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NASA NTRS1993

All-electron molecular Dirac-Hartree-Fock calculations - Properties of the group IV monoxides GeO, SnO, and PbO

Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.

Dyall, Kenneth G.↗
NASA NTRS1992

Negative-energy states in the Dirac-Hartree-Fock problem - The effect of omission of two-electron integrals involving the small component

The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.

Dyall, Kenneth G.↗
NASA NTRS1995

Pseudoclassical description of the Dirac Oscillator

In this paper we discuss the Dirac Oscillator wave equation in terms of pseudoclassical language, using Grassmann variables to describe the internal degrees of freedom of the oscillator. Regarding the original wave equation as a classical constraint, we use the theory of constrained systems, to develop a reparameterization invariant lagrangian, which is the pseudoclassical equivalent of the quantum case. The consistency of the Hamiltonian formalism and the quantization procedure are also analyzed.

Delsolmesa, Antonio↗
NASA NTRS1996

The General Necessary Condition for the Validity of Dirac's Transition Perturbation Theory

For the first time, from the natural requirements for the successive approximation the general necessary condition of validity of the Dirac's method is explicitly established. It is proved that the conception of 'the transition probability per unit time' is not valid. The 'super-platinium rules' for calculating the transition probability are derived for the arbitrarily strong time-independent perturbation case.

Quang, Nguyen Vinh↗
NASA NTRS1994

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

Dyall, Kenneth G.↗
NASA NTRS1977

Dirac cosmology

The large numbers hypothesis (LNH) linking the magnitude of large dimensionless ratios in physics (on the order of 10 to the 40th power) to cosmic time is examined. The LNH is checked against evidence on 3K background radiation of the universe and the (log N, log S)-relation for radio galaxies. Earlier criticisms of LNH by Gamow and Teller are examined, and alternative hypotheses put forth by Dicke and Carter (1974) are discussed. The discussion covers: continuous (additive or multiplicative) creation of matter, the Einstein metric and the atomic metric, and general cosmological and local astronomical implications of LNH. LNH is also viewed in relation to solar evolution and pulsar physics.

Canuto, V.↗
NASA NTRS1980

Primordial nucleosynthesis and Dirac's large numbers hypothesis

Consideration is given to the analysis of Falik (1979) which attempted to show that the cosmological model proposed by Canuto and Hsieh (1978) in which the gravitational constant varies with time contradicts observations of primordial helium. It is shown that the analysis was based on the assumptions that (1) the energy density of radiation in local thermodynamic equilibrium is approximately equal to the fourth power of the equilibrium temperature, where the product of the equilibrium temperature with the scale factor of the Robertson-Walker metric is constant, and (2) the gravitational constant is approximately equal to the inverse of the time even at early cosmological epochs. These assumptions are demonstrated to be invalid in the scale covariant theory of gravitation used to develop the model, thus negating the conclusion that the Canuto and Hsieh model excludes the primordial synthesis of helium.

Canuto, V.↗
NASA NTRS1989

A new way to interpret the DIRAC equation in a non-Riemannian manifold

The idea of internal mass terms introduced in ref. (1), is shown not to be an appropriate hypothesis when it is placed in connection with the components of the generalized (matrix) vierbeins being proportional to the Riemannian (gravitational) vierbeins. It would result in an undesirable canceling of the Electromagnetic and the Yang-Mills components in the generalized metric. Another hypothesis is introduced where the wave function psi is Taylor expanded in a small parameter p.

Marques-Bonham, Sirley↗
NASA NTRSDate not supplied

Digitally-Engineered Impact Resistant Aerogel Composites for MMOD Protection (DIRAC-MP)

This project implemented a digital-engineering approach to optimize the impact absorption performance of polymer aerogels and aerogel-based composites for Micrometeoroids and Orbital Debris (MMOD) containment. We developed a curated materials database and a machine-learning framework to derive composition-response relationships, enabling predictive design and targeted material selection. In support of experimental validation, a split Hopkinson pressure bar (SHPB) test rig, specifically adapted for low-density aerogel materials, was designed and built in-house. This project accelerates the development of new aerogel formulations, producing candidate materials tailored for enhanced impact-absorption behavior.

Sadeq Malakooti↗
NASA NTRS2012

Positron Interactions with Atoms and Ions

Dirac, in 1928, combining the ideas of quantum mechanics and the ideas of relativity invented the well-known relativistic wave equation. In his formulation, he predicted an antiparticle of the electron of spin n-bar/2. He thought that this particle must be a proton. Dirac published his interpretation in a paper 'A theory of electrons and protons.' It was shown later by the mathematician Hermann Weyl that the Dirac theory was completely symmetric between negative and positive particles and the positive particle must have the same mass as that of the electron. In his J. Robert Oppenheimer Memorial Prize Acceptance Speech, Dirac notes that 'Blackett was really the first person to obtain hard evidence for the existence of a positron but he was afraid to publish it. He wanted confirmation, he was really over cautious.' Positron, produced by the collision of cosmic rays in a cloud chamber, was detected experimentally by Anderson in 1932. His paper was published in Physical Review in 1933. The concept of the positron and its detection were the important discoveries of the 20th century. I have tried to discuss various processes involving interactions of positrons with atoms and ions. This includes scattering, bound states and resonances. It has not been possible to include the enormous work which has been carried out during the last 40 or 50 years in theory and measurements.

Bhatia, Anand K.↗
NASA NTRS1995

Notes on oscillator-like interactions of various spin relativistic particles

The equations for various spin particles with oscillator-like interactions are discussed in this talk. Topics discussed include: (1) comment on 'The Klein-Gordon Oscillator'; (2) the Dirac oscillator in quaternion form; (3) the Dirac-Dowker oscillator; (4) the Weinberg oscillator; and (5) note on the two-body Dirac oscillator.

Dvoeglazov, Valeri V.↗
NASA NTRS1988

Bounds on exotic-particle interactions from SN 1987A

The observation of a neutrino pulse from the supernova SN 1987A constrains the production of light exotic particles in the protoneutron star. A new bound on the axion decay constant is derived, f(a) of greater than about 10 to the 10th GeV. If right-handed (RH) neutrinos exist, 'RH Fermi constant' is G(RH) of less than about 10 exp-4 G(F), two orders of magnitude below laboratory bounds. The Dirac mass of hv sub m can be constrained below laboratory limits. The Dirac mass of the mu-neutrino can be constrained below laboratory limits.

Raffelt, Georg↗
NASA NTRS1991

Astrophysics and cosmology confront the 17 keV neutrino

A host of astrophysical and cosmological arguments severely constrain the properties of a 17 keV Dirac neutrino. Such a neutrino must have interactions beyond those of the standard electroweak theory to reduce its cosmic abundance (through decay or annihilation) by a factor of two hundred. A predicament arises because the additional helicity states of the neutrino necessary to construct a Dirac mass must have interactions strong enough to evade the astrophysical bound from SN 1987A, but weak enough to avoid violating the bound from primordial nucleosynthesis.

Kolb, Edward W.↗
NASA NTRS1991

Astrophysics and cosmology confront the 17-keV neutrino

A host of astrophysical and cosmological arguments severely constrain the properties of a 17 keV Dirac neutrino. Such a neutrino must have interactions beyond those of the standard electroweak theory to reduce its cosmic abundance (through decay or annihilation) by a factor of two hundred. A predicament arises because the additional helicity states of the neutrino necessary to construct a Dirac mass must have interactions strong enough to evade the astrophysical bound from SN 1987A, but weak enough to avoid violating the bound from primordial nucleosynthesis.

Kolb, Edward W.↗
NASA NTRS1991

Constraints from primordial nucleosynthesis on the mass of the tau neutrino

It is shown that primordial nucleosynthesis excludes a tau-neutrino mass from 0.3 to 25 MeV (Dirac) and 0.5 to 25 MeV (Majorana) provided that its lifetime is not less than about 1 sec, and from 0.3 to 30 MeV (Dirac) and 0.5 to 32 MeV (Majorana) for a lifetime of not less than about 1000 sec. A modest improvement in the laboratory mass limit - from 35 to 25 MeV - would imply that the tau-neutrino mass must be less than 0.5 MeV (provided the lifetime is not less than about 1 sec).

Kolb, Edward W.↗
NASA NTRS1991

Molecules and chains in a strong magnetic field - Statistical treatment

A Thomas-Fermi-Dirac-Weizsaecker statistical model is developed and employed to investigate diatomic molecules and infinite molecular chains in strong magnetic fields. The standard magnetic Thomas-Fermi-Dirac kinetic, potential, and exchange energy functionals are supplemented by a gradient correction to the kinetic energy. The numerical method used for solving this system in two spatial dimensions is detailed. Numerical solutions for a wide range of magnetic strengths and elements are presented to demonstrate the robustness, as well as the limitations, of the statistical approach. These calculations qualitatively reproduce many of the results of detailed quantum mechanical treatments. For example, the fractional binding energy is greatest for low atomic numbers and for strong magnetic fields.

Abrahams, Andrew M.↗