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NASA NTRS1978

Diagrammatic analysis of the density operator for nonlinear optical calculations Pulsed and CW responses

In the present paper a diagrammatic analysis of the density operator for the evaluation of nonlinear optical quantities is considered. The present approach extends earlier diagrammatic analysis by treating the time evolution of both the wave function and its complex conjugate. Time-ordered graphs result, each of which corresponds to a term in the density matrix. Examples involving the third-order susceptibility are discussed for both monochromatic and pulse excitation. In particular coherent rotational transient birefringence is discussed. The diagrams provide a convenient means by which nonlinear optical processes can be precisely defined and the susceptibility readily evaluated.

Yee, T. K.↗

NASA NTRS1978

Theoretical study of collinear Be + FH/nu1/ yields BeF/nu2/ + H

The potential energy surface for collinear Be + FH yields BeF + H was studied at various levels of ab initio approximation. A final surface was obtained from a first order configuration interaction wave function, using the iterative orbital method and a medium-sized basis of Slater atomic functions. The exothermicity is computed to be 6 kcal/mole; the barrier height is predicted to be about 28 kcal/mole at a geometry where both internuclear separations are extended by about 0.4 bohr from their asymptotic equilibrium values. This surface differs qualitatively from simple LEPS models.

Schor, H.↗

NASA NTRS1978

Variationally consistent approximation scheme for charge transfer

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

Halpern, A. M.↗

NASA NTRS1979

Dynamics of the collinear Be + FH yielding BeF + H reaction

Results of a study of the collinear reaction Be + FH(nu1) yielding BeF(nu2) + H are summarized. The surface was obtained by an ab initio first-order wave function CI calculation. Dynamics were studied using quasi-classical trajectories. A comparison study was made using a LEPS surface with similar characteristics. The ab initio surface was found to give rise to quite special results. Because of interest in the analogous Ba + HF system, the effect of varying the mass of the atom was observed.

Schor, H.↗

NASA NTRS1979

The physical basis for absorption of light

The effects of light absorption on the wave functions of gas-phase molecules and atoms are investigated by high resolution spectral measurements of radiation emerging from a sample. A Stark-modulated sample of methyl fluoride was irradiated at the 102 GHz rotational transition and the emergent radiation was resolved by means of a spectrum analyzer. For signal oscillator frequencies below or above the molecular resonance by one modulation frequency, the amplitudes of the upper and lower modulation sidebands are found to be of nonuniform intensity, which is inconsistent with amplitude modulation. Emission due to polarization is, however, calculated to be consistent with the results observed, indicating that light absorption should be considered as a subtractive stimulated emission.

Pickett, H. M.↗

NASA NTRS1979

Atomic electron excitation probabilities during orbital electron capture by the nucleus

Approximate probabilities of electron excitation (shakeup/shakeoff) from various atomic states during nuclear ns electron capture have been calculated in the sudden approximation, using Hartree-Fock wave functions. Total excitation probabilities are much lower than during inner-shell ionization by photons or electrons, and ns states are more likely to be excited than np states. This latter result is borne out by K-alpha X-ray satellite spectra.

Crasemann, B.↗

NASA NTRS1979

The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I - Collinear calculations. II - Three-dimensional treatment

A semiclassical approximation to treat vibrationally inelastic scattering is developed. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.

Cross, R. J., Jr.↗

NASA NTRS1979

L-shell Auger and Coster-Kronig spectra from relativistic theory

The intensities of L-shell Auger and Coster-Kronig transitions in heavy atoms have been calculated relativistically. A detailed comparison is made with measured Auger spectra of Pt and U. The pertinent transition energies were computed from relativistic wave functions with inclusion of the Breit interaction, self-energy, a vacuum-polarization correction, and complete atomic relaxation. Multiplet splitting is found to distribute Auger electrons from certain transitions among several lines. The analysis leads to reassignment of a number of lines in the measured spectra. Lines originally identified as L2-L3Ni in the U spectrum are shown to arise from M4,5 Auger transitions instead.

Chen, M. H.↗

NASA NTRS1979

Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.

Dixon, R. M.↗

NASA NTRS1980

Quasi-projection-operator calculation of inelastic resonances in He/-/ and Li

Feshbach resonances of electrons incident of He and Li(+) are calculated below the 3(S-3) target threshold by means of the inelastic quasi-projection-operator technique of Temkin and Bhatia (1972). A configuration-interaction-type wave function is employed with up to 46 configurations. The calculations reveal, with reasonable accuracy, all presently observed Feshbach resonances. The method does not reveal shape resonances, but, for isoelectronic systems with greater nuclear charge, it is argued that shape resonance should become less important. This is already apparent in the case of Li, for which the known resonances are calculated and higher resonances, for which there are as yet no experimental data, are predicted.

Wakid, S.↗

NASA NTRS1980

An ab initio calculation of the zero-field splitting parameters of the 3A-double prime state of formaldehyde

The spin dipole-dipole and spin-orbit contributions to the zero-field splitting of the 3A-double prime state of formaldehyde have been evaluated at the excited state experimental geometry. Ab initio CI wave functions were generated from a Dunning double zeta plus polarization bases set using 3A-double prime rhf orbitals. Twelve states of each symmetry were used to evaluate the second-order spin-orbit effect. The resulting values of D and E were 0.19 and 0.03 kayser with the principal magnetic axes rotated 36 deg from the CO bond. The values of alpha and beta relative to the inertial axes were calculated to be 0.03 and 0.01 kayser compared to the experimental values of 0.05 plus or minus 0.01 and 0.02 plus or minus 0.02 kayser.

Davidson, E. R.↗

NASA NTRS1980

Quasi-projection-operator calculation of autoionization states of O5/+/ /O VI/ and Si11/+/ /Si XII/

A practical approach to calculating diagnostic parameters includes both scattering and statelike (autoionization) elements. The paper presents inelastic quasi-projection-operator calculations of autoionization states of the three-electron ions of oxygen and silicon for states below the n = 3 manifod of the respective two-electron parent (O VI and Si XII). Wave functions containing up to 40 configurations are calculated. The O VI calculated results agree with experimental results within the experimental error (about + or - 2 eV) while for the Si XII case, it was necessary to include relativistic effects. Where formulas are available (states for which p + q = 2), the Si XII results are also in good agreement with experimental results for 2Se, 2Po, and 2De states. Since the calculated results for some of the higher states did not agree with identifications proposed by Trabert et al. (1979), alternative identifications are suggested.

Wakid, S.↗

NASA NTRS1980

Nonrelativistic hyperfine splitting in muonic helium by adiabatic perturbation theory

Huang and Hughes have discussed the hyperfine splitting delta mu of muonic helium using a variational approach. In this paper, the Born-Oppenheimer approximation is used to simplify the evaluation of delta mu in the nonrelativistic limit. The first-order perturbed wave function of the electron is obtained in closed form by modifying the method used by Dalgarno and Lynn. The result is close to those of Huang and Hughes which required a large Hylleraas expansion and considerable extrapolation.

Drachman, R. J.↗

NASA NTRS1981

A hybrid method for improving MCSCF convergence

It has been found that the convergence problems for many ill conditioned single-configuration SCF calculations arise from mixing among only a small number of orbitals. This orbital set includes the highest closed, the partially filled, and (possibly) a few of the lowest virtual orbitals. The fact that convergence problems can be, in very large measure, linked to a small orbital set is used to design a hybrid MCSCF procedure in which these orbitals are treated using a second-order MCSCF method, while other mixings are treated with a lower-order method which avoids the time consuming integral transformation. Tests on BeO show that the hybrid method yields convergence even when the simple lower-order treatment diverges. The method is expected to facilitate determination of MCSCF wave functions for large basis problems and for the construction of potential energy surfaces.

Bauschlicher, C. W., Jr.↗

NASA NTRS1981

On the use of corresponding orbitals in the calculation of nonorthogonal transition moments

Full valence and first-order CI wave functions are invariant with respect to unitary transformations among the valence orbitals. We exploit this degree of freedom and show that by transforming the valence orbitals into a corresponding orbital basis, nonorthogonal transition moment calculations become an easily managed task. Sample full valence calculations on several states of O2(+) and OF are also presented.

Lengsfield, B. H., III↗

NASA NTRS1981

Ab initio calculation of the third-order susceptibility of H2

The third-order susceptibility of H2 has been calculated under coherent anti-Stokes Raman-scattering conditions, with use of wave functions specifically designed for accurate calculations of sum-rule properties. The theoretical values are in good agreement with experiment.

Huo, W. M.↗

NASA NTRS1981

Oscillator strengths and collision strengths for S v

Observations of the optical extreme-ultraviolet spectrum of the Jupiter planetary system during the Voyager space mission revealed bright emission lines of some sulfur ions. The spectra of the torus at the orbit of Io are likely to contain S V lines. The described investigation provides oscillator strengths and collision strengths for the first four UV lines. The collision strengths from the ground state to four other excited states are also obtained. Use is made of a two-state calculation which is checked for convergence for some transitions by employing a three-state or a four-state approximation. Target wave functions for S V are calculated so that the oscillator strengths calculated in dipole length and dipole velocity approximations agree within 5%.

Van Wyngaarden, W. L.↗

NASA NTRS1981

Theoretical electronic transition moments for the Ballik-Ramsay, Fox-Herzberg, and Swan systems of C2

Electronic transition moments and their variation with internuclear separation are calculated for the Ballik-Ramsay (b 3 Sigma g - a 3 Pi u), Fox-Herzberg (e 3 Pi g-a 3 Pi u) and Swan (d 3 Pi g-a 3 Pi u) band systems of C2, which appear in a variety of terrestrial and astrophysical sources. Electronic wave functions of the a 3 Pi u, b 2 Sigma g -, d 3 Pi g and e 3 Pi g states of C2 are obtained by means of a self-consistent field plus configuration interaction calculation using an atomic basis of 46 Slater-type orbitals, and theoretical potential energy curves and spectroscopic constants for the four electronic states were computed. The results obtained for both the potential energy curves and electronic transition moments are found to be in good agreement with experimental data.

Cooper, D. M.↗