Lowest-order Effects Research Articles

Dual geometric field theory

A Weyl geometry with a gauge-invariant, Riemannian subgeometry is used to geometrize the combined Einstein-Maxwell theory. A generalized Hamilton-Jacobi equation from particle mechanics emerges as an immediate consistency requirement. The time-independent, Coulomb field case is found to include at least lowest-order quantum effects as in wave mechanics. Possible microscopic entropy is identified.

Roton second sound and roton scattering

The theory of roton second sound in superfluid helium-4 is considered. We first derive the hydrodynamic equations which determine the motion of a pure roton gas. The collisions between rotons are assumed to conserve energy, momentum, and the number of rotons. The hydrodynamic equations without dissipative terms have the same form as the corresponding equations for an ordinary fluid. When lowest-order dissipative effects are included, it is found that there are some extra dissipative processes in addition to heat conduction and viscosity. We next consider modifications of the hydrodynamic equations which occur when the effects of collisions between rotons and phonons are included, and when there are some roton-roton collisions in which the roton number changes. It is found that at the temperatures and pressures where roton second sound has so far been observed, the wave motion is best described as isothermal second sound. We show that current experimental data indicate that in nearly all collisions between rotons (> 99.97%) the total number of rotons is conserved.

Gravitational radiation damping of a binary system containing compact objects calculated using matched asymptotic expansions

This paper calculates the secular changes in orbital period, semimajor axis, and eccentricity for a gravitationally bound, slow-motion system of two compact bodies, directly from the Einstein field equation, using matched asymptotic expansions. Burke previously derived the radiation damping of a weak-field, slow-motion system, also using matched asymptotic expansions. However, no previous derivations extend to systems, such as the binary pulsar PSR 1913 + 16, containing objects with strong internal gravity. This calculation uses distinct wave-, near-, and body-zone expansions to seek a uniformly valid, one-parameter family of approximate space-times representing a bound system of compact objects undergoing gravitational radiation reaction. As in Burke's work, matching outward gives the lowest-order near-zone and radiation fields, and then matching back inward yields near-zone resistive potentials of $\frac{5}{2}$-post-Newtonian order, which contain the lowest-order time-odd effects of radiation. Matching inward again using my earlier technique for the problem of motion in external fields then gives the resulting deflections of the bodies from the world lines that they would otherwise follow. The secular changes in orbital parameters derived for the system of compact objects treated here agree with the standard formulas obeyed by weak-field systems.

Radial transport in the Elmo Bumpy Torus in collisionless electron regimes

One important area of disagreement between radial transport theory and the ELMO Bumpy Torus (EBT) experiment has been the degree of collisionality of the toroidal plasma electrons. Experiment shows relatively warm electrons (kTe ≈ 300–600 eV) and collisionless scaling, i.e. energy confinement increasing with temperature. But results of early one-dimensional (1-D), neoclassical transport models with radially inward pointing electric fields are limited to relatively cool electrons (kTe ∼ 100–200 eV) and collisional scaling. In this paper these early results are extended to include lowest-order effects of ion diffusion in regions where poloidal drift frequencies are small. The effects of direct, or non-diffusive, losses in such regions are neglected along with the effects of finite radial electric fields on electron transport coefficients and of self-consistent poloidal electric fields on ion transport coefficients. Results show that solutions in the collisionless electron regime do exist. Furthermore, when the effects of finite electron ring beta on magnetic fields near the plasma edge are included, these solutions occur at power levels consistent with experiment.

The effect of two plane walls on the motion of a small sphere in a viscous fluid

A theoretical study is made of the motion of a small sphere in an incompressible viscous fluid bounded by two plane walls. The analysis is based on the Stokes equations of motion and the method of reflexions is employed to obtain the lowest-order wall effect on the sphere, which is allowed either to rotate or not as it translates in an arbitrary direction. The effect of two plane walls on the force and torque (or angular velocity) experienced by the sphere is not accurately estimated by superposing the contributions from the two individual walls.

Low order effect of crand input in the Jovian atmosphere

Modeling of the Jovian atmosphere shows that cosmic ray induced albedo neutron decay is inadequate to account for Pioneer 10 and 11 projected electron levels on Jupiter. High energy solar protons must also be excluded as an important neutron decay source. Analysis of neutron flux data near the top of the Jovian atmosphere can lead to the determination of He/H2 and3He/4He ratios for the Jovian atmosphere.

Comments on the polarization of the quenched radiation from the2sstate of hydrogen

This paper examines two theoretical aspects of the measurement of polarization of the quenched radiation which comes from the application of a weak electric field to the $2s$ state of hydrogen. Specifically, it outlines the justification of the Bethe-Lamb phenomenological analysis of this problem from the external field approximation of quantum electrodynamics. Further, it includes the lowest-order effects of the $J$-breaking part of the hyperfine structure in Rayleigh-Schr\"odinger perturbation theory. While it was expected that these terms would contribute to the polarization fraction a correction to the lowest order of the relative size of the ratio of the hyperfine splittings to the fine-structure splitting of the $n=2$ state or about one part in ${10}^{3}$, cancellations occur and these $J$-breaking terms give a correction in the fourth place of the polarization fraction.

Lowest-order average effect of turbulence on atmospheric profiles derived from radio occultation

Turbulence in planetary atmospheres and ionospheres causes changes in angles of refraction of radio waves used in occultation experiments. Atmospheric temperature and pressure profiles, and ionospheric electron concentration profiles, derived from radio occultation measurements of Doppler frequency contain errors due to such angular offsets. The lowest-order average errors are derived from a geometrical-optics treatment of the radio-wave phase advance caused by the addition of uniform turbulence to an initially homogeneous medium. It is concluded that the average profile errors are small and that precise Doppler frequency measurements at two or more wavelengths could be used to help determine characteristics of the turbulence, as well as accuracy limits and possible correction terms for the profiles. However, a more detailed study of both frequency and intensity characteristics in radio and optical occultation measurements of turbulent planetary atmospheres and ionospheres is required to realize the full potential of such measurements.

Further development of the new bound-state formalism

The new bound-state formalism developed previously is here extended in two important respects. First is the inclusion of self-energy effects and the demonstration of the implementability of the usual renormalization procedure by means of a calculation of the lowest-order self-energy effects comprising the Lamb shift in a hydrogenlike atom. Second is the derivation of the two-body equation for the particle-antiparticle case where annihilation effects enter. This is exemplified by the derivation of the positronium equation and a calculation of a (known) annihilation contribution to its singlet-triplet splitting. The entire development is facilitated by a modified functional formulation which chooses the fully interacting physical system as the unperturbed one.

Hydrodynamic Pressure Field on a Slender Ship Moving Over a High-Frequency Wavy Shallow Bottom

The hydrodynamic pressure field for the unsteady subcritical potential flow of a slender ship moving over a wavy wall in shallow water is analyzed using perturbation techniques. For the case of wall wavelength much smaller than the ship length but larger than the transverse ship dimensions, a combination of the methods of matched asymptotic expansions and multiple scales is used to obtain the lowest-order effect of the bottom variation.

2S13→1S01+onephotontransition in heliumlike ions: Exact result for the lowest-order effect of the electron-electron interaction

2S13→1S01+onephotontransition in heliumlike ions: Exact result for the lowest-order effect of the electron-electron interaction

Inertial Taylor columns on a beta plane

An investigation is conducted concerning the lowest-order effect of variable Coriolis parameters on Taylor-column formation, taking into account the flow over a bump on a beta plane. The model considered involves a two-layer fluid on a beta plane. The governing equations for the two layers are discussed along with the characteristics of the general solutions, solutions for two retrograde currents, solutions for two prograde currents, experiments related to the single-layer problem, and the geophysical implications of the results of the investigation.

Thermodynamic perturbation theory for simple polar fluids. II

The study of polar fluids begun in a previous paper is continued. Calculations for the Stockmayer potential are extended to include the term of order μ6, where μ is the dipole moment. The effects of higher-order terms are then approximated by means of a simple Padé extrapolation procedure, and the liquid-gas coexistence curve is located in this approximation. An orientation-independent but temperature-dependent potential that is thermodynamically equivalent to an arbitrary orientation-dependent potential is introduced and used to assess the lowest-order thermodynamic effects that result from the presence of quadrupole and octupole terms in the pair-potential. Several values of quadrupole and octupole moments representative of a dipolar molecule (HCl) as well as linear molecules (N2, O2 and CO2, for which μ=0) are considered.

High-Momentum-Transfer Electron Scattering fromLi6in a Deformed Cluster Model

A simplified version of the $\ensuremath{\alpha}\ensuremath{-}d$ cluster formalism developed by Neudatchin, Smirnov, and their collaborators gives good agreement with the most recent elastic and inelastic (2.189-MeV) electron scattering data of Li et al. for momentum transfer ${q}^{2}\ensuremath{\lesssim}6.5$ ${\mathrm{fm}}^{\ensuremath{-}2}$. Inclusion of lowest-order effects of dynamical volume deformations of the intercluster density extends the agreement to ${q}^{2}\ensuremath{\lesssim}10.5$ ${\mathrm{fm}}^{\ensuremath{-}2}$. The contribution of the latter to the elastic form factor may be interpreted as due to an effective spherically symmetric distribution superimposed upon the smoothly varying distribution responsible for the scattering at lower momentum transfer. This modulating charge is calculated explicitly and exhibits an oscillatory behavior. A similar analysis is carried out in the inelastic channel.

Core polarization and the effective interaction between nucleons in a nucleus

Core polarization is taken into account to all orders by systematic inclusion of particle-hole scattering, self-screening of phonons and modification of the vertices connecting single-particle to two-particle one-hole states, and single-hole to two-hole one-particle states. Problems of convergence are overcome by converting the sum of perturbation theory diagrams into closed equations. A set of coupled nonlinear equations for the particle-hole interaction is derived and solved, and the solution is used to compute the effect of core polarization to all orders. The self-screening strongly suppresses the RPA enhancement of the core phonons, the net effect being close to TDA phonons, while the vertex modification drastically changes the contributions of the various phonons. The final result for the core polarization is very different from the lowest-order effect for low-lying energy levels, being generally quite small.

Single-site approximations in the electronic theory of liquid metals

The electronic structure of liquid metals is described by a multiple scattering formalism. Alternate methods based on a single site description of the liquid are developed and compared. The first method, the quasicrystalline approximation of Lax, is used to interpret and extend the work of Ziman and Anderson and McMillan. The second method, discussed here for the first time, extends the coherent potential theory of binary substitutional alloys to the liquid problem. Formally, this method is based on the introduction of a local self-energy operator associated with each site, and the subsequent self-consistent decoupling of the multiple scattering hierarchy. The lowest-order effects of one and two atom clusters are then discussed in connection with the expansion of the total scattering operator. It is shown that in the liquid, as in the alloy, these effects are treated more accurately by the self-consistent methods than by their non-self-consistent counterparts, the quasicrystalline and average t matrix approximations. It is in fact possible to establish a parallel between the self-consistent and coherent potential approximations on the one hand and the quasicrystalline and average t matrix approximations on the other. In the evaluation of second-order corrections to the work of Anderson and McMillan, unitarity requirements suggest an expansion in terms of the reaction matrix rather than the scattering matrix. This procedure treats the damping of electrons more carefully, eliminating spurious contributions. These formal considerations are illustrated by a calculation of the complex band structure and density of states for liquid Cu.

Glory Scattering in Molecular Collisions: Formal Expressions for the Total Cross Section

An extended distorted-wave treatment is used to obtain formal expressions for the total cross section when two rigid diatomic molecules with orbital and nuclear-spin angular momenta collide. Explicit expressions are obtained through second order, including the lowest-order inelastic effects.

Three-body forces in nuclear matter

An earlier claim about the smallness of three-body effects in nuclear matter is examined in the light of a criticism. Our conclusion is that, whereas the lowest-order three-body effect is small, second-order effects are larger, with the net result of ≈ 2.5 MeV per particle additional binding at the saturation density. Although these results depend on the way one extrapolates off the pion mass shell, different ways which seem to us to be reasonable give roughly the same result.

Nonlinear generation of transverse fluctuations from longitudinal fluctuations in an infinite stable plasma

The stationary spectrum of transverse electric field fluctuations, generated by nonlinear interaction of longitudinal waves, in a homogeneous and isotropic electron plasma of infinite extension and in the absence of external fields, is calculated. Only the lowest-order nonlinear effect, yielding transverse waves with frequencies somewhat above 2ωd and, respectively, small compared toωd, is considered, including, however, nonresonant modes. An estimate of the order of magnitude of the effect is given for equilibrium fluctuations, which may serve as a starting point for evaluating its importance in cases where enhanced longitudinal fluctuations are present.

Electromagnetic interaction of mesons resulting from a broken symmetry

The Nambu, Jona-Lasinio broken symmetry theory is restated in terms of Green’s functions in the presence of an external current source. Using these Green’s functions, it is possible to calculate the lowest-order effects of electromagnetic interactions on the initially massless pseudoscalar mesons induced by the broken symmetry. It is found that the uncharged meson acquires no mass and hence the results are consistent with the Goldstone theorem applied to the fully interacting system.