B-2 



+ikjr-£l 

 ^(L-E^) = I ^ . ^ I (B-2) 



and B. is a complex number. The external field acting on the j-th scatterer is 

 defined as 



p^(r) = p(r) - B. E(r, r.) (B-3) 



The scattering properties of the scatterers are furthermore assumed to be char- 

 acterized by the relationship Bj = g(sj, «J) pj(rj), making the strength of the 

 scattered wave proportional to the external field acting on it. The value g(s^,uu) 

 will be referred to as the scattering coefficient for the j-th scatterer and will be 

 abbreviated to g. . All the models for pulsating air bubbles suspended in water 

 satisfy this condition. For the adopted model (Model III) 



p. a 

 inc 



uu 



1 - i & (a, 0)) 



\ (JU / 



where uUq and 6 (a, w) are functions only of the bubble radius a, the frequency of 

 the incident sound o), and various parameters of the gas in the bubble and the 

 surrounding medium. Then the bubble radius is the scattering parameter and 



g(a) = — — ^ 



uu 



— j - 1 - i & (a, (JU) 



(JU / 



The basic problem is then the following: Given the function g(s, w), the distribu- 

 tion function n(r, s) for the scatters and the wave function p (r) which is present 

 in the m.edium in the absence of the scatterers, find <^ p(r) > , the configurational 

 average of p (r), in the presence of scatterers. 



Consider a particular configuration of scatterers. Then 

 p(r) - p (r) + V" B. E(r, r.) , p^ (r) - p (r) +S^ B. E(r, r.,) (B-4) 



represent the total field and the incident field on the j-th scatterer. Substituting 

 the relationship B. = g. pJ (r.) in the above gives 



p(r) = p^(r) +^ g. pJ (r.) E(r, r. ) (B-5) 



anhur Sl.ltUtleJnt. 



S-7001-0307 



