The X(2)Σ(1/2)(+), A(2)Π(1∕2), A(2)Π(3∕2), and B(2)Σ(1/2)(+) potential energy curves and associated dipole matrix elements are computed for M + Ng at the spin-orbit multi-reference configuration interaction level, where M = K, Rb, Cs and Ng = He, Ne, Ar. Dissociation energies and equilibrium positions for all minima are identified and corresponding vibrational energy levels are computed. Difference potentials are used together with the quasistatic approximation to estimate the position of satellite peaks of collisionally broadened D2 lines. The comparison of potential energy curves for different alkali atom and noble gas atom combinations is facilitated by using the same level of theory for all nine M + Ng pairs.

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The cluster statistics of percolation theory are used to find the distributions of hydraulic conductivity, K, of anisotropic (truncated) random fractal media. Rescaling of variables to transform anisotropic to isotropic media also produces deformations of, for example experimental volumes, and the resulting non-equidimensional shapes may generate interesting size effects on K. Previously, the most likely value of K was obtained by comparing the correlation length from percolation theory with system dimensions, a procedure analogous to those developed for hopping conduction in disordered systems to calculate the longitudinal conductivity of thin films. The result probably explains the frequent tendencies of measurements of K in anisotropic fracture networks and agricultural soils to increase with the scale of measurement, similarly to how the longitudinal conductivity of a thick film would be larger than the corresponding conductivity of a thin film (three-rather than two-dimensional conduction). However, the same procedure applied to the conductivity in the perpendicular direction (analogous to the transverse electrical conductivity of a thin film) shows a diminishing function of spatial scale. Collectively, these 'scale effects' disappear if the shape of the experimental volume is selected to maintain the relationships of conduction in the various directions as the scale of the experiment is increased analogously to equidimensional volumes in isotropic media. The increase in K is, thus, merely due to an increase in the dimensionality of conduction from one to three with increasing system size. The paper, thus, provides a solid argument against a common assumption in the porous media communities that the connectivity of highly conducting regions of a medium should increase with increasing scale of measurement.

The ability to calculate soil hydraulic properties from soil physical data has been a dominant objective of soil physics research since the 1950s. The purpose of this study was to develop an approach based on modern physics to deal with an arbitrary porous medium. Some important advances resulted from applying critical path analysis from percolation theory and percolation scaling to a truncated random fractal model (Rieu and Sposito) of a soil. In fact, some of the perceived limitations of the fractal model at high and low saturations were reevaluated as strengths in the previous application. Nevertheless, it is not realistic to expect all media to be characterized accurately in such a simple fashion. We developed an appropriate generalization of the description of the medium to an arbitrary pore size distribution while maintaining the complications related to fluid connectivity at high and low saturations relating to percolation theory. It also maintains the relevance of the pore size distribution to the hydraulic conductivity through the application of critical path analysis. A numerical routine was constructed to apply these concepts to an arbitrary pore size distribution, which in our case was inferred from experimentally determined particle size data. Although more than 50 soils were investigated, our preliminary study does not indicate what the general relevance of fractal models is.