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NASA NTRS1976

Electronic energy states

One-electron wave functions are reviewed and approximate solutions of two-electron systems are given in terms of these one-electron functions. The symmetry effects associated with electron spin are reviewed and the effects of electron exchange on energy levels of the two-electron system are given. The coupling of electronic orbital and spin angular momentum is considered next and the Lande interval rule for Russell-Saunders or LS coupling is derived. The configurations possible for various multi-electron LS couplings are enumerated (examples from the first two rows of the periodic table are given), and the meaning of the spectroscopic nomenclature is discussed, particularly with respect to the degeneracies of the electron states involved. Next the nomenclature, symmetries, and degeneracies for electron states of diatomic molecules are discussed, and some examples for N2, O2, and NO are presented. The electronic partition functions and derivative thermodynamic properties are expressed in terms of these energies and degeneracies, and examples are given for some of the simple gas species encountered in the earth's atmosphere.

Source record↗
NASA NTRS1976

Orbital electron capture by the nucleus

The theory of nuclear electron capture is reviewed in the light of current understanding of weak interactions. Experimental methods and results regarding capture probabilities, capture ratios, and EC/Beta(+) ratios are summarized. Radiative electron capture is discussed, including both theory and experiment. Atomic wave function overlap and electron exchange effects are covered, as are atomic transitions that accompany nuclear electron capture. Tables are provided to assist the reader in determining quantities of interest for specific cases.

Bambynek, W.↗
NASA NTRS1976

Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

Chen, M. H.↗
NASA NTRS1976

Single-electron Born approximations for charge transfer from multielectron atoms to protons

The Born approximation, including the internuclear interaction, is used to compute cross sections for the transfer of one electron from a multielectron atom to an incident proton. When the full internuclear interaction is included, the results lie far above high-energy experimental K-shell data for protons and argon. However, when only enough internuclear interaction is included so that the total projectile-target interaction goes to zero asymptotically in accordance with plane-wave functions actually used, fair agreement at high energies is obtained. The latter form of the Born approximation is compared with data on K-shell capture from helium as well as argon and with the simpler approximation of Oppenheimer and of Brinkman and Kramers (OBK), where no internuclear interaction is included. The OBK results typically lie a factor of 2 to 8 above the data, while the present Born results are within a factor of 2 of most of the existing high-velocity K-shell data.

Omidvar, K.↗
NASA NTRS1977

Angular distribution of Auger electrons due to 3d-shell ionization of krypton

Cross sections for electron impact ionization of krypton due to ejection of a 3rd shell electron have been calculated using screened hydrogenic and Hartree-Slater wave functions for target atom. While the total ionization cross sections in the two approximations are within 10% of each other, the Auger electron angular distribution, related to cross sections for specific magnetic quantum numbers of the 3rd electrons, is widely different in the two approximations. The angular distribution due to Hartree-Slater approximation is in excellent agreement with measurement. The physical reason for the discrepancies in the two approximations is explained.

Omidvar, K.↗
NASA NTRS1977

Total Born approximation cross sections for single electron loss by atoms and ions colliding with atoms

The first born approximation (FBA) is applied to the calculation of single electron loss cross sections for various ions and atoms containing from one to seven electrons. Screened hydrogenic wave functions were used for the states of the electron ejected from the projectile, and Hartree-Fock elastic and incoherent scattering factors were used to describe the target. The effect of the target atom on the scaling of projectile ionization cross sections with respect to the projectile nuclear charge was explored in the case of hydrogen-like ions. Scaling of the cross section with respect to the target nuclear charge for electron loss by Fe (+25) in collision with neutral atoms ranging from H to Fe is also examined. These results were compared to those of the binary encounter approximation and to the FBA for the case of ionization by completely stripped target ions.

Rule, D. W.↗
NASA NTRS1977

Atomic electron energies including relativistic effects and quantum electrodynamic corrections

Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state.

Aoyagi, M.↗
NASA NTRS1976

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations for Z between 2 and 106

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

Huang, K.-N.↗
NASA NTRS1976

Theoretical investigation of protonated carbon dioxide

The equilibrium structure of CO2H(+) has been obtained from self-consistent field and configuration interaction wave functions. Only one stable form has been found, a linear O-C-O chain with the hydrogen bonded to oxygen and slightly off axis, in analogy with known isoelectronic species. A second structure protonated at carbon, which has been inferred from mass spectrometric studies, is found to be unstable with respect to spontaneous rearrangement. The proton affinity of CO2 is calculated to be 136 kcal/mole, in reasonable agreement with the most recent experimental value.

Green, S.↗
NASA NTRS1977

Total Born-approximation cross sections for single-electron loss by atoms and ions colliding with atoms

The first Born approximation (FBA) is applied to the calculation of single-electron-loss cross sections for various ions and atoms containing from one to seven electrons. Screened hydrogenic wave functions are used for the states of the electron ejected from the projectile, and Hartree-Fock elastic and incoherent scattering factors are used to describe the target. The effect of the target atom on the scaling of projectile ionization cross sections with respect to the projectile nuclear charge is explored in the case of hydrogenlike ions. Also examined is the scaling of the cross section with respect to the target nuclear charge for electron loss by Fe(25+) in collision with neutral atoms ranging from H to Fe. These results are compared with those of the binary-encounter approximation (BEA) and with the FBA for the case of ionization by completely stripped target ions. Electron-loss cross sections are also calculated for the ions O(i+) (i = 3-7) and N(i+) (i = 0-6) in collision with He targets in the energy range of approximately 0.1 to 100 MeV/nucleon. These results are found to be in excellent agreement with the available data near the peak of the ionization cross section.

Rule, D. W.↗
NASA NTRS1977

Some O I oscillator strengths and the interstellar abundance of oxygen

Calculated and experimental oscillator strengths for the O I intersystem line at 1356 A and for other O I lines of interest in interstellar absorption-line studies are discussed. Attention is given to experimental f-values for the lines at 1302, 1305, and 1306 A, previous work on the f-values for the lines at 1356 and 1359 A, wave-function expansion, and calculations for permitted as well as intercombination lines. Copernicus observations of several interstellar absorption lines due to O I, C II, P II, and Ni II toward Zeta Oph are reported, equivalent widths are determined, and a curve-of-growth analysis is performed for the O I absorption lines. Oscillator strengths are recommended for the far-UV resonance lines of O I, and it is concluded that the oxygen in the interstellar H I regions toward Zeta Oph is depleted by 45% to 69%.

Zeippen, C. J.↗
NASA NTRS1977

Elastic scattering of deuterons by carbon

Deuteron-carbon elastic scattering is studied within the framework of the Glauber approximation. The full Glauber multiple scattering series is evaluated with simplified nuclear wave functions. An approximation in which deuteron-nucleus scattering is expressed in terms of nucleon-nucleus scattering amplitudes is shown to be accurate for small momentum transfers. The effects of the Coulomb field and the deuteron D state are investigated. The impressive fit to the 650 MeV d-(C-12) elastic scattering data, obtained in a recent calculation, is shown to be due to additional approximations made in that analysis.

Varma, G. K.↗
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.↗