Fast evaluation of Gaunt coefficients: Recursive approach

Journal of Computational and Applied Mathematics

Volumn 85, Issue 1, 1997, Pages 53-65

  Xu, Yu Lin ^a  

^a University of Florida   (United States)

Author keywords

Clebsch Gordan coefficients; Computational method; Electromagnetic multisphere scattering; Gaunt coefficients; Wigner 3jm symbols

Indexed keywords

ELECTROMAGNETIC WAVE SCATTERING; INTEGRAL EQUATIONS; PROBLEM SOLVING; RECURSIVE FUNCTIONS;

ELECTROMAGNETIC MULTISPHERE SCATTERING; GAUNT COEFFICIENTS; LEGENDRE FUNCTIONS;

COMPUTATIONAL METHODS;

EID: 0031556622     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00128-3     Document Type: Article

References (20)

1. G. Arfken, Mathematical Methods for Physicists, Academic Press, Orlando, FL, 1985.
2. J.H. Bruning, Ph.D. Dissertation Department of Electrical Engineering, University of Illinois, 1969.
3. J.H. Bruning, Y.T. Lo, Multiple scattering of EM waves by spheres, Part I - Multipole expansion and ray-optical solutions, IEEE Trans. Ant. Prop. AP-19 (1971) 378-400.
4. O.R. Cruzan, Translational addition theorems for spherical vector wave functions, Quart. Appl. Math. 20 (1962) 33-40.
5. A.R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, 1957.
6. B. Friedman, J. Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12 (1954) 13-23.
7. K.A. Fuller, Ph.D. Dissertation, Department of Physics, Texas A&M University, 1987.
8. K.A. Fuller, G.W. Kattawar, Consummate solution to the problem of classical electromagnetic scattering by ensembles of spheres. I: linear chains, Opt. Lett. 13 (1988) 90-92.
9. K.A. Fuller, G.W. Kattawar, Consummate solution to the problem of classical electromagnetic scattering by ensembles of spheres. II: clusters of arbitrary configuration, Opt. Lett. 13 (1988) 1063-1065.
10. J.A. Gaunt, On the triplets of helium, Philos. Trans. Roy. Soc. (Lond.) Ser. A 228 (1929) 151-196.
11. S.-T. Lai, Y.-N. Chiu, Exact computation of the 3-j and 6-j symbols, Comput. Phys. Commun. 61 (1990) 350-360.
12. M. Rotenberg, R. Bivins, N. Metropolis, J.K. Wooten Jr., The 3-j and 6-j Symbols, The Technology Press, MIT, Cambridge, MA, 1959.
13. S. Stein, Addition theorems for spherical wave functions. Quart. Appl. Math. 19 (1961) 15-24.
14. W.J. Thompson, Angular Momentum, Wiley, New York, 1994.
15. E.P. Wigner, On the matrices which reduce the Krönecker products of representations of simply reducible groups, in: L.C. Biedenharn, H. van Dam (eds.), Quantum Theory of Angular Momentum, Academic Press, New York, 1965, pp. 89-132.
16. Y.-I. Xu, Electromagnetic scattering by an aggregate of spheres, Appl. Opt. 34 (1995) 4573-4588.
17. Y.-I. Xu, Fast evaluation of the Gaunt coefficients, Math. Comput. 65 (1996) 1601-1612.
18. Y.-I. Xu, Calculation of the addition coefficients in electromagnetic multisphere-scattering theory, J. Comput. Phys. 127 (1996) 285-298.
19. Y.-I. Xu, B.Å.S. Gustafson, A complete and efficient multisphere scattering theory for modeling the optical properties of interplanetary dust, in: B.Å.S. Gustafson, M. Hanner (Eds.), Physics, Chemistry, and Dynamics of Interplanetary Dust, A.S.P. CONF. SER. Vol. 104, Pub. Astron. Soc. Pacific, San Francisco, 1996, pp. 419-422.
20. Y.-I. Xu, Efficient calculation of vector translation coefficients in multiparticle light-scattering theories in terms of recursive evaluation of Wigner 3jm symbols and Gaunt coefficients, J. Comput. Phys. (1997) to be published.