Universal Factorization of 3n−j(j>2)3n-j (j > 2) Symbols of the First and Second Kinds for SU(2) Group and Their Direct and Exact Calculation and Tabulation

We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and through a definition of a reduced $6-j$ symbol. The resulting $3n-j$ symbols thereby take a combinatorial form which is simply the product of two factors. The one is an integer or polynomial which is the single sum over the products of reduced $6-j$ symbols. They are in the form of summing over the products of binomial coefficients. The other is a multiplication of all the triangle relations appearing in the symbols, which can also be rewritten using binomial coefficients. The new formulation indicates that the intrinsic structure for the general recoupling coefficients is much nicer and simpler, which might serves as a bridge for the study with other fields. Along with our newly developed algorithms, this also provides a basis for a direct, exact and efficient calculation or tabulation of all the $3n-j$ symbols of the SU(2) group for all range of quantum angular momentum arguments. As an illustration, we present teh results for the $12-j$ symbols of the first kind.Comment: Add tables and reference

Ultra-cold ion-atom collisions: near resonant charge exchange

Accurate calculations of the near resonant charge exchange crosssections in HD+, HT+ and Dr at very low energies are presented. The charge exchange process between an ion and its parent atom is a near resonant process that becomes inelastic when two different isotopes are involved. We find that, at very low energies, the charge exchange cross-section follows Wigner's law for inelastic processes and becomes much larger than the cross-section for elastic collisions which tends to a finite limit. The efficiency of inelastic charge exchange increases as the mass difference between the two isotopes decreases. © IOP Publishing Ltd and Deutsche Physikalische Gesellscha

Theoretical Study of Pressure Broadening of Lithium Resonance Lines by Helium Atoms

Quantum mechanical calculations are performed of the emission and absorption profiles of the lithium 2s-2p resonance line under the influence of a helium perturbing gas. We use carefully constructed potential energy surfaces and transition dipole moments to compute the emission and absorption coefficients at temperatures from 200 to 3000 K at wavelengths between 500 nm and 1000 nm. Contributions from quasi-bound states are included. The resulting red and blue wing profiles are compared with previous theoretical calculations and with an experiment, carried out at a temperature of 670 K.Comment: 10 figure

Potential energy curves for the interaction of Ag(5s) and Ag(5p) with noble gas atoms

We investigate the interaction of ground and excited states of a silver atom with noble gases (NG), including helium. Born-Oppenheimer potential energy curves are calculated with quantum chemistry methods and spin-orbit effects in the excited states are included by assuming a spin-orbit splitting independent of the internuclear distance. We compare our results with experimentally available spectroscopic data, as well as with previous calculations. Because of strong spin-orbit interactions, excited Ag-NG potential energy curves cannot be fitted to Morse-like potentials. We find that the labeling of the observed vibrational levels has to be shifted by one unit

Physics of planetary atmospheres III - The time-dependent coupled Hartree-Fock approximation

Coupled Hartree-Fock approximation for calculating frequency-dependent refractive index of helium ga

Physics of planetary atmospheres. i- ray- leigh scattering by helium

Physics of planetary atmospheres - Variation method used to calculate Rayleigh scattering cross sections of helium as wavelength functio