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Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

The intensities of L-shell Auger and Coster-Kronig transitions in heavy atoms have been calculated relativistically. A detailed comparison is made with measured Auger spectra of Pt and U. The pertinent transition energies were computed from relativistic wave functions with inclusion of the Breit interaction, self-energy, a vacuum-polarization correction, and complete atomic relaxation. Multiplet splitting is found to distribute Auger electrons from certain transitions among several lines. The analysis leads to reassignment of a number of lines in the measured spectra. Lines originally identified as L2-L3Ni in the U spectrum are shown to arise from M4,5 Auger transitions instead.

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.

The effect on low-energy atomic inner-shell Coster-Kronig and super Coster-Kronig transitions that is produced by relaxation and by exchange between the continuum electron and bound electrons was examined and illustrated by specific calculations for transitions that deexcite the 3p vacancy state of Zn. Taking exchange and relaxation into account is found to reduce, but not to eliminate, the discrepancies between theoretical rates and measurements.

Analysis of the Ag L-series X-ray spectrum has been performed, based on relaxed-orbital relativistic transition-energy calculations. Satellite energies were computed in intermediate coupling. It is found that satellites arising from LN double-hole states generally fall within the natural width of the parent diagram lines. Contrary to previous assumption, the observed high-energy satellites are due to LM double-hole states produced by L1-L3M4,5 Coster-Kronig transitions and by shakeoff. The observed peak structure in the satellite spectrum is due to multiplet splitting of the initial and final double-hole states. Theoretical L1-L3M4,5 transition rates based on the Coster-Kronig energies computed by Chen et al. (1977) are closer to experiment than previous results, but still are too large by a factor of about 2, indicating an as-yet undetected flaw in the theory.

Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state.

Two-electron electrostatic interaction integrals were computed with Dirac-Hartree-Fock-Slater wave functions. Results are listed for all orbitals in atoms with atomic numbers from Z = 2 through Z = 106.

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

A modified method of calculating crater circularity based on the average deviation of crater radius from mean radius is presented and used to calculate circularity of Martian craters. Calculation of the circularity indices of over 200 Martian craters yields values similar to circularity indices of terrestrial meteorite craters and different from indices of terrestrial calderas.

Selected Apollo 16 photographs of lunar rilles have been analyzed with a new technique that includes a finite Fourier analysis. Preliminary results suggest that it will be possible to classify rilles quantitatively by their planimetric shape. Shapes of possible terrestrial analogs for lunar rilles also can be compared to the shapes of lunar rilles by using this new technique. Preliminary results also suggest that the new technique may be useful for demonstrating structural control of shape of lunar rilles.

Mathematical models for estimating block up-and-down design of sensory thresholds

Monte Carlo cratering simulation model to show nonrandomness of formation of Mars tangential meteorite craters

Statistical characteristics of spontaneous electrical activity of nerve units that exhibit stochastic dead time following impulses

A large number of Mars craters are nearly tangential to other craters. They occur in clusters or as isolated crater doublets. Results of probability calculations and a Monte Carlo cratering simulation model show conclusively that many of the Mars craters could not have resulted from random single-body impact. The possibility that these craters are calderas is considered possible only if calderas on Mars form by mechanisms different from those on earth. However, clusters and doublets could be caused by meteoroid breakup resulting from stresses induced in the meteoroid by the gravitational field of Mars. It is concluded that, under certain conditions, doublets should be produced on Mars as a direct result of breakup of an impacting meteoroid. The impact process can yield nonrandom crater distributions that should be observed in different degrees of development on different planetary surfaces.