THEORY OF BINARY BOSON SOLUTIONS. Page: 18 of 30
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resort to a much less accurate procedure. Let rm (,13) be the position of
the first maximum in g i(r); then the ratio of effective volumes occupied
by a He3 and a He4 atom is approximately given by13
2r (4,3) * r (4,4) 3
1+ m1 (41
With rm(4,4) 3.37A and r , 3.54A, we obtain C: _ 0.33 .not inconsis-
tent with the experimental values, a 0.284 - 0.301.14 In an earlier
paper, we actually computed a from 1 P4. The value obtained was
much more reliable, even though the values of t1(p4) are not as satisfactory.
In our present calculation the inclusion of proper correlations leads to
a significantly improved value of at p4 = 0.021 8-3. We are confident
that similar improvement in a will be found if properly computed from
E p 1(P4 g. However the amount of computer time required prevents us from
carrying out a thorough investigation. The results of our previous work
as well as results obtained by Davison and Feenberg16 from a second order
perturbation calculation are included in Table 2 for comparison.
The significance of a is that it is related directly to the long
wavelength limit of the effective interaction, V, between two He quasi-
particles in the dilute 3e3-He4 solution. For, varying the ground state
energy with respect to the number density of the mass-3 bosons, we obtain
the chemical potential of a mass-3 boson in the solution at finite concen-
trations; and the variation of this chemical potential with respect to the
number density of mass-3 bosons, holding the chemical potential of He4
constant, leads to V0. Starting with Eq. (38), we obtain first the chemical
potential. To first order in the concentration x,
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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/m1/18/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.