Interaction regular approximation transformed

This operator is very similar to the 2 operator of the free-particle Foldy-Wouthuysen transformation it has a regularizing factor multiplied by (spin-free and spin-dependent operators from the Coulomb, Gaunt, and Breit interactions in an entirely analogous fashion to the Foldy-Wouthuysen transformation. As an example, the two-electron spin-orbit interaction in the regular approximation is... 

Abstract Some aspects of self-assembly of quantum dots in thin solid films are considered. Nonlinear evolution equations describing the dynamics of the fihn instability that results in various surface nanostructures are analyzed. Two instability mechanisms are considered the one associated with the epitaxial stress and the other caused by the surface-energy anisotropy. It is shown that wetting interactions between the film and the substrate transform the instability spectrum from the long- to the short-wave type, thus yielding the possibility of the formation of spatiaUy-regular, stable arrays of quantum dots that do not coarsen in time. Pattern formation is analyzed by means of ampbtude equations near the insta-bibty threshold and by numerical solution of the strongly nonlinear evolution equations in the small-slope approximation. 

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