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Expressions for the incoherent-scattering function and the inelastic-scattering crosssection differential with respect to the solid angle for detection of scattered x rays from atomic, molecular, and condensed-matter targets are derived in the relativistic impulse approximation for Compton scattering. It is shown that the incoherent-scattering functions, defined as an integral over Compton profiles, can be computed easily by means of a "linear" approximation. Numerical results for Al, Fe, and Pb are compared with available experimental values and with the Wailer-Hartree theory.

A basic quantum-mechanical model for wave functions and current flow in open quantum dots or billiards is investigated. The model involves non-Hertmitian quantum mechanics, parity-time (PT ) symmetry, and PT -symmetry breaking. Attached leads are represented by positive and negative imaginary potentials. Thus probability densities, currents flows, etc., for open quantum dots or billiards may be simulated in this way by solving the Schrödinger equation with a complex potential. Here we consider a nominally open ballistic quantum dot emulated by a planar microwave billiard. Results for probability distributions for densities, currents (Poynting vector), and stress tensor components are presented and compared with predictions based on Gaussian random wave theory. The results are also discussed in view of the corresponding measurements for the analogous microwave cavity. The model is of conceptual as well as of practical and educational interest.

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Recent measurements of the Compton profile of polycrystalline vanadium have been interpreted by means of a renormalized-free-atom model. The electronic configurat. 'on has been varied, and it has been found that the configuration in vanadium must be close to Bd44s~in atomic notations, in agreement with earlier experience.