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At least 91 records · Page 5

Theoretical Studies of N2-broadened Half-widths of H2O Lines Involving High j States

Based on the properties of the energy levels and wave functions of H2O states, one can categorize H2O lines into individually defined groups such that within the same group, the energy levels and the wave functions associated with two paired lines have an identity property while those associated with different pairs have a similarity property. Meanwhile, by thoroughly analyzing processes used to calculate N2-broadened half-widths, it was found that the 'Fourier series' of W(sup a)(sub L(sub 1))(sub K(sub 1))(sub K(sub 1)) (t; j(sub f) T(sub f) and W(sup a)(sub L(sub 1))(sub K(sub 1))(sub K(sub 1)) (t; j(sub i) T(sub i), and a factor P(sub 222) (j(sub f) T(sub f) j(sub i) T(sub i)) are the key items in the Robert-Bonamy formalism to distinguish contributions to ReS2(r(sub c)) among different transitions of j(sub f) T(sub f) - j(sub i). However, these items are completely determined by the energy levels and the wave functions associated with their initial and final states and they must bear the latter's features as well. Thus, it becomes obvious that for two paired lines in the same group, their calculated half-widths must be almost identical and the values associated with different pairs must vary smoothly as their ji values vary. Thus, the pair identity and the smooth variation rules are established within individual groups of lines. One can use these rules to screen half-width data listed in HITRAN and to improve the data accuracies.

water

Two-photon excitation cross-section in light and intermediate atoms

The method of explicit summation over the intermediate states is used along with LS coupling to derive an expression for two-photon absorption cross section in light and intermediate atoms in terms of integrals over radial wave functions. Two selection rules, one exact and one approximate, are also derived. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum defect method are used. A relationship between the cross section and the oscillator strengths is derived. Cross sections due to selected transitions in nitrogen, oxygen, and chlorine are given. The expression for the cross section is useful in calculating the two-photon absorption in light and intermediate atoms.

Omidvar, K.

Electron impact excitation of highly charged sodium-like ions

Optical transition probabilities and electron collision strengths for Ca X, Fe XVI, Zn XX, Kr XXVI and Mo XXXII are calculated for transitions between n equal to 3 and n equal to 4 levels. The calculations neglect relativistic effects on the radial functions. A semi-empirical approach provides wave functions of the excited states; a distorted wave function without exchange is employed to obtain the excitation cross sections. The density dependence of the relative intensities of certain emission lines in the sodium isoelectronic sequence is also discussed.

Blaha, M.

Radiative transitions involving the (2p2)(3 Pe) metastable autodetaching of H(-)

The absorption coefficient for the free-bound transition H (ls) + e(-)+ h omega yields H(-)(2 sq p,(3)P(e)) is calculated (together with the differential emission rate for the inverse process) using ls - 2s - 2p close coupling continuum wave functions and a Hylleraas bound state wave function. A maximum in the absorption and emission spectra is found to occur at a photon wavelength of 1219.5 A, which is 2 A closer to the Lyman alpha line than predicted by the calculations of Drake, and is in closer agreement with the stellar absorption feature identified by Heap and Stecher. The free-bound absorption process appears to be a significant source of continuous ultraviolet opacity.

Jacobs, V. L.

Parabolized stability equations

The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.

Herbert, Thorwald

Two-photon excitation cross section in light and intermediate atoms in frozen-core LS-coupling approximation

Using the method of explicit summation over the intermediate states two-photon absorption cross sections in light and intermediate atoms based on the simplistic frozen-core approximation and LS coupling have been formulated. Formulas for the cross section in terms of integrals over radial wave functions are given. Two selection rules, one exact and one approximate, valid within the stated approximations are derived. The formulas are applied to two-photon absorptions in nitrogen, oxygen, and chlorine. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum-defect method have been used. A relationship between the cross section and the oscillator strengths is derived.

Omidvar, K.

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

Green, T. J.

General contraction of Gaussian basis sets. Part 2: Atomic natural orbitals and the calculation of atomic and molecular properties

A recently proposed scheme for using natural orbitals from atomic configuration interaction (CI) wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outmost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital (ANO) sets.

Almloef, Jan

General contraction of Gaussian basis sets. II - Atomic natural orbitals and the calculation of atomic and molecular properties

A recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.

Almlof, Jan

Homogeneous quantum electrodynamic turbulence

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Shebalin, John V.

Development of New Open-Shell Perturbation and Coupled-Cluster Theories Based on Symmetric Spin Orbitals

A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.

Lee, Timothy J.

Electron-impact excitation of atomic oxygen

A close-coupling approximation is employed to theoretically investigate the excitation of the 3s3S0 and 3p3P states of atomic oxygen for electron impact energies ranging from 13.87-100 eV. The target states included in the expansion of the total wave function are modeled by accurate configuration-interaction wave functions. The results are consistent with recent experimental findings for the dipole-allowed 3P-3s3S0 transition.

Tayal, S. S.

Spin bipolaron in the framework of emery model for high-T(sub c) copper oxide superconductors

The high-T(sub c) oxide compounds discovered recently exhibit a number of interesting physical properties. Two-dimensional antiferromagnetic spin order has been observed in these materials at the oxygen deficiency. This fact can be explained by strong correlation of the spins, situated on Cu sites in the conducting planes of the oxide superconductors. The doping or the oxygen deficiency lead to the occurrence of holes, occupying the oxygen p-orbitals according to the Emery model. At the small hole concentration they can move along the antiferromagnetic lattice of spins, localized on Cu sites. Researchers consider the two holes situation and describe in what way their behavior depends on the antiferromagnetic exchange interation J. It is known that in the framework of Hubbard model with strong on-site Coulomb repulsion, a single hole can form a spin polaron of the large radius. It is reasonable to admit that two holes with parallel spins (triplet) form the spin bipolaron complex owing to the hole excitations' capability to polarize Cu spin surroundings. Such an excitation was considered in the phenomenological way. Here the problem is discussed on the basis of the microscopic approach in the framework of the variational principle. A special kind of wave function is used for such a purpose. The wave function is constructed by generalizing the trial functions proposed in over two holes excitation situation (triplet) and then the region of spin bipolaron existance in the framework of Emery model is studied. In this model the Hamiltonian can be easily rewritten by forming the oxygen states transforming as the irreducible representations of the group D(sub 4).

Golub, A. A.

Photoionization cross-sections for atoms and ions of aluminum, silicon, and argon.

Photoionization cross sections for all levels belonging to the configurations of atoms and ions of aluminum, silicon, and argon have been calculated using Hartree-Fock bound-electron wave functions and close-coupling approximation free-electron wave functions. The results are presented in the form of a computationally convenient interpolation formula and should find wide astrophysical application.

Chapman, R. D.

Line strengths, collision strengths and excitation rates for multiply-charged silicon ions

In the present paper, the line strengths, collision strengths, and rate coefficients are calculated for a variety of transitions in multiply charged silicon ions from Si(VI) to Si(XIV). The line strengths are obtained by using Clementi wave functions for the ground-state configuration, and excited-state wave functions generated by a semiempirical method. The collision strengths are calculated in an LS coupling scheme in the distorted-wave approximation, neglecting exchange except for the helium-like transitions. These results are then integrated over a Maxwellian velocity distribution function to yield rate coefficients. The rates are presented graphically and also in terms of a two-parameter fit.

Davis, J.

Photoionization from excited states of helium

The cross sections for photoionization from the 2 1S, 2 3S, 2 1P and 2 3P excited states of helium are calculated for photoelectron energies below the n = 2 threshold of He(+) using Hylleraas bound state wave functions and 1s-2s-2p close coupling final state wave functions. The resonant structures associated with the lowest-lying 1S, 1P, 3P, and 1D autoionizing states of helium are found to be characterized by large values of the line profile parameter q. The cross sections and the photoelectron angular distribution asymmetry parameters for the P-states are calculated for various polarization states of the target atom and the incident photon. Experiments which would lead to the separate determinations of the S- and D- wave partial photoionization cross sections are discussed.

Jacobs, V. L.

Studies of radar backscatter as a function of wave properties and the winds in the turbulent marine atmosphere

The research on model functions for ADEOS and ERS-1 are summarized and an analysis of the differences between the three kinds of models is provided in this final report. The success of the AMI on ERS-1 obtained at GSFC and NMC is highlighted. The problem of wind stress description is reviewed within and the scatterometer model being developed for high winds monitoring for the AMI on ERS-1 and ERS-2 is described.

Pierson, Willard J., Jr.