978-1-940366-36-4_WholeBook

Superconductivity and Superfluidity
where M 4 is mass of helium atom, ̂v 0 is their averaged velocity of harmonic zero-point
oscillations.
Hence, after simple transformations we obtain:
where the notation is introduced:
̂v 0 = cα 3 { n
n 0
}
, (11.17)
√
n 0 = α2 M4
a 3 . (11.18)
B
2m e
If the expression in the curly brackets
we obtain
n
n 0
= 1, (11.19)
̂v 0 = cα 3 ∼ = 116.5 m/s. (11.20)
The density of liquid helium. The condition (11.19) can be considered as the definition
of the density of helium atoms in the superfluid state:
n = n 0 = α2
a 3 B
√
M4
2m e
∼ = 2.172 · 10 22 atom/cm 3 . (11.21)
According to this definition, the density of liquid helium-4
γ 4 = nM 4
∼ = 0.1443 g/cm
3
(11.22)
that is in good agreement with the measured density of the liquid helium 0.145 g/cm 3 for
T ≃ T λ .
Similar calculations for liquid helium-3 gives the density 0.094 g/cm 3 , which can be
regarded as consistent with its density 0.082 g/cm 3 experimentally measured near the
boiling point.
The dielectric constant of liquid helium. To estimate the dielectric constant of helium
we can use the Clausius-Mossotti equation [56]:
ε − 1
ε + 2 = 4π nA. (11.23)
3
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