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Results for “relativistic corrections”

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NASA NTRS1993

Relativistic Corrections to the Properties of the Alkali Fluorides

Relativistic corrections to the bond lengths, dissociation energies and harmonic frequencies of KF, RbF and CsF have been obtained at the self-consistent field level by dissociating to ions. The relativistic corrections to the bond lengths, harmonic frequencies and dissociation energies to the ions are very small, due to the ionic nature of these molecules and the similarity of the relativistic and nonrelativistic ionic radii.

Dyall, Kenneth G.↗

NASA NTRS1986

Relativistic corrections to the Bethe sum rule

Relativistic corrections to the Bethe sum rule have been obtained for a one-electron system. The relativistic sum is first derived assuming completeness by employing the Dirac Hamiltonian. Then, a semirelativistic approach to order v-squared/c-squared is presented following the Foldy-Wouthuysen transformation scheme to exclude the contributions from the negative-energy states. The results have wide applications in high-Z systems at large momentum transfers.

Leung, P. T.↗

NASA NTRS1994

General relativistic corrections in the gamma-ray emission from pulsars

We examine the importance of general relativistic corrections to the production of gamma rays near the surface of a neutron star. Due to the change in the magnetic dipole field in curved spacetime, the polar cap angle decreases by 30% compared to flat spacetime. However, the curved photon trajectories compensate for the decrease in the polar cap angle, and, as a result, the pulse profile of the photons emitted parallel to the field is expected to be very similar in curved spacetime and in flat spacetime. We find that the curved spacetime metric significantly increases the magnitude of the magnetic field and, therefore, the attenuation coefficients of curvature radiation gamma rays for pair production in a magnetic field can be increased by factors as large as 100. As a resutl the survival distance of 1 GeV photons for pair production is decreased by a factor of 2 for B is approximately 10(exp 12) G.

Gonthier, P. L.↗

NASA NTRS2026

Atacama Cosmology Telescope A Measurement of Galaxy Cluster Temperatures Through Relativistic Corrections to the Thermal Sunyaev-Zeldovich Effect

The high electron temperature in galaxy clusters (> 1 keV or > 107 K) leads to corrections at the level of a few percent in their thermal Sunyaev-Zeldovich effect signatures. Both the size and frequency dependence of these corrections, which are known as relativistic temperature corrections, depend upon the temperature of the objects. In this work we exploit this effect to measure the average temperature of a stack of Compton-y selected clusters. Specifically, we apply the “spectroscopic method” and search for the temperature that best fits the clusters’ signal measured at frequencies from 30 to 545 GHz by the Atacama Cosmology Telescope and Planck satellite. We measure the average temperature of clusters detected in the Atacama Cosmology Telescope maps to be 8.5 2.4 keV, with an additional systematic error of comparable amplitude dominated by passband uncertainty. Upcoming surveys, such as the Simons Observatory and CMB-S4, have the potential to dramatically improve upon these measurements and thereby enable precision studies of cluster temperatures with millimeter observations. The key challenge for future observations will be mitigating instrumental systematic effects, which already limit this analysis.

William R Coulton↗

NASA NTRS1993

Finite nucleus effects on relativistic energy corrections

The effect of using a finite nucleus model in quantum-chemical calculations is examined. Relativistic corrections from the first order Foldy-Wouthuysen terms are affected indirectly by the change in wavefunction, but also directly as a result of revised expressions for the Darwin and spin-orbit terms due to the change in nuclear potential. A calculation for the Rn atom indicates that the mass-velocity and Darwin corrections are much more sensitive to the finite nucleus than the non-relativistic total energy, but that the total contribution for these two terms is quite stable provided the revised form of the Darwin term is used. The spin-orbit interaction is not greatly affected by the choice of nuclear model.

Dyall, Kenneth G.↗

NASA NTRS1972

Relativistic time corrections for Apollo 12 and Apollo 13

Results are presented of computer calculations on the relativistic time corrections relative to a ground-based clock of on-board clock readings for a lunar mission, using simple Newtonian gravitational potentials of earth and moon and based on actual trajectory data for Apollo 12 and Apollo 13. Although the second order Doppler effect and the gravitational red shift give rise to corrections of opposite sign, the net accumulated time corrections, namely a gain of 560 (+ or - 1.5) microseconds for Apollo 12 and gain of 326 (+ or - 1.3) microseconds for Apollo 13, are still large enough that with present day atomic frequency standards, such as the rubidium clock, they can be measured with an accuracy of about + or - 0.5 percent.

Lavery, J. E.↗

NASA NTRS1993

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

Zylka, Christian↗

NASA NTRS1982

Calculation of the relativistic Bloch correction to stopping power

Bloch's technique of joining the nonrelativistic Bethe and Bohr stopping-power expressions by taking into account wave-packet effects for close collisions is extended to the relativistic case. It is found that Bloch's nonrelativistic correction term must be modified and that charge asymmetric terms appear. Excellent agreement is observed by comparing the results of these calculations to recent data on the stopping power of relativistic heavy ions.

Ahlen, S. P.↗

NASA NTRS1992

All-electron molecular Dirac-Hartree-Fock calculations - Properties of the XH4 and XH2 molecules and the reaction energy XH4 yields XH2 + H2, X = Si, Ge, Sn, Pb

Relativistic corrections to a number of properties of the Group IV hydrides are calculated using the Dirac-Hartree-Fock method. The use of first-order perturbation theory is sufficient to obtain relativistic corrections for Ge, but the effects of spin-orbit interaction and other higher-order effects begin to show for Sn and become important for Pb. The energy of the reaction XH4 yields XH2 + H2 (X = Si, Ge, Sn, and Pb) is also calculated. The results are compared with relativistic effective core potential calculations, first-order perturbation theory calculations, and limited experimental data.

Dyall, Kenneth G.↗

NASA NTRS1974

Extreme ultraviolet spectra of highly ionized oxygen and fluorine

The foil-excitation method has been used to study the extreme ultraviolet spectra of highly ionized oxygen and fluorine. Several previously unreported lines in heliumlike fluorine are reported and other newly reported lines in heliumlike oxygen have been measured to higher accuracy. Included in the measurements are certain heliumlike oxygen transitions of significance in interpretation of solar-flare spectral observations. The wavelength determinations are usually in good agreement with calculated results which includes relativistic corrections, but discrepancies arise when nonrelativistic calculations are used. A comparison of the present results and those recently obtained by theta-pinch and laser-induced plasma sources is made for both heliumlike and lithiumlike ions; a few discrepancies occur, with results in most cases in better agreement with relativistically corrected calculations. Certain unidentified lines in the spectra may be attributable to radiative transitions between quartet states of lithiumlike ions.

Pegg, D. J.↗

NASA NTRS1991

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 NTRS1993

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

Dyall, Kenneth G.↗

NASA NTRS1980

Thermal bremsstrahlung from high-temperature plasmas

Analytic expressions are derived for the total bremsstrahlung energy-loss rate per unit volume and the spectral emission rate of a very hot (10 million K to 1 billion K) plasma. At these temperatures the principal contribution to emission can be computed from the nonrelativistic limit of electron-ion bremsstrahlung in the Born approximation. Modifications to this rate are evaluated from (1) relativistic corrections to the thermal-electron velocity distribution function, (2) relativistic and spin corrections to the nonrelativistic electron-ion bremsstrahlung cross section, (3) electron-electron bremsstrahlung, and (4) first-order Born approximation corrections to electron-ion bremsstrahlung.

Gould, R. J.↗

NASA NTRS1995

High accuracy time transfer synchronization

In July 1994, the U.S. Naval Observatory (USNO) Time Service System Engineering Division conducted a field test to establish a baseline accuracy for two-way satellite time transfer synchronization. Three Hewlett-Packard model 5071 high performance cesium frequency standards were transported from the USNO in Washington, DC to Los Angeles, California in the USNO's mobile earth station. Two-Way Satellite Time Transfer links between the mobile earth station and the USNO were conducted each day of the trip, using the Naval Research Laboratory(NRL) designed spread spectrum modem, built by Allen Osborne Associates(AOA). A Motorola six channel GPS receiver was used to track the location and altitude of the mobile earth station and to provide coordinates for calculating Sagnac corrections for the two-way measurements, and relativistic corrections for the cesium clocks. This paper will discuss the trip, the measurement systems used and the results from the data collected. We will show the accuracy of using two-way satellite time transfer for synchronization and the performance of the three HP 5071 cesium clocks in an operational environment.

Wheeler, Paul J.↗

NASA NTRS1984

Relativistic dispersion, the cyclotron maser instability, and auroral kilometric radiation

It is demonstrated that relativistic effects can significantly modify the wave dispersion in auroral kilometric radiation (AKR), even for only mildly relativistic electrons, when the ratio of the square of the electron plasma frequeny omega(pe) to the square of the electron cyclotron frequency Omega(e) is much less than one, which is frequently the case in the AKR source region. The k-parallel dispersion relation for waves in a relativistic Maxwellian plasma is considered for the case of omega(pe) much less than Omega(e). The results of Shkarovsky (1966) are used to evaluate the relativistic corrections to the R-X mode cutoff. The general relativistic dispersion tensor is applied to evaluate the dispersion relation for a delta function ring distribution in p-perpendicular, again assuming omega(pe) much less than Omega(e). The effect of finite velocity spread is studied by analyzing the Dory-Guest-Harris distribution in the semirelativistic approximation. The results of computer simulations for ring and shell distributions are presented.

Pritchett, P. L.↗

NASA NTRS1994

Relativistic effects on the motion of asteroids and comets

We study the effects arising from relativistic perturbations on the motion of asteroids and comets and show that for a number of such objects, inclusion of relativistic contributions in the equations of motion gives rise to significant improvements in the orbital solutions. Furthermore we argue that ignoring relativistic corrections to the equations of motion, while using masses derived from relativistic ephemerides yields incorrect solutions corresponding to an inconsistent, non-Newtonian, nonrelativistic model.

Shahid-Saless, Bahman↗

NASA NTRS1997

Compton Scattering by Static and Moving Media: The Transfer Equation and its Moments - Part 1

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering, as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first angular moments, both in the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in Epsilon/m(sub e), T(sub e)/m(sub e), and V, where Epsilon is the photon energy, T(sub e) and m(sub e) are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second order in V should usually be retained, because if the radiation energy density is sufficiently large, compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second order in V can be as important as the effects described by the terms that are first order in V, even when V is small. The system- and fluid-frame equations that we derive are correct to first order in Epsilon/m(sub e). Our system-frame equations, which are correct to second order in V, may be used when V is not too large. Our fluid-frame equations, which are exact in V, may be used when V approaches 1. Both sets of equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V(sup 2) is greater than 3T(sub e)/m(sub e).

Psaltis, Dimitrios↗

NASA NTRS1996

Relativistic Navigation: A Theoretical Foundation

We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an isolated astronomical N-body system in metric theories of gravity. To do this, we generalize the Fock-Chandrasekhar method of the weak-field and slow-motion approximation (WFSMA) and develop a theory of relativistic reference frames (RF's) for a gravitationally bounded many-extended-body problem. In any proper RF constructed in the immediate vicinity of an arbitrary body, the N-body solutions of the gravitational field equations are formally presented as a sum of the Riemann-flat inertial space-time, the gravitational field generated by the body itself, the unperturbed solutions for each body in the system transformed to the coordinates of this proper RF, and the gravitational interaction term. We develop the basic concept of a general WFSMA theory of the celestial RF's applicable to a wide class of metric theories of gravity and an arbitrary model of matter distribution. We apply the proposed method to general relativity. Celestial bodies are described using a perfect fluid model; as such, they possess any number of internal mass and current multipole moments that explicitly characterize their internal structures. The obtained relativistic corrections to the geodetic equations of motion arise because of a coupling of the bodies' multiple moments to the surrounding gravitational field. The resulting relativistic transformations between the different RF's extend the Poincare group to the motion of deformable self-gravitating bodies. Within the present accuracy of astronomical measurements we discuss the properties of the Fermi-normal-like proper RF that is defined in the immediate vicinity of the extended compact bodies. We further generalize the proposed approximation method and include two Eddington parameters (gamma, Beta). This generalized approach was used to derive the relativistic equations of satellite motion in the vicinity of the extended bodies. Anticipating improvements in radio and laser tracking technologies over the next few decades, we apply this method to spacecraft orbit determination. We emphasize the number of feasible relativistic gravity tests that may be performed within the context of the parameterized WFSMA. Based on the planeto-centric equations of motion of a spacecraft around the planet, we suggested a new null test of the Strong Equivalence Principle (SEP). The experiment to measure the corresponding SEP violation effect could be performed with the future Mercury Orbiter mission. We discuss other relativistic effects, including the perihelion advance and the redshift and geodetic precession of the orbiter's orbital plane about Mercury, as well as the possible future implementation of the proposed formalism in software codes developed for solar-system orbit determination. All the important calculations are completely documented, and the references contain an extensive list of cited literature.

Turyshev, Slava G.↗