THEORY OF BINARY BOSON SOLUTIONS. Page: 7 of 30

P gQ )r ) , N (N ) d11 dr(1 (r))N1, (6)
where dr(L ) denotes drldr 2-drN with dr and dr omitted. Again
a and p can be 4 or 3, and 1 = F 12 dr1dr2..'d g
the probability (relative to a random distribution) that, given a particle
of type a at the origin, a particle of type f will be found at a distance
r1 i away.
We shall also need the three-particle distribution functions
defined by
Pa g (c (if j, ik ) = N (N -l>(YI -2) ) I ,
(7)
Pa2 (mcr'O(i j k ) -- N(N -O)N riti2 drk )
It is implied in the definitions, Eqs. (6)-(7) that these dis-
tribution functions are unaffected by a permutation of their superscripts
and arguments.
The pair distribution functions must have the usual physical
properties:
(i) g (r) is a purely radial function;
(ii) limE(a."o)() - 1] = 0;
r-WA
(iii) g (r) satisfies the normalization condition
sx g1 COr -lj (8)
The importance of taking into account the difference in corre-
lations between (4,4), (4,3) and (3,3) pairs is clear. Because of the
lighter mass, a mass-3 particle has a larger zero-point energy and there-
fore occupies a larger specific volume than a mass-4 particle. A measure

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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/m1/7/ocr/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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