Relativistic and relaxation effects in the near-edgeKphotoabsorption of xenon and radon

The relativistic photoabsorption cross section in the vicinity of the xenon and radon K-absorption edges is calculated using the Dirac-Fock method. The relaxation is included by constructing separate solutions for the initial ground state and for the final 1s-hole state and by including the resulting overlap integrals into the transition amplitude. The relativistic effect is found to lower the cross section with 12% and 35% for xenon and radon, respectively. One-third of this effect results from the change in the K-ionization energy and two-thirds from the change in the ormation on a lattice. A maximum-likelihood growth algorithm is formulated to supplement the integral solution of Laplace's equation. This allows us to study diffusion-limited aggregation and viscous flow in porous media. Our deterministic solution for the aggregation process displays the same fractal dimension (D{}1.7) as Monte Carlo diffusion-limited aggregation. We also compare our solution to Laplace's equation with the experimentally observed pattern in one limit of a Hele-Shaw cell experiment. Lastly, we present a second deterministic algorithm which results in a pattern with tips which appear parabolic.