The Fourier transform of Equation (C.5) is 



G*(k,K) 



- - K ( k r) - G„*(k,K:) 



(C.6) 



and from the definition given in Equation (38) , G^* is given 



G3*(k 



->=i J 



K d£ 



1/2 1/2 

 -«- (k +£ ) [(k+£ ) -K] 



(C.7) 



In Equation (C.5), K (x) is the modified Bessel function. For small r, K ( k r) can 



o o 



be expanded 



K ( k r) = - in 



Ik r 



- Y 



(C.8) 



where y = 0.577... is Euler's constant. 



By substitution of Equation (C.8) into Equation (C.6), for small y and z, G* is 



G*(k,K:) = - 



TT 



k r 



+Y 



G* 



= Sd - ¥ f*(k,K,K) 



(C.9) 



where G„ is Equation (33), G„* is Equation (C.7), and f* is given by 



f*(k,K,K) = In ^^ iTT + ttG„* 



Ikl ^ 



(CIO) 



56 



