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The equations of motion of a spinning body in the gravitational field of a much larger mass are found using both the Corinaldesi-Papapetrou spin supplementary condition (SSC) and the Pirani SSC. These equations of motion are compared with our previous result derived from Gupta's quantum theory of Gravitation. It is found that the spin-dependent terms differ in each of the above three results due to a different location of the center of mass of the spinning body. As expected, these terms are not affected by the choice of either Schwarzschild or isotropic coordinates. Finally, for the presently planned Stanford gyroscope experiment, we find the maximum secular displacement of the orbit of the gyro with respect to the orbit of its non-rotating housing to be of the order of (10−7 cm/year)t, a result much smaller than Schiff's result which is proportional to time squared.

We find the precession of the spin and the precession of the orbit for the two-body problem in general relativity with arbitrary masses, spins, and quadrupole moments. One notable result which emerges is that, in the case of arbitrary masses ${m}_{1}$ and ${m}_{2}$, the spin-orbit contribution to the spin precession of body 1 is a factor $\frac{({m}_{2}+\frac{\ensuremath{\mu}}{3})}{({m}_{1}+{m}_{2})}$ times what it would be for a test body moving in the field of a fixed central mass (${m}_{1}+{m}_{2}$). Here $\ensuremath{\mu}$ denotes the reduced mass $\frac{{m}_{1}{m}_{2}}{({m}_{1}+{m}_{2})}$. This contrasts with the result of Robertson for the periastron precession where the corresponding factor is unity. These results may be of interest for binary neutron stars and, in particular, for binary pulsars such as PSR 1913+16.

We consider, in lowest order of the gravitational coupling constant G, the gravitational potential between two neutrons. As we have previously pointed out [1],the quantum (including spin) contributions to the gravitational field dominate for distances smaller than the Compton wavelength of the neutron. At such distances the gravitational force between two neutrons may be repulsive. In particular, the gravitational forces which are analogous to the familiar Darwin and Fermi forces of quantum electrodynamics are capable of stopping gravitational collapse. Our discussion is within the framework of Einstein's theory, but on a microscopic level. We conclude that gravitational collapse may be halted without the necessity of extending Einstein's theory a la Cartan or otherwise.

A variational method is used to obtain solutions to Schroddinger's equation for a particle in a static screened Coulomb potential. Energy eigenvalues are obtained for the lowest 45 states. The analytic wave functions generated by this method are used to obtain the probabilities for spontaneous emission in the dipole approximation as a function of screening length, for transitions between tiie six lowest states. (auth)

For transition energies ω ⪢ mc 2 (rest-energy of the electron) our previously derived exact analytical results for the internal conversion coefficients (ICC) for all shells and for all transition energies (point-nucleus, no screening model) simplify considerably. We find to lowest order in 1/ω that the ICC are proportional to 1/ω and that for a particular Z and shell designation, the electric and magnetic ICC for all multipoles are equal. The corresponding numerical results, are presented for the K, L and M subshells.

The $\ensuremath{\beta}$-decay rate of a polarized neutron source in a constant, uniform magnetic field of arbitrary strength is calculated. We show that the decay rate is substantially changed if the magnetic field is of order ${10}^{13}$ G or larger. Fields of such strength have been speculated to exist in the early universe or in neutron stars.

Electron anomalous magnetic moment effect on nonlinear Lagrangian of electromagnetic field, deriving additional nonlinear corrective term

We present the recent results of our continuing program of investigation of the behavior of matter in strong to super-strong magnetic fields (B ∼ 106−1012 G). This work was motivated by the discovery of strong magnetic fields (B ∼ 107 G) in some white dwarfs and the likely existence of super-strong fields (B ∼ 1012 G) in pulsars. Magnetic white dwarfs were discovered from observations of the continuous spectrum and one of the most intriguing challenges for the theorist is to provide an explanation for the observed wavelength dependence of the fractional circularly and linearly polarized radiation. Our initial response to this question was the determination of an exact solution of Kemp's harmonic oscillator model. These results are used as input to the ATLAS model atmosphere program and then comparison is made with observations. The disparities still existing between theory and observation convince us of the necessity for developing a new model of the continuum radiation, two likely possibilities being photoionization and free-free absorption. This leads us to present a general formulation of radiation absorption and emission processes in a magnetic field. Next we calculate the cross section for the photoionization, correct to first order in B. For the purpose of obtaining exact results for this cross section, the effect of a magnetic field on the energy spectrum and wave functions of hydrogen, helium, etc. must be obtained. The results for hydrogen are presented here. They will be useful also in determining accurate values for the displacements due to the quadratic Zeeman effect in the line spectra of DA stars, particularly for the higher excited states.

The ground state energy of the Heii (singly ionized helium) atom is determined in magnetic fields up to 1012 G. The 13 lowest excited states and bound-bound transition probabilities are calculated in magnetic fields from 107 to 109 G.

Summary A digital method of structural analysis is developed using equivalent electrical circuit analogies in the systemization of the digital computer program. This method is shown to possess particular advantages in the analysis of redundant structural systems, in that the redundancies need not be determined in order to form a statically determinate system. The method is com­ pletely independent of such redundancies. In addition, all of the procedures except the development of the equivalent electrical analogy may be carried out in a simple, routine manner with very little prior experience in the method. HE METHOD of structural analysis presented here involves a formalization of the digital computation in terms of an equivalent electrical circuit representa­ tion of the structural system. This method of electri­ cal circuit representation is familiar to the users of the direct analog computer (Network Analyzer), and is detailed in the references. In the usual context, the structural system is expressed in terms of simple structural elements which are in turn represented by equivalent electrical networks. These networks are then used as building blocks in constructing an electri­ cal model of the structural system. At this point, the electrical model is implemented by means of the Net­ work Analyzer, and the analysis is conducted using the electrical model in much the same way an actual struc­ tural model would be used. In the present method, it is proposed that the electri­ cal circuit representation be developed as though for use on a Network Analyzer, and that this representa­ tion be used to facilitate the systemization of the digital computer program. In a sense, this involves the use of a digital computer as a Network Analyzer simulator. At this point it may be well to direct a few remarks to the structural engineer, who may very likely be thoroughly repelled by any suggestion of expressing a structural problem in terms of an electrical circuit. However, the electrical concepts involved are extremely basic and are surely familiar to engineers of all dis­ ciplines. Furthermore, the usual approach (even for those with electrical backgrounds) is to interpret the electrical circuits largely in structural terms, using elec­ trical concepts only where they contribute to the sim­ plicity and understanding of the system.

Publisher Summary This chapter discusses the important effects resulting from finite nuclear size. There are two distinct effects due to finite nuclear size: (1) static and (2) dynamic. The static effect relates to the modification of the electron wave functions, particularly close to the nucleus. The dynamic effect arises from the fact that the electron does actually penetrate the nucleus some of the time. The most comprehensive calculation of internal conversion coefficients (ICCs) includes nuclear size and screening effects. The static effect of nuclear size on the ICCs is taken into account in a very simple fashion, giving results in excellent agreement with other more sophisticated approaches. At present, there is a better understanding of the effects of screening on the ICCs at different transition energies.

High-energy K-conversion coefficients are calculated using relativistic Hartree-Fock-Slater wave functions for 114Cd and 150Sm, multipolarities E1, E2 and M1 and for gamma-ray transition energies from 1 MeV to 17 MeV (existing tabulations do not exceed 2.5 MeV). All the available data for the elements in this energy region are compared, and the serious disagreements are examined. It is concluded that the present results are correct, and that the present theory is valid in this energy domain.

Coulomb field effects on K shell internal conversion coefficients for threshold values of the gamma-ray energy are investigated using exact wave functions to describe both the bound and the continuum state electrons. Exact results for the internal conversion coefficients are obtained in terms of gamma functions and confluent hypergeometric functions. To facilitate numerical evaluation, the exact result is expanded in a series in αZ and the first three terms of this series are retained. The dominant terms are identical to the expressions obtained by Drell and by Dancoff and Morrison, in the non-relativistic approximation. Terms of order αZ times the dominant term are shown to be zero but the α2Z2 corrections to the non-relativistic results are seen to bring the analytical results into closer agreement with the numerical results of Spinrad. The effects of finite nuclear size and screening are also considered.

An expression for the third-order Coulomb wave function, correct to order ( alpha Z)/sup 3/ for all momenta and energies, is derived. Using this wave function the total cross section for single-photon emission resulting from a positron annihilating with a K-shell electron (single quantum annihilation), valid to relative order ( alpha Z)/sup 2/, is calculated numerically. The results for lead are compared to the exact answer of Jaeger and Hulme, and the results for silver are also given graphically. The effect of the third-order term in the cross section is found to be significant, especially for low and intermediate positron energies. The cross section for lead is found to be qualitatively correct while that for silver is essentially exact. The question of how to treat the normalization factors of the various wave functions is also discussed. (auth)

The influence of the Coulomb field on the decay of a polarized muon from the $K$ shell of a $\ensuremath{\mu}$ atom is considered. Analytical results valid to order ${\ensuremath{\alpha}}^{3}{Z}^{3}$ are presented for the total decay rate and for the electron angular distribution. Formulas valid to order ${\ensuremath{\alpha}}^{2}{Z}^{2}$ are given for the energy spectrum of the emitted electron.

An analytic expression is derived for the energy spectrum of hydrogenlike atoms in an intense radiation field, which is valid up to intensities for which R/sub 0/ much less than a Bohr radius, where R/sub 0/ is the amplitude of the classical displacement of a free electron in the radiation field. (auth)

An analytic expression is derived for the critical temperature which marks the boundary between the two regimes in which the disappearance of spectral lines (emitted by transitions from levels near the continuum) from a hydrogen-like plasma is caused by either the Inglis Teller effect or the Debye-Huckel screening effect.

Generalized solutions to the equations for a massless free field with arbitrary spin are written down. It is shown that they lead immediately to generalizations of all the usual conservation laws.

We show that if one assumes (following Cowsik and Pal and Shen in their explanation of the flux of galactic gamma rays) that the recently measured far-infrared radiation is galactic, then one must also accept the existence of the x-ray flux, with a magnitude in agreement with observations but with a large anisotropy, in sharp disagreement with the measured isotropy.

Cosmic-ray electron spectrum in disk-halo galactic model, studying inconsistencies in Ramaty and Lingenfelter analysis

BECAUSE of the widespread interest in measuring forces between spinning cylinders and disks1,2 and the speculative nature of the conclusions reached in previous discussions, we have made a quantitative calculation of the magnitude of the forces. As in earlier calculations3, our approach is based on a weak field low velocity (EIH) approximation to general relativity. By methods familiar from potential theory in electrodynamics we first compute the first order corrections to a fiat space metric due to the presence of a spinning cylinder.

It is shown that there is a contribution to the precession of a gyroscope due to the quadrupole moment of the Earth. The magnitude of this additional precession is a maximum for a gyroscope in a satellite in equatorial orbit around the Earth at a moderate altitude, and exceeds the experimental error for observations which cover a span of about one year or greater.

Gravitation wave radiation rate from binary stars, using Brans-Dicke general relativity theory

The energy spectrum of He I is calculated by a variational method for magnetic fields B in the range 0–3 × 10 11 gauss. Improved results for the electron affinity of H - are also presented.

We show that spin contributions to the gravitational field of an electron dominate for distances between the classical radius and the Compton wavelength of the electron. At such distances the gravitational force between two electrons may be repulsive, depending on the spin orientations.

THE origin of magnetic fields in degenerate matter is an interesting question at present because of the discovery of large magnetic fields in some white dwarfs1, 2 and because of the even higher fields of the order of the critical magnetic field Bc≡(m2c3/eh)=4.4×l013 G that are thought to exist in pulsars (accepting the rotating neutron star theory3). An equally intriguing question is why some—but not all4—white dwarfs are magnetic. The fact that some supernovae do not have associated pulsars might also lead one to speculate that perhaps the collapse of all supernovae does indeed result in a neutron star, but that all neutron stars are not magnetic.

Motivated by the desire to provide a model for the polarized radiation observed from some white dwarfs, we calculate the intensities of right and left circularly polarized bremsstrahlung radiation emitted by electrons in the atmospheres of magnetic white dwarfs.

The anomalous magnetic moment of the electron is accounted for by adding a phenomenonological Pauli term to the Dirac equation. The resultant eigenvalues are applied to (a) the non-linear Lagrangian of the E-M field and (b) spontaneous pair production.

Arguments are presented to show that the BCS theory of superfluidity in its original form may not be applicable to neutron star matter over a wide range of density.

RECENT advances in the production of large magnetic fields in the laboratory1,2 have generated interest in the effect of intense magnetic fields on various phenomena3,4. The largest field that can be produced in the laboratory1,2 at present is about 106 G, which is considerably lower than the quantum critical field value5 of Hc = m2c3/eV = 4.4 × 1013 G; but the “cosmic laboratory” may be a source of much stronger fields and it has been suggested6 that magnetic fields as large as 1014−1016 G may exist in neutron stars. Hoyle7 has cited the possibility of a large primordial magnetic field, and Brownell and Callaway8 speculate that neutron stars and the dense early universe may be ferromagnetic. One of us (R. F. O.) has examined9 various effects of a large magnetic field and has indicated an effect of magnetic fields which has been often ignored in astrophysical investigations, namely, that the rates of all elementary particle processes will be affected. Pursuing this idea, we examine here the effect of a magnetic field on the β decay rate of a neutron. This is a fundamental process in many astrophysical phenomena and in particular it is very important10 in a problem of current interest, that is, the production of He in the “big-bang” expansion of the universe11. In addition, our calculations should be applicable to other elementary particle processes. We present here only the main ideas ; the calculation details will be published elsewhere12.

Our previous work on the effect of a constant magnetic field on neutron decay in a vacuum is extended to the case where the process takes place in dense bodies (white dwarfs, neutron stars), at zero temperature.