3,753 research outputs found
Universal Factorization of Symbols of the First and Second Kinds for SU(2) Group and Their Direct and Exact Calculation and Tabulation
We show that general 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 symbol. The resulting 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 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 symbols of the SU(2)
group for all range of quantum angular momentum arguments. As an illustration,
we present teh results for the 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
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