THEORY OF BINARY BOSON SOLUTIONS. Page: 9 of 30
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If the g 's are known, (V can be computed immediately; for computing
(T however, the correlating function u must also be known.
Equations relating the correlating functions to the distribution
functions are derived by -applying appropriate differentiation operators
to the definitions of the latter,6 Eq. (6). We obtain the following
V1 (44 (T ) - 4g (r12 12 u(,>12}
+P4 g(4,4,4) (1 34u4 (r 13 )dr3. +3 (4,4,3) (1,2,t ) Ltdu( )(r IN)dir,
g (4,3) (rW = g (4,) (r N31 (N)
+s Sg(4,4,3)(1,2,DI)V2u (4,3 ) dr+ g +,1N ( , Nl
(rf~~ r + 0N) 1 ) u'}
N-1V N (3,3)(r1 ,N ) (3,3) rN-,N N-1Nu (rN- 1,N
+P jg(4,3,3)(1,'-1,N)lu(4,3)(rl )d + g drN22,N-1,N 2 (u (r
These equations are obvious extensions of the BBGKY equation for a one-
component fluid. The analogues for classical liquids have been used by
Alder and others.9 As they stand, the equations are eXact, albeit insoluble.
They may be reduced to a tractable form by introducing the generalized
superposition approximation (SA):
8gC (i , i , g )(ri g(0,Y) (ri i )g ri ) (1 )
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Massey, W.E. & Tan, H. THEORY OF BINARY BOSON SOLUTIONS., report, October 31, 1970; United States. (https://digital.library.unt.edu/ark:/67531/metadc1032575/m1/9/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.