Free Green Function for Overlapping Spheres

Delphine Cabaret/ Christian Brouder/ and Philippe Sainctavit  

F-75252 PARIS Cedex 05, FRANCE LMPSM, Universite de Nancy I Boite Postale 239 

The first section is devoted to the derivation of the two-center expansion of the Green function in overlapping spheres. This expansion is a notoriously difficult problem (Sack, 1964) that was finally solved by Sun and Su. In the second section, we discuss the use of this overlapping Green function. 

We have to calculate the integral /(/c) of Eq.(2) which depends on the spherical Bessel functions and is expressed as  

According to Cauchy s theorem, plus the integral over the large half-circle Cm 

Since ji —qr) = -iyji qr) and / + ( + / is even (property of the Gaunt coefficients), is rewritten as follows  

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