quantum-mechanical theory of pressure broadening of spectral lines is discussed in the framework of the adiabatic approximation, and a “Unified Franck-Condon” (UFC) line shape is derived. The UFC formula permits computation of the entire line profile and yields both the impact and the quasistatic approximations in the appropriate limits. The JWKB approximation is applied in order to simplify the general UFC formula, and Sandos theory of satellite bands is shown to be a limiting case. A simple extension of Sandos theory allows any number of Condon points to be treated in a way which includes pairwise interference effects and yields the appropriate quasistatic contribution for isolated points but yet, for an initial Maxwellian energy distribution, is almost as easy to apply as the binary quasistatic theory. The possibility of real and complex Condon points is discussed and sample calculations are given of corresponding wing profiles. Finally, satellite-band shapes are compared in various approximations for Lennard-Jones potentials.

Profiles of line wings and rainbow satellites associated with optical and radiative collisions

Abstract The principles and applications of the quasimolecular treatment of optical and radiative collisions are discussed. Main attention is focused on the uniform approximation to the unified Franck-Condon (UFC) line shape of near- and far-wings and of rainbow satellites associated with pressure-broadened spectral lines, on radiative-collision cross-sections, and on collisional redistribution of radiation. In the review of experimental data the emphasis is placed upon those results which test theoretical predictions and knowledge of the interactions.

Relativistic Hartree-Fock oscillator strengths for the lowest s→p and p→d transitions in the first few members of the Ag(I) and Au(I) isoelectronic sequences, with allowance for cope polarization

Abstract Relativistic single-configuration Hartree-Fock oscillator strengths for the lowest ns2S 1 2 → np2P 1 2 , 3 2 transitions in the first few members of the rubidium (n = 5) and cesium (n = 6) isoelectronic sequences have been studied, both with and without allowance for core polarization. The effect of polarization of the core of the atom or ion by the valence electron is included by introducing a polarization potential in the one-electron Hamiltonian and by employing the corresponding correction for the dipole-moment operator in the transition matrix element. The results obtained compare well with available experimental data and indicate a significant influence of core-polarization effects on oscillator strengths. The behaviour of the oscillator strengths for the low Z part of the isoelectronic sequences is discussed.

Relativistic oscillator strengths and excitation energies for the ns2 1S0-nsnp 3P1, 1P1 transitions. II. Cadmium isoelectronic sequence

For pt.I see ibid., vol.18, no.8, p.1533 (1985). Relativistic excitation energies and oscillator strengths for both the resonance transition 5s2 1S0-5s5p 1P1 and the intercombination lines 5s2 1S0-5s5p 3P1 in the cadmium isoelectronic sequence are computed in an approach which combines limited relativistic configuration mixing to represent intravalence correlation with a polarisation model to account for valence-core correlation. This approach is able to greatly reduce the discrepancies between the theoretical and experimental oscillator strengths for these transitions. A substantial part of the remaining discrepancy, particularly for ionised systems, can probably be attributed to uncertainties in the available experimental data. Systematic trends along the sequence in both the oscillator strengths and in the relative contributions of intravalence and valence-core electron correlation are discussed and compared with those obtained previously for the mercury sequence. It is found that for spin-allowed transitions the share of intravalence correlation increases for lighter (lower Z) homologous systems in corresponding ionisation stages, whereas that of core-valence correlation decreases. For the spin-forbidden transitions, however, both correlation contributions seem to increase for lower Z homologues in the same ionisation stages.

Influence of atomic core polarisation on oscillator strengths for 2S1/2-2P1/2,3/2 and 2P1/2,3/2-2D3/2,5/2 transitions in Cu I, Ag I and Au I spectra

The recently proposed model potential for including correlation effects in relativistic Hartree-Fock calculations is applied to computations of oscillator strengths for the lowest transitions in Cu I, Ag I and Au I spectra. The present results remove the large discrepancies between the measured fik values for resonance transitions and the values from single-configuration calculations.

Relativity in Clifford's Geometric Algebras of Space and Spacetime

Of the various formalisms developed to treat relativistic phenomena, those based on Cliffords geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships between formulations of special relativity in the spacetime algebra (STA) Cℓ1,3 of the underlying Minkowski vector space, and in the algebra of physical space (APS) Cℓ3. STA lends itself to an absolute formulation of relativity, in which paths, fields, and other physical properties have observer-independent representations. Descriptions in APS are related by a one-to-one mapping of elements from APS to the even subalgebra STA+ of STA. With this mapping, reversion in APS corresponds to hermitian conjugation in STA. The elements of STA+ are all that is needed to calculate physically measurable quantities (called measurables) because only they entail the observer dependence inherent in any physical measurement. As a consequence, every relativistic physical process that can be modeled in STA also has a representation in APS, and vice versa. In the presence of two or more inertial observers, two versions of APS present themselves. In the absolute version, both the mapping to STA+ and hermitian conjugation are observer dependent, and the proper basis vectors of any observer are persistent vectors that sweep out time-like planes in spacetime. To compare measurements by different inertial observers in APS, we express them in the proper algebraic basis of a single observer. This leads to the relative version of APS, which can be related to STA by assigning every inertial observer in STA to a single absolute frame in STA. The equivalence of inertial observers makes this permissible. The mapping and hermitian conjugation are then the same for all observers. Relative APS gives a covariant representation of relativistic physics with spacetime multivectors represented by multiparavectors in APS. We relate the two versions of APS as consistent models within the same algebra.

Influence of core polarisation on oscillator strengths along the copper isoelectronic sequence

The influence of core polarisation on relativistic oscillator strengths has been studied for the 4s2S12/-4p2P1/2,3/2 and 4p2P1/2,3/2-4d2D3/2,5/2 transitions along the copper isoelectronic sequence. Core polarisation effects are included in a relativistic Hartree-Fock method as well as in a relativistic semi-empirical model-potential approach by introducing a core polarisation potential in the calculation of wavefunctions and by employing the corresponding correction for the dipole moment operator in the transition matrix element. The results obtained are compared with available theoretical and experimental data and the influence of core polarisation effects is discussed.

The Pauli algebra approach to special relativity

The Pauli algebra P, in which the usual dot and cross products of 3-space vectors are combined in an associative, invertible, but non-commutative multiplication, provides a simple but powerful approach to problems in special relativity. Even though the Pauli algebra is the Clifford algebra for Euclidean 3-space, Minkowski 4-vectors and their products in the Minkowski metric appear in a natural and covariant way as elements of P. The authors review the algebra and develop a formulation which, although closely tied to elementary vector and functional analysis, nevertheless allows a compact coordinate-free treatment of essentially all problems in special relativity. They derive a number of useful results and show how the elements are related both to traditional Minkowski-space tensors and to elements of the Dirac algebra.

Light polarization: A geometric‐algebra approach

The geometric algebra of three‐dimensional space (the ‘‘Pauli algebra’’) is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the three‐dimensional Stokes subspace to describe the polarization of an approximately monochromatic collimated beam of electromagnetic radiation. The coherency density ρ is a real element of the algebra whose components are the four Stokes parameters: a scalar representing the total photon flux density plus a three‐dimensional vector whose direction and length in the Poincare sphere give the type and degree of polarization. The detection of the radiation and the incoherent and coherent modification of the polarization by various optical elements are calculated by algebraic multiplication which has faithful representations in 2×2 matrices. One matrix representation of ρ is the coherency matrix with which Jones and Mueller matrices are related whereas another representation is the spin density matrix. However, the calculations a...

Photon position operators and localized bases

We extend a procedure for construction of the photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field. Symmetries broken by a choice of gauge are re-established by transformations within the gauge group. The approach allows several previous proposals to be related. Because of the coupling of the photon momentum and spin, our position operator, like that proposed by Pryce, is a matrix that does not commute with the spin operator. Unlike the Pryce operator, however, our operator has commuting components, but the commutators of these components with the total angular momentum require an extra term to rotate the matrices for each vector component around the momentum direction. Several proofs of the nonexistence of a photon position operator with commuting components are based on overly restrictive premises that do not apply here.