Atomic Molecular And Optical Physics

It is shown that the Maxwell's equations for surface electromagnetic TM-waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending of |{\bf E}|, can be integrated in quadrature.

The D -dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with an {\it Aufbau Prinzip} is applied to produce a D -dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of an Hamiltonian, invariant under the q -deformed algebra U q ( so (D)) , that breaks down the SO( D+1 ) dynamical symmetry of the hydrogen atom in D dimensions. The D=2 case (Flatland) is investigated with some details. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values q=0.8 and q=1 , respectively, of the deformation parameter q .

The energy dependence of the nonradiative electron capture cross-section is discussed in the relativistic domain. A simple analytic expression is obtained for inner-shell transitions using second-order perturbation theory. We have confirmed that the leading-order term is found to have the following energy dependence: Q ~ E^{-1}ln^2 E. This is attributed to a combination of kinematic features of the process and retardation effects. Electron capture without change of spin is the dominant transition.

We discuss three-body recombination of ultra-cold atoms to a weakly bound s level. In this case, characterized by large and positive scattering length a for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability and makes simple Jastrow-like approaches absolutely inadequate. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: α rec =3.9ℏ a 4 /m , where m is the atom mass.

Magnetic- and electric-dipole two-photon absorption (MED-TPA), recently introduced as a new spectroscopic technique for studying transitions between states of opposite parities, is investigated from a theoretical point of view. A new approximation, referred to as {\it weak quasi-closure approximation}, is used together with symmetry adaptation techniques to calculate the transition amplitude between states having well-defined symmetry properties. Selection rules for MED-TPA are derived and compared to selection rules for parity-forbidden electric-dipole two-photon absorption (ED-TPA).

We have calculated X-ray and UV spectra of Be-like Fe (FeXXIII) ion in collisional-radiative model including all fine-structure transitions among the 2s^2, 2s2p, 2p^2, 2snl, and 2pnl levels where n=3 and 4, adopting data for the collision strengths by Zhang & Sampson (1992) and by Sampson, Goett, & Clark (1984). Some line intensity ratios can be used for the temperature diagnostics. We show 5 ratios in UV region and 9 ratios in X-ray region as a function of electron temperature and density at 0.3keV < T_e < 10keV and n e =1− 10 25 c m −3 . The effect of cascade in these line ratios and in the level population densities are discussed.

We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential appears only through the matrix elements of the second order Ursell operator U 2 . Our results remain valid for significant degree of degeneracy of the gas, but not when Bose Einstein (or BCS) condensation is reached, or even too close from this transition point. We apply them to the study of the thermodynamic properties of degenerate quantum gases: equation of state, magnetic susceptibility, effects of exchange between bound states and free particles, etc. We compare our predictions to those obtained within other approaches, especially the ``pseudo potential'' approximation, where the real potential is replaced by a potential with zero range (Dirac delta function). This comparison is conveniently made in terms of a temperature dependent quantity, the ``Ursell length'', which we define in the text. This length plays a role which is analogous to the scattering length for pseudopotentials, but it is temperature dependent and may include more physical effects than just binary collision effects; for instance at very low temperatures it may change sign or increase almost exponentially, an effect which is reminiscent of a precursor of the BCS pairing transition. As an illustration, numerical results for quantum hard spheres are given.

The dispersion coefficients C 6 , C 8 , and C 10 for the interactions between H, He, and Li are calculated using variational wave functions in Hylleraas basis sets with multiple exponential scale factors. With these highly correlated wave functions, significant improvements are made upon previous calculations and our results provide definitive values for these coefficients.