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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Exact, E = 0, classical and quantum solutions for general power-law oscillators

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

Nieto, Michael Martin↗
NASA NTRS2002

D-wave Resonances in Positronium Hydride

We have recently reexamined the problem of calculating the positions and widths of the lowest-lying S- and P-state resonances in the Ps+H scattering system. The resonances are generated by bound Rydberg states in the closed rearranged channel (e(+)+H(-)), shifted somewhat by coupling with the open scattering channel. This picture had been successfully applied for S-waves, but more recent results showed unexpectedly large shifts in both P- and D-wave resonances. Our recalculation for the S- and P-waves showed that the series of resonances begins with the second Rydberg state, giving rise to an apparent large shift. Now we have extended the calculations to D states. Here we find the expected results: The 3D Rydberg state produces a resonance very close to the result of Yan and Ho, and inclusion of the 4D state gives a second resonance only slightly shifted.

Drachman, Richard J.↗
NASA NTRS1965

Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States

The bracketing theorem in the partitioning technique for solving the Schrödinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of ``inner projections'' on finite manifolds in the Hilbert space. The method is here applied to the ground state and excited states of a Hamiltonian H=H(sub 0)+V having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers.

Loewdin, Per-Olov↗
NASA NTRS1988

The rate parameters for coupled vibration-dissociation in a generalized SSH approximation

A theoretical study of vibrational excitations and dissociations of nitrogen undergoing a nonequilibrium relaxation process upon heating and cooling is reported. The rate coefficients for collisional induced vibrational transitions and transitions from a bound vibrational state into a dissociative state have been calculated using an extension of the theory originally proposed by Schwarz (SSH) et al. (1952). High-lying vibrational states and dissociative states were explicitly included but rotational energy transfer was neglected. The transition probabilities calculated from the SSH theory were fed into the master equation, which was integrated numerically to determine the population distribution of the vibrational states as well as bulk thermodynamic properties. The results show that: (1) the transition rates have a minimum near the middle of the bound vibrational levels, causing a bottleneck in the vibrational relaxation and dissociation rates; (2) high vibrational states are always in equilibrium with the dissociative state; (3) for the heating case, only the low vibrational states relax according to the Landau-Teller theory; (4) for the cooling case, vibrational relaxation cannot be described by a rate equation; (5) Park's (1985, 1988) two-temperature model is approximately valid; and (6) the average vibrational energy removed in dissociation is about 30 percent of the dissociation energy.

Sharma, Surendra P.↗
NASA NTRS2010

Analytical Dimensional Reduction of a Fuel Optimal Powered Descent Subproblem

Current renewed interest in exploration of the moon, Mars, and other planetary objects is driving technology development in many fields of space system design. In particular, there is a desire to land both robotic and human missions on the moon and elsewhere. The landing guidance system must be able to deliver the vehicle to a desired soft landing while meeting several constraints necessary for the safety of the vehicle. Due to performance limitations of current launch vehicles, it is desired to minimize the amount of fuel used. In addition, the landing site may change in real-time in order to avoid previously undetected hazards which become apparent during the landing maneuver. This complicated maneuver can be broken into simpler subproblems that bound the full problem. One such subproblem is to find a minimum-fuel landing solution that meets constraints on the initial state, final state, and bounded thrust acceleration magnitude. With the assumptions of constant gravity and negligible atmosphere, the form of the optimal steering law is known, and the equations of motion can be integrated analytically, resulting in a system of five equations in five unknowns. It is shown that this system of equations can be reduced analytically to two equations in two unknowns. With an additional assumption of constant thrust acceleration magnitude, this system can be reduced further to one equation in one unknown. It is shown that these unknowns can be bounded analytically. An algorithm is developed to quickly and reliably solve the resulting one-dimensional bounded search, and it is used as a real-time guidance applied to a lunar landing test case.

Rea, Jeremy R.↗
NASA NTRS1974

Three-body Coulomb systems using generalized angular-momentum S states

An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound S states of three-body Coulomb systems. The results for He, H(-), e(-)e(+)e(-), and pmu(-)p are compared with the results of other computational approaches.

Whitten, R. C.↗
NASA NTRS2007

Theoretical Studies of Routes to Synthesis of Tetrahedral N4

A paper [Chem. Phys. Lett. 345, 295 (2001)] describes theoretical studies of excited electronic states of nitrogen molecules, with a view toward utilizing those states in synthesizing tetrahedral N4, or Td N4 a metastable substance under consideration as a high-energy-density rocket fuel. Several ab initio theoretical approaches were followed in these studies, including complete active space self-consistent field (CASSCF), state-averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD). Standard double zeta polarized and triple zeta double polarized one-particle basis sets were used. The CASSCF calculations overestimated the excitation energies, while SACASSCF calculations partly corrected these overestimates. The accuracy of the CIS calculations varied, depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results were in generally good agreement. The energies of the lowest six excited singlet states of Td N4 as calculated by the LRCCSD were compared with the energies of possible excited states of N2 + N2 fragments, leading to the conclusion that the most likely route for synthesis of Td N4 would involve a combination of two bound quintet states of N2.

Lee, Timothy J.↗
NASA NTRS2001

Theoretical Studies of Possible Synthetic Routes for the High Energy Density Material Td N4: Excited Electronic States

Vertical electronic excitation energies for single states have been computed for the high energy density material (HEDM) Td N4 in order to assess possible synthetic routes that originate from excited electronic states of N2 molecules. Several ab initio theoretical approaches have been used, including complete active space self-consistent field (CASSCF), state averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D)) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD), which is the highest level of theory employed. Standard double zeta polarized (DZP) and triple zeta double polarized (TZ2P) one-particle basis sets were used. The CASSCF calculations are found to overestimate the excitation energies, while the SA-CASSCF approach rectifies this error to some extent, but not completely. The accuracy of the CIS calculations varied depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results are in generally good agreement. Based on the LRCCSD calculations, the lowest six excited singlet states are 9.35(l(sup)T1), 10.01(l(sup)T2), 10.04(1(sup)A2), 10.07(1(sup)E), 10.12(2(sup)T1), and 10.42(2(sup)T2) eV above the ground state, respectively. Comparison of these excited state energies with the energies of possible excited states of N2+N2 fragments, leads us to propose that the most likely synthetic route for Td N4 involving this mechanism arises from combination of two bound quintet states of N2.

Lee, Timothy J.↗
NASA NTRS1991

Theoretical characterization of the potential energy surface for H + N2 yields HN2. III - Calculations for the excited state surfaces

Additional calculations which characterize potential energy sources (PESs) for the excited 3A-double-prime state, for a bound 2(2A-prime) state, for HN2(+), and for the Rydberg states associated with HN2(+). It is anticipated that these excited state PESs will be important in interpreting and designing experiments to characterize the ground state HN2 species via neutralized ion beam techniques.

Walch, Stephen P.↗
NASA NTRS1993

Electronic excitation of ground state atoms by collision with heavy gas particles

Most of the important chemical reactions which occur in the very high temperature air produced around space vehicles as they enter the atmosphere were investigated both experimentally and theoretically, to some extent at least. One remaining reaction about which little is known, and which could be quite important at the extremely high temperatures that will be produced by the class of space vehicles now contemplated - such as the AOTV - is the excitation of bound electron states due to collisions between heavy gas particles. Rates of electronic excitation due to free electron collisions are known to be very rapid, but because these collisions quickly equilibrate the free and bound electron energy, the approach to full equilibrium with the heavy particle kinetic energy will depend primarily on the much slower process of bound electron excitation in heavy particle collisions and the subsequent rapid transfer to free electron energy. This may be the dominant mechanism leading to full equilibrium in the gas once the dissociation process has depleted the molecular states so the transfer between molecular vibrational energy and free electron energy is no longer available as a channel for equilibration of free electron and heavy particle kinetic energies. Two mechanisms seem probable in electronic excitation by heavy particle impact. One of these is the collision excitation and deexcitation of higher electronic states which are Rydberg like. A report, entitled 'Semi-Classical Theory of Electronic Excitation Rates', was submitted previously. This presented analytic expressions for the transition probabilities, assuming that the interaction potential is an exponential repulsion with a perturbation ripple due to the dipole-induced dipole effect in the case of neutral-neutral collisions, and to the ion-dipole interaction in the case of ion-neutral collisions. However the above may be, there is little doubt that excitation of ground state species by collision occurs at the point where the initial and final potentials cross, or at least come very close. Therefore, this mechanism would be applicable to the case where a gas is initially at very low temperature suddenly subjected to high energy heavy particle bombardment. This situation would model the measurement of excitation cross section by molecular beam techniques, for example. The purpose is to report values of cross sections and rate coefficients for collision excitation of ground state atoms estimated with the Landau-Zener transition theory and to compare results with measurement of excitation cross sections for a beam of Hydrogen atoms impacting Argon atom targets. Some very dubious approximations are used, and the comparison with measurement is found less than ideal, but results are at least consistent within order of magnitude. The same model is then applied to the case of N-N atom collisions, even though the approximations then become even more doubtful. Still the rate coefficients obtained are at least plausible in both magnitude and functional form, and as far as I am aware these are the only estimates available for such rate coefficients.

Hansen, C. Frederick↗
NASA NTRS1987

Mean-square error bounds for reduced-error linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗
NASA NTRS1987

Mean-square-error bounds for reduced-order linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Liapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗
NASA NTRS1994

Electronically Controlled Mechanical Seal for Aerospace Applications -- Part 1: Design, Analysis, and Steady State Tests

An electronically-controlled mechanial seal, for use as the purge gas seal in a liquid oxygen turbopump, has been designed, analyzed, and built. The thickness of the lubricating film between the faces is controlled by adjusting the coning of the carbon face. This is done by applying a voltage across a piezoelectric element to which the carbon face is bound. Steady state tests have shown that the leakage rate (and film thickness) can be adjusted over a substantial range, utilizing the available range of voltage.

Salant, Richard F.↗
NASA NTRS2016

Electronically Excited States of Anistropically Extended Singly-Deprotonated PAH Anions

Polycyclic Aromatic Hydrocarbons (PAHs) play a significant role in the chemistry of the interstellar medium (ISM) as well as in hydrocarbon combustion. These molecules can have high levels of diversity with the inclusion of heteroatoms and the addition or removal of hydrogens to form charged or radical species. There is an abundance of data on the cationic forms of these molecules, but there have been many fewer studies on the anionic species. The present study focuses on the anionic forms of deprotonated PAHs. It has been shown in previous work that PAHs containing nitrogen heteroatoms (PANHs) have the ability to form valence excited states giving anions electronic absorption features. This work analyzes how the isoelectronic pure PAHs behave under similar structural constructions. Singly-deprotonated forms of benzene, naphthalene, anthracene, and teteracene classes are examined. None of the neutral-radicals possess dipole moments large enough to support dipole-bound excited states in their corresponding closed-shell anions. Even though the PANH anion derivatives support valence excited states for three-ringed structures, it is not until four-ringed structures of the pure PAH anion derivatives that valence excited states are exhibited. However, anisotropically-extended PAHs larger than tetracene will likely exhibit valence excited states. The relative energies for the anion isomers are very small for all of the systems in this study.

Theis, Mallory L.↗
NASA NTRS1987

The calculation of high-temperature equilibrium and nonequilibrium specific heat data for N2, O2 and NO

Specific heat data for high-temperature air species are needed to compute the temperature and enthalpy of gas mixtures in aerothermodynamics flowfield calculations. Accurate data are known only for temperatures under 6000 K, but are required for temperatures exceeding 25,000 K. In the present study, CP data are computed for N2, O2 and NO. The calculations are based on summations over all the vibration-rotation energy levels for all known bound electronic states. Estimates are made for the error introduced by the neglect of possible additional high-lying electronic states. In addition, a scheme for the partitioning of the internal energy into vibrational, rotational and electronic contributions is presented which consistently accounts for the nonseparable nature of the various energy modes. The multitemperature specific heat data are recommended for use in nonequilibrium flowfield models.

Jaffe, Richard L.↗