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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 541 records · Page 30
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NASA NTRS1973

Intermediate energy nucleon-deuteron elastic scattering

The adequacy of a multiple scattering description of nucleon-deuteron scattering at intermediate energy is examined. Although the multiple-scattering series is expected to converge slowly, model calculations indicate that the higher-order multiple-scattering terms contribute only to the low-order partial waves. The first two terms, nucleon exchange and single scattering, are assumed to describe the high-order partial waves completely. It is assumed that the deuteron is coupled only to the nucleon channel and that the internal structure is adequately defined by a nonrelativistic wave function.

Wilson, J. W.↗
NASA NTRS1974

Quadrupole moment of CO, N2, and NO/+/

Evaluation of quadrupole moments obtained for CO, N2, and NO(+) with multiconfiguration self-consistent-field wave functions chosen by the optimized valence configuration (OVC) approach of Wahl and Das (1972). The quadrupole moments thus obtained are compared with both experimental and Hartree-Fock values. The Hartree-Fock results are found to be not very accurate for N2, especially if vibrational averages over vibrational levels greater than 1 or 2 are to be taken. The agreement between the OVC quadrupole moment and the experimental values is found to be best for CO.

Billingsley, F. P., II↗
NASA NTRS1974

Analytic variational calculation of the ground-state binding energy of hydrogen in intermediate and intense magnetic fields

The present work investigates analytically the effect of an intermediate or intense magnetic field, such as probably exist in white dwarfs and near pulsars, on the binding energy of the hydrogen ground state. A wave-function 'prescription' is given for an analytic variational calculation of the binding energy. The calculation still gives a smooth transition between intermediate and intense fields. An explicit calculation of the ground-state binding energy as B goes to infinity is provided for the Yafet et al. (1956) trial function.

Wilson, L. W.↗
NASA NTRS1974

Spin projection of single-determinant wavefunctions

The components of the one- and two-particle density matrices resulting from spin projection of a single-determinant wave function are rederived by the method of expansion in terms of the natural orbitals of charge density, and the results are found to diverge from those given by Harriman and Sando for the two-particle case. The theory is generalized to include molecules with unequal numbers of electrons and basis orbitals and is applied to a number of organic molecules and ions. The correctness and internal consistency of the results argue in favor of the modification described.

Phillips, D. H.↗
NASA NTRS1974

Proton-deuteron double scattering

A simple but accurate form for the proton-deuteron elastic double scattering amplitude, which includes both projectile and target recoil motion and is applicable at all momentum transfer, is derived by taking advantage of the restricted range of Fermi momentum allowed by the deuteron wave function. This amplitude can be directly compared to approximations which have neglected target recoil or are limited to small momentum transfer; the target recoil and large momentum transfer effects are evaluated explicitly within the context of a Gaussian model.

Wilson, J. W.↗
NASA NTRS1975

Asymptotic form of the charge exchange cross section in the three body rearrangement collisions

A three body general rearrangement collision is considered where the initial and final bound states are described by the hydrogen-like wave functions. Mathematical models are developed to establish the relationships of quantum number, the reduced mass, and the nuclear charge of the final state. It is shown that for the low lying levels, the reciprocal of n cubed scaling law at all incident energies is only approximately satisfied. The case of the symmetric collisions is considered and it is shown that for high n and high incident energy, E, the cross section behaves as the reciprocal of E cubed. Zeros and minima in the differential cross sections in the limit of high n for protons on atomic hydrogen and positrons on atomic hydrogen are given.

Omidvar, K.↗
NASA NTRS1974

Rotational-vibrational coupling in the theory of electron-molecule scattering

The adiabatic-nuclei approximation of vibrational-rotational excitation of homonuclear diatomic molecules can be simply augmented to describe the vibrational-rotational coupling by including the dependence of the vibrational wave function on j. Appropriate formulas are given, and the theory, is applied to e-H2 excitation, whereby it is shown that deviations from the simple Born-Oppenheimer approximation measured by Wong and Schultz can be explained. More important, it can be seen that the inclusion of the j-dependent centrifugal term is essential for transitions involving high-rotational quantum numbers.

Temkin, A.↗
NASA NTRS1974

Angular distribution of photoelectrons from atomic oxygen, nitrogen and carbon

The angular distributions of photoelectrons from atomic oxygen, nitrogen, and carbon are calculated. Both Hartree-Fock and Hartree-Slater (Herman-Skillman) wave functions are used for oxygen, and the agreement is excellent; thus only Hartree-Slater functions are used for carbon and nitrogen. The pitch-angle distribution of photoelectrons is discussed, and it is shown that previous approximations of energy-independent isotropic or sin squared theta distributions are at odds with the authors' results, which vary with energy. This variation with energy is discussed, as is the reliability of these calculations.

Manson, S. J.↗
NASA NTRS1975

Stability of localized plasma model in two and three dimensions

Stability against catastrophic radial collapse is demonstrated for initially well-behaved, localized solutions in a class of two- and three-dimensional wave equations characterized by saturating nonlinearities, which model various electrostatic and electromagnetic 'caviton' structures in an asymptotically uniform plasma. This result contrasts sharply with mathematical predictions of equations with low-order nonlinearities. Discrete classes of possible quasistationary modes exhibit features comparable to atomic wave functions and differ qualitatively from one-dimensional structures.

Wilcox, J. Z.↗
NASA NTRS1975

Asymptotic form of the charge-exchange cross section in three-body rearrangement collisions

A three-body general-type rearrangement collision is considered in which the initial and final bound states are described by hydrogen-like wave functions. It is shown that the charge-exchange amplitude in the first Born approximation can be expanded at all incident energies in terms of the inverse powers of the principal quantum number (n). By expanding the exchange amplitude in this way, it is demonstrated conclusively that the cross section for capture into the s, p, and d states as well as for the sum over all the angular-momentum states is proportional to 1/n-cubed plus terms proportional to higher inverse odd powers of n. It is found that the low-lying levels cannot be scaled to the 1/n-cubed law irrespective of the value of the incident energy except in the case of capture into the s states in accordance with the Oppenheimer-Brinkman-Kramers approximation. Zeros and minima in the differential cross sections are given in the limit of high principal quantum number for electron capture by protons from atomic hydrogen and for positronium formation by proton-atomic hydrogen collisions.

Omidvar, K.↗
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.↗