THEORY OF BINARY BOSON SOLUTIONS. Page: 15 of 30
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The formal solution to the equations is thus seen to consist of a very
complicated set of coupled recursion relations. The actual process of
solving these equations is arduous but straightforward.
In terms of these functions, the expectation value of the
Hamiltoxian for the binary boson solution finally appears as follows:
- N (p )>+N3 14+ 2 (p31p4), (38)
where Io and t are as defined earlier in Eqs. (26)-(27), and
E2P 4 ( + 22(2) + (3) + 84
- 1 8 u 3,3) (r (3,3) (r)dr ,
2(2) p4 v~(3,3) d,
2 (3) r 43 (r)d
2 1 p (4,3) ( r
- (4 2 4I T.x(1)( S(r)dr
(4) h4 (4 )
2 -4,-)9 S(r)dr,
AM- + 13
can be interpreted as the interaction energy between the
mass-3 bosons. g2(1) and s2 give the direct interaction energy between
the mass-3 bosons. g2(3) describes an indirect contribution through inter-
actions between mass-3 bosons and the He atoms in the background. -2(4)
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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/m1/15/: accessed April 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.