Semiclassical study of atoms by periodic orbit theory: Diffraction in atoms

The density of states of non-hydrogenic Rydberg atoms both in a pure magnetic field and in parallel electric and magnetic fields are analysed semiclassically in this work. The first quantitative calculations for atoms performed using periodic and diffractive periodic orbit theories are presented. The first scaled semiclassical calculations on the parallel field system using either closed orbits (for photoabsorption) or periodic or diffractive periodic orbits (for eigenvalue spectra) are also presented. Oscillatory contributions observed in the density of states of Rydberg atoms, not present in the hydrogenic density of states, are reproduced using diffractive periodic orbit theory. Previously unexplained and puzzling alterations in the amplitude of spectral modulations associated with primitive periodic orbits (core-shadowing and core-brightening) are reproduced by the inclusion of additional diffractive orbits. For the first time a complete prescription is provided for the calculation of the diffractive contribution to the density of states in non-hydrogenic atoms. Particular attention has been paid to the calculation of contributions associated with high repetition and high diffraction number orbits. Comparisons with quantum results, calculated by well established R-matrix type methods, provide compelling evidence of the accuracy of the semiclassical theory developed and presented in this work. A brief analysis of the spectral statistics of the target systems is conducted. Numerical investigation of the spectral rigidity and nearest neighbour spacing statistic of hydrogenic and non hydrogenic Rydberg atoms is carried out and a discussion of the method by which diffractive contributions could be included in theoretical semiclassical statistic calculations is provided. This theme is developed as a relevant area for future research; there is significant interest in the implications of this work for spectral statistics, since diffraction has been associated with a new generic class of behaviour termed 'half-poisson'.