Frank Biggs

Hartree-Fock Compton profiles for the elements

Orbital and total-atom Compton profiles are given for the elements. Hartree-Fock wavefunctions were used in the numerical calculations for atomic numbers 1 less than or equal to Z less than or equal to 36 and relativistic Dirac- -Hartree--Fock wavefunctions for atomic numbers 36 less than or equal to Z less than or equal to 102.

Six-gaussian representation of the angular-brightness distribution for solar radiation

Abstract The angular distribution of circumsolar radiation varies with changing atmosphere and influences the solar irradiance at the receiver of a concentrating system. In order to facilitate calculation of this irradiance, five typical sunshapes are chosen from the widest to the narrowest shape in the Lawrence Berkeley Laboratory data and are approximated by a sum of 6 gaussian distributions. An effective sunshape can then be obtained by convolution with error-cone distributions that represent a statistical description of uncertainties encountered in an optical concentrating system. Convolution of circular-normal error cones first with the sum of gaussians and then with actual sunshape indicates good agreement whenever the error-cone dispersion is greater than 0.0012. Thus the analytic convolution can replace more costly (in time and computer storage) numerical calculation. A simple prescription indicates how each of the analytic representations may be transformed to approximate sunshapes appropriate for slightly different atmospheric conditions.

Relativistic hartree—fock compton profiles for the rare gases and lead☆

Abstract Calculations of relativistic Hartree-Fock Compton profile J ( q ) for the rare gases and Pb, performed for values of q between 0 and 100, are compared with the nonrelativistic calculations. Comparison with experimental profile data is made for Ar and Kr. For q between 0.0 and 0.4 in Kr, much closer agreement with experiment is obtained when the relativistic Hartree-Fock wavefunction is used to perform the profile calculation than when the non-relativistic Hartree-Fock wavefunction is used. Percentage decreases in J (0) due to using a relativistic wavefunction are found to be 0.187% in Ar, 0.712% in Kr, 1.47% in Xe, and 5.24% in Pb. Our studies show that relativistic profile flattening in the outer s and p orbitals is significant. This tends to a larger flattening of the total profile than might be expected a priori.

USE OF NUMERICALLY INVERTED LAPLACE TRANSFORMS IN TIME-DEPENDENT TRANSPORT CALCULATIONS.

Abstract A time-dependent transport problem in which a monoenergetic point source emits a pulse of radiation into an infinite medium has been solved by Laplace transform techniques. Auxiliary information inferred from the physical nature of the problem is incorporated into the Laplace inversion procedure to eliminate the oscillatory solutions which usually result from attempts to numerically invert Laplace transforms. This simultaneous utilization of mathematical and physical information has made it possible to obtain credible time-dependent solutions for the transport problem under consideration.