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At least 145 records · Page 8

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NASA NTRS1990

Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions

The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.

Schwenke, David W.↗

NASA NTRS1992

Radial vibrations of a sodium ion inside icosahedral C60

The very high symmetry of icosahedral C60 suggests that, as a first approximation, an atom trapped inside C60 would be subject to a potential that is radially symmetric about the center. All-electron local-density-functional calculations of the total energy of a sodium ion as a function of radial displacement from the center along the fivefold axis of C60 serve to refine such a radial potential. In particular, the calculations suggest studying potentials that have minima displaced from the center. An analytic functional form for a radial potential having a positive cusp at the origin is proposed, and the s-wave radial solutions of the corresponding Schroedinger equation are examined.

Ballester, J. L.↗

NASA NTRS1993

Alternative descriptions of wave and particle aspects of the harmonic oscillator

The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.

Schuch, Dieter↗

NASA NTRS1992

Characteristics of obliquely propagating, nonlinear Alfven waves

Consideration is given to properties of obliquely propagating (with respect to the large-scale magnetic field) nonlinear Alfven and fast magnetosonic waves as described by the derivative nonlinear Schroedinger equation. The focus is on those waves which in the parallel-propagating limit are circularly polarized, exact solutions to the MHD equations. Results are presented of a study of the changes in the structure of these waves as the propagation angle is increased. Attention is also given to the evolution of initial conditions which do not correspond to stationary wave propagations. It is found that, as the propagation angle with respect to the mean field increases, the functional forms of the wave magnetic field components in the two directions orthogonal to the propagation direction become increasingly dissimilar. The angle about the mean field within which stationary waves resemble parallel-propagating, circularly polarized waves becomes smaller as the wavelength increases. If the 'initial condition' wave train is close to parallel-propagating, then there is little subsequent evolution in its form.

Spangler, Steven R.↗

NASA NTRS1993

The evolution of strongly modulated, low-frequency, moderate-amplitude wave packets in a dispersive plasma

The evolution of strongly modulated wave packets in a dispersive plasma that propagate parallel to the magnetic field is studied. Modulation effects are shown to reduce significantly (about 30 percent) the rate of spreading from that due to dispersion alone. For fluidlike behavior, nonlinearity has its greatest impact on evolution when the linear sound speed and initial wave packet speeds are well matched, resulting in a strong coupling between the wave magnetic and sonic components. Ion kinetic processes reduce the impact of nonlinearity and cause the rate of spreading to approach that expected from dispersion alone as the ratio of ion and electron temperatures, Ti/Te approaches 4. For Beta equal to or greater than 1 and Ti/Te of about 1, the coupled waveforms correspond qualitatively to kinetic treatments of the derivative nonlinear Schroedinger equation.

Vasquez, Bernard J.↗

NASA NTRS1993

Vibrational predissociation of methylnitrite using phase-locked ultrashort laser pulses

We solve numerically the time-dependent Schroedinger equation to study the behavior of a molecule interacting with two phase-locked ultrashort laser pulses. The 2D model used in the calculations mimics the properties of the CH3ONO molecule. The two pulses are identical except for their relative phase and are tuned to excite an upper electronic state of the molecule. After excitation the molecule predissociates, and we calculate the dependence of the NO yield and of the NO vibrational population on the delay time between the pulses.

Dateo, Christopher E.↗

NASA NTRS1992

The evolution of large-amplitude MHD waves near quasi-parallel shocks in the solar wind

We discuss attempts to explain the steepening of magnetohydrodynamic waves upstream of the Earth's bow shock and the formation of short-wavelength 'shocklets' in terms of simple analytic models. The effort involves use of the Derivative Nonlinear Schroedinger Equation (DNLS) to describe the wave evolution. We review shortcomings of previous attempts to model foreshock wave phenomena in terms of wave packet evolution according to the DNLS. It is pointed out that: (1) the oblique propagation of the waves and (2) their growth by unstable particle distribution are conducive to the processes of wave steepening and shocklet formation. Numerical solutions of the DNLS with initial conditions corresponding to envelope-modulated, obliquely propagating wave packets yield evolved wave packets with many properties similar to the observed waves.

Spangler, S. R.↗

NASA NTRS1993

Characteristics of 0.8- and 0.2-microns gate length In(x)Ga(1-x) As/In(0.52)Al(0.48)As/InP (0.53 less than or equal to x less than or equal to 0.70) modulation-doped field-effect transistors at cryogenic temperatures

The performance characteristics of InP-based In(x)Ga(1-x)As/In(0.52)Al(0.48)As (0.53 is less than or equal to x is less than or equal to 0.70) pseudomorphic modulation-doped field-effect transistors (MODFET's) as a function of strain in the channel, gate, length, and temperature were investigated analytically and experimentally. The strain in the channel was varied by varying the In composition x. The temperature was varied in the range of 40-300 K and the devices have gate lengths L(sub g) of 0.8 and 0.2 microns. Analysis of the device was done using a one-dimensional self consistent solution of the Poisson and Schroedinger equations in the channel, a two-dimensional Poisson solver to obtain the channel electric field, and a Monte Carlo simulation to estimate the carrier transit times in the channel. An increase in the value of the cutoff frequency is predicted for an increase in In composition, a decrease in temperature, and a decrease in gate length. The improvements seen with decreasing temperature, decreasing gate length, and increased In composition were smaller than those predicted by analysis. The experimental results on pseudomorphic InGaAs/InAlAs MODFET's showed that there is a 15-30 percent improvement in cutoff frequency in both the 0.8- and 0.2-micron gate length devices when the temperature is lowered from 300 to 40 K.

Lai, Richard↗

NASA NTRS1987

Computational chemistry research

Task 41 is composed of two parts: (1) analysis and design studies related to the Numerical Aerodynamic Simulation (NAS) Extended Operating Configuration (EOC) and (2) computational chemistry. During the first half of 1987, Dr. Levin served as a member of an advanced system planning team to establish the requirements, goals, and principal technical characteristics of the NAS EOC. A paper entitled 'Scaling of Data Communications for an Advanced Supercomputer Network' is included. The high temperature transport properties (such as viscosity, thermal conductivity, etc.) of the major constituents of air (oxygen and nitrogen) were correctly determined. The results of prior ab initio computer solutions of the Schroedinger equation were combined with the best available experimental data to obtain complete interaction potentials for both neutral and ion-atom collision partners. These potentials were then used in a computer program to evaluate the collision cross-sections from which the transport properties could be determined. A paper entitled 'High Temperature Transport Properties of Air' is included.

Levin, Eugene↗

NASA NTRS1995

Harmonic oscillator representation in the theory of scattering and nuclear reactions

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Smirnov, Yuri F.↗

NASA NTRS1995

The relativistic many body problem with an oscillator interaction

We start with the total energy E for a system of three scalar relativistic particles that, because of Einstein's relation, will have square roots of functions of the momenta. By taking powers of this relation, we finally get a fourth degree polynomial in E(exp 2), where the square roots have disappeared, and which we can convert into a type of Schroedinger equation. To be in the center of mass frame we pass to Jocobi momenta and then replace them by creation and annihilation operators. We thus get an equation in terms of the generators of a U(2) group, which, in principle, we can solve in an elementary way. Finally, we rewrite our equation in a Poincare invariant form.

Moshinsky, Marcos↗

NASA NTRS1994

Barrier potential design criteria in multiple-quantum-well-based solar-cell structures

The barrier potential design criteria in multiple-quantum-well (MQW)-based solar-cell structures is reported for the purpose of achieving maximum efficiency. The time-dependent short-circuit current density at the collector side of various MQW solar-cell structures under resonant condition was numerically calculated using the time-dependent Schroedinger equation. The energy efficiency of solar cells based on the InAs/Ga(y)In(1-y)As and GaAs/Al(x)Ga(1-x)As MQW structues were compared when carriers are excited at a particular solar-energy band. Using InAs/Ga(y)In(1-y)As MQW structures it is found that a maximum energy efficiency can be achieved if the structure is designed with barrier potential of about 450 meV. The efficiency is found to decline linearly as the barrier potential increases for GaAs/Al(x)Ga(1-x)As MQW-structure-based solar cells.

Mohaidat, Jihad M.↗

NASA NTRS1994

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Birn, Joachim↗

NASA NTRS1995

The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems they can be grouped into two types: those based on the Schroedinger equation and those based on the Lippmann-Schwinger equation. The application of the Schwinger variational (SV) method to e-molecule collisions and photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions.

Huo, Winifred M.↗

NASA NTRS1995

Accurate ab Initio Quartic Force Fields, Vibrational Frequencies, and Heats of Formation for FCN, FNC, ClCN, and ClNC

The XCN and XNC (X = F, Cl) isomers have been investigated using the CCSD(T) method in conjunction with correlation consistent basis sets. Equilibrium geometries, harmonic frequencies, anharmonic constants, fundamental frequencies, and heats of formation have been evaluated. Agreement with experiment for the fundamental frequencies is very good, even for nu(sub 2), for CICN, which is subject to a strong Fermi resonance with 2nu(sub 3). It is also shown that a second-order perturbation theory approach to solving the nuclear Schroedinger equation gives results in excellent agreement with essentially exact variational calculations. This is true even for nu(sub 2) of ClCN, provided that near-singular terms are eliminated from the perturbation theory formulas and the appropriate Fermi interaction energy matrix is then diagonalized. A band at 615/cm, tentatively assigned as the Cl-N stretch in ClNC in matrix isolation experiments, is shown not to be due to ClNC. Accurate atomization energies are determined and are used to evaluate accurate heats of formation (3.1 +/- 1.5, 33.2 +/- 1.5, 72.6 +/- 1.5, and 75.9 +/- 1.5 kcal/mol for FCN, ClCN, FNC, and ClNC, respectively). It is expected that the theoretical heats of formation for FCN, FNC, and ClNC are the most accurate available.

Lee, Timothy J.↗

NASA NTRS1995

The FEM-R-Matrix Approach: Use of Mixed Finite Element and Gaussian Basis Sets for Electron Molecule Collisions

For the calculation of electron molecule collision cross sections R-matrix methods automatically take advantage of the division of configuration space into an inner region (I) bounded by radius tau b, where the scattered electron is within the molecular charge cloud and the system is described by an correlated Configuration Interaction (CI) treatment in close analogy to bound state calculations, and an outer region (II) where the scattered electron moves in the long-range multipole potential of the target and efficient analytic methods can be used for solving the asymptotic Schroedinger equation plus boundary conditions.

Thuemmel, Helmar T.↗

NASA NTRS2004

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗

NASA NTRS2007

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition: Inclusion of Correlation Effects - III

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

Shertzer, Janine↗