Theoretical Atomic Spectroscopy

Rudzikas, Zenonas

doi:10.1017/cbo9780511524554

Cited by 127 publications

(168 citation statements)

References 0 publications

Supporting

Mentioning

165

Contrasting

Order By: Relevance

“…To do so, the remarkable angular momentum recoupling techniques developed by the Lithuanian school [13,14] are used. As an application of the general results, the most common experimental case of an isotropic sample (disordered molecules, liquids, polycrystals or powders) is described in detail.…”

Section: Introductionmentioning

confidence: 99%

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

2014

View full text Add to dashboard Cite

Abstract:A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected. PACS

show abstract

Section: Introductionmentioning

confidence: 99%

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

2014

View full text Add to dashboard Cite

show abstract

“…An irreducible tensorial operator (γ) ( ) acts on the spin-angular variables of the -th electron in the space of one-electron relativistic wave functions (4-spinors) [19] Functions | , | are 2-spinors. In (1) the factor X = 1/2.…”

Section: Coupling Schemes Of Ranks For a Two-particle Operatormentioning

confidence: 99%

“…For antisymmetric coupled two-electron wave functions, the submatrix element of operator (γ) γ is expressed as The explicite expressions of (24), (33) submatrix elements of Coulomb, magnetic and retardation interactions can be found, for instance, in [12,19].…”

Section: Two-subshell Formulamentioning

confidence: 99%

See 1 more Smart Citation

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

Jursenas

Merkelis

2010

Open Physics

View full text Add to dashboard Cite

show abstract

“…The 9j symbols, characterizing the coupling of four angular momenta, are involved for instance in the computation of the matrix elements of the products of tensor operators, and in the transformation from LS to jj coupling [1,2]. The triple sum series of Jucys and Bandzaitis [3] is the simplest known algebraic form for the 9j coefficient.…”

mentioning

confidence: 99%

A note on recursive calculations of particular 9jcoefficients

Pain¹

2011

Lith. J. Phys.

View full text Add to dashboard Cite

The calculation of angular-momentum coupling transformation matrices can be very time consuming and alternative methods, even if they apply only in special cases, are helpful. We present a recursion relation for the calculation of particular 9j symbols used in the quantum theory of angular momentum.Keywords: angular momentum, 9j coefficient, recursion relation 03.65.Fd, The coupling of N angular momenta is related to the definition of a 3(N − 1)j symbol. The 9j symbols, characterizing the coupling of four angular momenta, are involved for instance in the computation of the matrix elements of the products of tensor operators, and in the transformation from LS to jj coupling [1,2]. The triple sum series of Jucys and Bandzaitis [3] is the simplest known algebraic form for the 9j coefficient. Fourty years ago, Ališauskas and Jucys [4][5][6][7][8] derived an algebraic expression, in which 9j symbols are written as the threefold summation of multiplications and divisions of factorials. More recently, Wei [9,10] proposed to express 9j symbols as a summation of the products of binomial coefficients and devised an algorithm to calculate the binomial coefficients recursively. Although some relationships between particular 9j symbols have been obtained in special cases [11], it is quite difficult to find recursion formulas for the 9j symbol itself, due to the fact that it contains nine arguments. PACSThe general recursion relations for arbitrary 9j symbols were introduced in [12], [3] (with incorrect phase factors), and in [13] (in corrected form). However, as a rule in these relations, several angular momentum parameters are changing. It seems that relations with changing single momentum parameter are possible only if some other parameters of the 9j accept extreme or fixed small values. For instance, the following 9j symbol:

show abstract

Theoretical Atomic Spectroscopy

Cited by 127 publications

References 0 publications

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

A note on recursive calculations of particular 9jcoefficients

Contact Info

Product

Resources

About