B-5 



Integrating its flux, p* v p - p v p* over a sphere of area A centered about 



oC- ISC' SLr oC- 



£1 , we find that the total flux is 



4nik^|gi| ^A^ (B-15) 



Dividing this by i kg A^ , the flux per unit area normal to k^ in the incident wave, 

 we obtain the scattering cross section 



f7g^-4rr| gi| = . (B-16) 



Integrating the flux per unit area caused by both incident and scattered waves over 

 the same sphere, gives 



4 TT ik^ j gi , 2 A =+ 4tt (gi - gi*) ^ (B-17) 



The negative of this quantity represents the net inward flux. Dividing this by the 

 incident flux per unit area gives the absorption cross section 



,. =.4.|g,|3. ilLMSLl (B-18) 



ab '^'1 k 



o 



Expressed in terms of the cross section, the scattering coefficient gi is 



/a ^ Q \^'^ ik a 



s o e o ex /d io\ 



gi =7^ - i^J^ T^T— (B-19) 



where o^^ = a^t) + "^sc ^^ *^he extinction cross section. The scattering cross 

 section per unit volume, Sg^ir), is given by 



S (r) = (o (s)n(r,s)ds - 4TT(Jg(s)|^n(r,s)ds . (B-20) 



sc — J sc — Jf* I — 



Similarly the extinction cross section per unit volume is 



S (r) = I a (s)n(r,s)ds = - 4^ (im [gis)\ n(r,s)ds = - ^ Im G(r) 

 ex- j ex - k^J L J - k^ 



(B-21) 



!^xthm SI.ILittleJnt. 



S-7001-Q307 



