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The perturbing interaction appropriate for the Dirac-Fock formalism is used to formulate relativistic radiationless transitions. The transition rate between two jj-coupled many-electron configurations is expressed as a linear combination of radial integrals, suitable for numerical computation. The correlation and relaxation effects and the generalisation of the present work are discussed briefly.
The paper presents an analytical treatment of transparent-emitter devices, particularly solar cells, that is more complete than previously available treatments. The proposed approach includes the effects of bandgap narrowing, Fermi-Dirac statistics, built-in field due to impurity profile, and a finite surface recombination velocity at the emitter surface. It is demonstrated that the transparent-emitter model can predict experimental values of Voc observed on n(plus)-p thin diffused junction silicon solar cells made on low-resistivity (0.1 ohm-cm) substrates. A test is included for the self-consistent validity of the transparent-emitter model. This test compares the calculated transit time of minority carriers across the emitter with the Auger-impact minority-carrier lifetime within the emitter region.
Relativistic calculations of radiationless transition rates to L -subshell vacancy states in selected atoms with Z in the 70-96 range have been performed. The Auger and Coster-Kronig transition probabilities are calculated from perturbation theory, assuming frozen orbitals, in the Dirac-Hartree-Slater approach. Transition rates, fluorescence yields, and Coster-Kronig yields are compared with nonrelativistic theoretical results and with experiment. Relativity is found to affect the L -subshell Auger widths by (10-25)% and individual transition rates to certain j-j configurations by as much as 40% at Z = 80. The widths of L sub i vacancy states and the L sub 2 Coster-Kronig yields f33 from these relativistic calculations agree much better with experiment than earlier nonrelativistic theoretical values.
To provide theoretical support for investigating different ways to obtain high open-circuit voltages in p-n junction silicon solar cells, an analytical treatment of heavily doped transparent-emitter devices is presented that includes the effects of bandgap narrowing, Fermi-Dirac statistics, a doping concentration gradient, and a finite surface recombination velocity at the emitter surface. Topics covered include: (1) experimental determination of bandgap narrowing in the emitter of silicon p-n junction devices; (2) heavily doped transparent regions in junction solar cells, diodes, and transistors; (3) high-low-emitter solar cell; (4) determination of lifetimes and recombination currents in p-n junction solar cells; (5) MOS and oxide-charged-induced BSF solar cells; and (6) design of high efficiency solar cells for space and terrestrial applications.
Systematic relativistic (Dirac-Hartree-Slater) calculations of atomic K-shell Auger transition probabilities are reported for 25 elements with Z between 18 and 96, inclusive. K-level Auger widths are found to be enhanced by relativistic effects, while total K-level widths are reduced. Relativistic theoretical K-shell fluorescence yields are in excellent agreement with experiment. Theoretical relative intensities of K-LX Auger transitions in heavy elements, calculated in j-j coupling, agree well with measurements; for low Z, configuration interaction and intermediate coupling must apparently be included.
Theoretical K-LL Auger spectra from relativistic Dirac-Hartree-Slater calculations in intermediate coupling with configuration interaction (ICWCI) are considered. Calculated transition rates for 25 elements with Z between 18 and 96, inclusive, are listed and compare well with experimental data. Relativistic effects are found to be important above Z equal to about 35, and ICWCI is necessary to describe the spectra for Z less than about 60.
Self-consistent Dirac-Slater multiple scattering calculations are presented for UF6. The results are compared critically to other relativistic calculations, showing that the results of all molecular orbital calculations are in qualitative agreement, as measured by energy levels, population analyses, and spin-orbit splittings. A detailed comparison is made to the relativistic X alpha(RX alpha) method of Wood and Boring, which also uses multiple scattering theory, but incorporates relativistic effects in a more approximate fashion. For the most part, the RX alpha results are in agreement with the present results.
The cross sections for the excitation and deexcitation of the quantized transverse energy levels of an electron in a magnetic field are calculated for electron-proton and electron-electron collisions in light of the importance of the cross sections for studies of X-ray pulsar emission. First-order matrix elements are calculated using the Dirac theory of the electron, thus taking into account relativistic effects, which are believed to be important in accreting neutron stars. Results for the collisional excitation of ground state electrons by protons are presented which demonstrate the importance of proton recoil and relativistic effects, and it is shown that electron-electron excitations may contribute 10 to 20% of the excitation rate from electron-proton scattering in a Maxwellian plasma. Finally, calculations of the cross section for electron-proton small-angle scattering are presented which lead to relaxation rates for the electron velocity distribution which are modified by the magnetic field, and to a possible increase in the value of the Coulomb logarithm.
A velocity- and mass-independent search for moving magnetic monopoles is being performed by continuously monitoring the current in a 20-sq cm area superconducting loop. A single candidate event, consistent with one Dirac unit of magnetic charge, has been detected during five runs totaling 151 days. These data set an upper limit of 6.1 x
A self-consistent formulation of physics at the classical level embodying Dirac's large numbers hypothesis (LNH) is developed based on units covariance. A scalar 'field' phi(x) is introduced and some fundamental results are derived from the resultant equations. Some unusual properties of phi are noted such as the fact that phi cannot be the correspondence limit of a normal quantum scalar field.
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
Relativistic plane-wave Born-approximation calculations of cross sections for M-shell ionization of Ho-67, Au-79, U-92 by protons with incident energies from 0.05 to 1 MeV are reported. Dirac-Hartree-Slater wave functions were employed and binding-energy change and Coulomb deflection were taken into account. Associated X-ray production cross sections were also computed. Results are compared with previous theoretical predictions and with experimental data. Definite improvement in the theory has been attained by the use of realistic wave functions and consistent inclusion of the effects of relativity.
Radiationless transitions filling vacancies in atomic M1, M2, and M3 subshells have been calculated relativistically with Dirac-Hartree-Slater wave functions for ten elements with atomic numbers 67-95. Results are compared with those of nonrelativistic calculations and experiment. Relativistic effects are found to be significant. Limitations of an independent-particle model for the calculation of Coster-Kronig rates are noted.
Ffowcs Williams and Hawkings (1969) based their derivation of the fundamental equation of the sound generated by arbitrarily moving aerodynamic surfaces on the study of mass and momentum balance of a control volume imbedding a mathematical surface(s) exactly corresponding to real surface(s). These investigators also sketched an alternative method, employing generalized functions, for its derivation. This latter method, which was later developed by Farassat (1975), is purely mathematical and formal. Goldstein (1976) used the free-space Green function to produce an implicit derivation of the Ffowcs Williams and Hawkings equation. In the study presented here, Lowson's (1965) concept of moving point singularities is generalized to moving surface singularities, and a new derivation is given of the fundamental equation. The derivation is based on topological considerations of the underlying space, the fluid medium, and the integral properties of the Dirac delta function.
This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.
Fourier transforms and the Wiener-Hopf technique are used in conjunction with plane elastostatics to examine the singular crack tip stress field in the double cantilever beam (DCB) specimen. In place of the Dirac delta function, a family of functions which duplicates the important features of the concentrated forces without introducing unmanageable mathematical complexities is used as a loading function. With terms of order h-squared/a-squared retained in the series expansion, the dimensionless stress intensity factor is found to be K (h to the 1/2)/P = 12 to the 1/2 (a/h + 0.6728 + 0.0377 h-squared/a-squared), in which P is the magnitude of the concentrated forces per unit thickness, a is the distance from the crack tip to the points of load application, and h is the height of each cantilever beam. The result is similar to that obtained by Gross and Srawley by fitting a line to discrete results from their boundary collocation analysis.
First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory.