Calculation of the Addition Coefficients in Electromagnetic Multisphere-Scattering Theory

✍ Scribed by Yu-lin Xu

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 372 KB
• Volume: 127
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0175

✦ Synopsis

One of the most intractable problems in electromagnetic multisphere-scattering theory is the formulation and evaluation of vector Rotational addition theorems are well known for scalar addition coefficients introduced by the addition theorems for vector spherical wave functions [27][28][29][30] and well formulated for spherical harmonics. This paper presents an efficient approach for vector spherical harmonics [25, 26]. Therefore, this paper the calculation of both scalar and vector translational addition coefconcentrates on the calculation of the scalar and vector ficients, which is based on fast evaluation of the Gaunt coefficients.

translational addition coefficients. Common to the analyti-

The paper also rederives the analytical expressions for the vector translational addition coefficients and discusses the strengths and cal expressions for these coefficients is a product of two limitations of other formulations and numerical techniques found associated Legendre functions that in turn may be exin the literature. Numerical results from the formulation derived in pressed in terms of a linearization expansion involving the this paper agree with those of a previously published recursion Gaunt coefficients [31]. Considerable research work has scheme that completely avoids the use of the Gaunt coefficients, but the method of direct calculation proposed here reduces the been conducted on the calculation of the Gaunt coefficomputing time by a factor of 4-6. ᮊ 1996 Academic Press, Inc.

cients, including those of Bruning [32], Fuller [33] and Xu [34]. Stein [25] and, later, Mackowski [21] showed that the vector translational addition coefficients can be evaluated