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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Viscel: A general purpose computer program for analysis of linear viscoelastic structures, volume 2

The VISCEL program is a general purpose computer program developed for equilibrium analysis of linear viscoelastic structures. The program is written in FORTRAN 5 language to operate on the Univac 1108 computer under the EXEC 8 operating system. The program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form written for the IBM 7094 computer. Finite element matrix displacement approach coupled with the synchronized material property concept, utilizing incremental time steps, was adopted for the solution presented. The step-by-step procedure involves solution of recursive equations in the time domain, which takes into account the memory of material properties. Incremental and accumulative displacements and stresses are obtained at the end of each time step. In order to minimize the extent of computations resulting from accumulative effects of material memory, the program provides an option which enables the employment of constant time steps in the logarithmic scale. Program documentation is presented.

Gupta, K. K.↗
NASA NTRS1972

VISCEL: A general-purpose computer program for analysis of linear viscoelastic structures (user's manual), volume 1

This program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form (written in FORTRAN 2 for the IBM 7094 computer). A synchronized material property concept utilizing incremental time steps and the finite element matrix displacement approach has been adopted for the current analysis. A special option enables employment of constant time steps in the logarithmic scale, thereby reducing computational efforts resulting from accumulative material memory effects. A wide variety of structures with elastic or viscoelastic material properties can be analyzed by VISCEL. The program is written in FORTRAN 5 language for the Univac 1108 computer operating under the EXEC 8 system. Dynamic storage allocation is automatically effected by the program, and the user may request up to 195K core memory in a 260K Univac 1108/EXEC 8 machine. The physical program VISCEL, consisting of about 7200 instructions, has four distinct links (segments), and the compiled program occupies a maximum of about 11700 words decimal of core storage.

Gupta, K. K.↗
NASA NTRS1972

Quantum-mechanical transport equation for atomic systems.

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Berman, P. R.↗
NASA NTRS1973

Polarization phenomena in multiphoton ionization of atoms

The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photoelectron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.

Jacobs, V. L.↗
NASA NTRS1973

Optical potential approach to the electron-atom impact ionization threshold problem

The problem of the threshold law for electron-atom impact ionization is reconsidered as an extrapolation of inelastic cross sections through the ionization threshold. The cross sections are evaluated from a distorted wave matrix element, the final state of which describes the scattering from the Nth excited state of the target atom. The actual calculation is carried for the e-H system, and a model is introduced which is shown to preserve the essential properties of the problem while at the same time reducing the dimensionability of the Schrodinger equation. Nevertheless, the scattering equation is still very complex. It is dominated by the optical potential which is expanded in terms of eigen-spectrum of QHQ. It is shown by actual calculation that the lower eigenvalues of this spectrum descend below the relevant inelastic thresholds; it follows rigorously that the optical potential contains repulsive terms. Analytical solutions of the final state wave function are obtained with several approximations of the optical potential.

Temkin, A.↗
NASA NTRS1973

Energy partitioning of gaseous ions in an electric field.

The partitioning of ion energy among thermal energy, drift energy, and random-field energy is studied by solution of the Boltzmann equation. An expansion in powers of the square of the electric field strength is obtained by Kihara's method. Numerical calculations for several ion-neutral force laws show that Wannier's constant mean-free-time model gives a reasonable first approximation. The formal extension to multicomponent mixtures is also given. The matrix elements obtained are tabulated, and can be used to study the field dependence of other moments of the ion-distribution function.

Hahn, H.-S.↗
NASA NTRS1973

Polarization phenomena in multiphoton ionization of atoms.

The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.

Jacobs, V. L.↗
NASA NTRS1974

Effects of anisotropic electron-ion interactions in atomic photoelectron angular distributions

The photoelectron asymmetry parameter beta in LS-coupling is obtained as an expansion into contributions from alternative angular momentum transfers j sub t. The physical significance of this expansion of beta is shown to be that: (1) the electric dipole interaction transfers to the atom a charcteristic single angular momentum j sub t = sub o, where sub o is the photoelectron's initial orbital momentum; and (2) angular momentum transfers indicate the presence of anisotropic interaction of the outgoing photoelectron with the residual ion. For open shell atoms the photoelectron-ion interaction is generally anisotropic; photoelectron phase shifts and electric dipole matrix elements depend on both the multiplet term of the residual ion and the total orbital momentum of the ion-photoelectron final state channel. Consequently beta depends on the term levels of the residual ion and contains contributions from all allowed values of j sub t. Numerical calculations of the asymmetry parameters and partial cross sections for photoionization of atomic sulfur are presented.

Dill, D.↗
NASA NTRS1974

Evaluation of atomic constants for optical radiation, volume 1

Atomic constants for optical radiation are discussed which include transition probabilities, line strengths, and oscillator strengths for both dipole and quadrupole transitions, as well as the associated matrix elements needed for line broadening calculations. Atomic constants were computed for a wide selection of elements and lines. An existing computer program was used, with modifications to include, in an approximate manner, the effect of equivalent electrons, and to enable reordering and restructuring of the output for publication. This program is suitable for fast, low cost computation of the optical constants, using the Coulomb approximation formalism for LS coupling.

Kylstra, C. D.↗
NASA NTRS1975

A combined representation method for use in band structure calculations. 1: Method

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Friedli, C.↗
NASA NTRS1976

IR pumped third-harmonic generation and sum-frequency generation in diatomic molecules

The potential efficiency of using nonlinear up-conversion techniques for the high efficiency type lasers (CO,CO2, and chemical) is assessed. Results indicate that: the small pump photon energy necessitates the use of molecular media for conversion if resonance enhancement is to be used and that molecular systems present several problems. These difficulties include: their levels are complex; their transition probabilities are often unknown; and the oscillator strengths among vibrational levels in the ground electronic state of a molecule are much smaller than those among electronic states of an atom, thus limiting the magnitude of nonlinear interactions. It is shown that this problem can be eliminated by making use of vibronic transitions which, being primarily electronic transitions have much larger matrix elements and efficient conversion can be achieved with molecular systems.

She, C. Y.↗
NASA NTRS1976

Two-electron bond-orbital model, 2

The two-electron bond-orbital model of tetrahedrally-coordinated solids is generalized and its application extended. All intrabond matrix elements entering the formalism are explicitly retained, including the direct overlap S between the anion and cation sp3 hybrid wavefunctions. Complete analytic results are obtained for the six two-electron eigenvalues and eigenstates of the anion-cation bond in terms of S, one-electron parameters V2 and V3, and two-electron correlation parameters V4, V5 and V6. Refined formulas for the dielectric constant and the nuclear exchange and pseudodipolar coefficients, as well as new expressions for the valence electron density, polarity of the bond and the cohesive energy, are then derived. The theory gives a good account of the experimentally observed trends in all properties considered and approximate quantitative agreement is achieved for the pseudodipolar coefficient.

Huang, C.↗
NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum mechanical theories of collision induced electronic transitions. Within the two state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases are considered: the avoided crossing between two potential surfaces; and the spin orbit interaction due to a P-2 halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗
NASA NTRS1977

Shuttle Program. Euler angles, quaternions, and transformation matrices working relationships

A brief mathematical development of the relationship between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion is presented. The analysis and equations presented apply directly to current space shuttle problems. The twelve three-axis Euler transformation matrices are given as functions of the Euler angles, the equations for the quaternion as a funtion of the Euler angles, and the Euler angles as a function of the transformation matrix elements.

Henderson, D. M.↗
NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum-mechanical theories of collision-induced electronic transitions. Within the two-state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases have been considered: (1) the avoided crossing between two potential surfaces, and (2) the spin-orbit interaction due to a 2P halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗
NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗