Abstract
The ground-state wave function of He-II is calculated in the “two sums over k” approximation, i.e. in the form of the Jastrow function and the first correction:lnΨ0=12!∑k≠0a2(k)ρkρ−k+13!1N∑k1,k2≠0k1+k2≠0a3(k1,k2)ρk1+k2ρ−k1ρ−k2,where the function a2(k) is found numerically from the Vakarchuk equation relating a2(k) and a3(k1,k2) with the structure factor. Knowing Ψ0, we calculated the amount of single- and two-particle condensates in He-II at T=0; this is the first derivation of a formula for a two-particle condensate in the “two sums” approximation. The model contains no adjustable parameters or functions. The results for the condensates are strongly dependent on the number of corrections an included in the expansion of lnΨ0: in the “single sum” approximation (a3=0) 27% of the atoms are in the single-particle condensate and about 53% of the atoms with momentum k>0 are in the two-particle condensate; in the more accurate “two sums” approximation (a3≠0) the percentages are 6% and 16%, respectively. For the “two sums” approximation we also found that the higher-order s-particle condensates (s⩾3) are absent in He-II at T=0.
Published Version
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