THEORY OF BINARY BOSON SOLUTIONS. Page: 22 of 30
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Appendix: Solution of the Coupled Integral Equations
The set of coupled integral equations (12)-(14) for ui (r),
u ' (r), and ii '(r) are solved by an iteration procedure defined as
i) For a given g( r) and g(4,3)(r) equations (18) and (17) are
solved for u (r) and u (4,3)' (r) using the procedure discussed in the
appendix of ref. (6);
ii) Defining q0(r12) by Eq. (23) we write (17) (uesina the SA);
u44) (r12 (,4) 12 (4,4)(r23) g(4'4)(13) X
u4' (r1) cos(12,13)dr3 ( 4) . (A1)
14 3 1 (r2
Direct iteratton of this equation, using u' (r) as a starting approximation,
yields the solution
u(4 ) 12 12 (4, 12 (AZ)
(4,4) (4,3) (3,3)(r)
ii) For the sme g (r) and &(4 ) and a given g(, Eqs. (12)-
(14) are solved by direct iteration, using u (4,3) (r) and u (r) as
starting approximations. Terms which contribute to the energy in orders
higher than x are neglected. Direct substitution of Eqs. (12)-(14) in
Eqs. (10)-(ll) for (H) shows that the term in Eq. (14) involving -
(', -2,H-1,N) contributes to (E) only -in order "x .' Equations "(12)-
(14) are then written
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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/m1/22/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.