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- Superconductivity,
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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and Superfluidity 11.3.2 The Estimation of Characteristic Properties of He-3 The estimation of characteristic properties of He-3. The results of similar calculations for the helium-3 properties are summarized in the Table 11.2. Table 11.2 The characteristic properties of liquid helium-3. parameter defining formula calculated value measured value The velocity of zero-point oscillations of ̂v 0 = cα 3 116.5 helium atom The density of atoms √ in liquid n 3 = M 3 α 2 2m e a 3 B m/s 1.88 · 10 22 helium-3 atom/cm 3 The density of liquid γ = M 3n 3 93.7 82.3 helium-3, g/l The dielectric constant √ ε−1 = 4π ε+2 3 α2 M 3 2m e 1.035 of liquid helium-3 The boiling temperature T boil ≃ 4 E x+y 3.27 3.19 3 k of helium-3,K The sound velocity in liquid c s = 2 ̂v 0 233 helium-3 m/s 116 Science Publishing Group

Chapter 11 Superfluidity as a Subsequence of Ordering of Zero-Point Oscillations There is a radical difference between mechanisms of transition to the superfluid state for He-3 and He-4. Superfluidity occurs if complete ordering exists in the atomic system. For superfluidity of He-3 electromagnetic interaction should order not only zero-point vibrations of atoms, but also the magnetic moments of the nuclei. It is important to note that all characteristic dimensions of this task: the amplitude of the zero-point oscillations, the atomic radius, the distance between atoms in liquid helium - all equal to the Bohr radius a B by the order of magnitude. Due to this fact, we can estimate the oscillating magnetic field, which a fluctuating electronic shell creates on “its” nucleus: H Ω ≈ e a 2 B a B Ω 0 c ≈ µ B A 3 , (11.31) where µ B = e 2m is the Bohr magneton, A ec 3 is the electric polarizability of helium-3 atom. Because the value of magnetic moments for the nuclei He-3 is approximately equal to the nuclear Bohr magneton µ nB = e 2m pc , the ordering in their system must occur below the critical temperature T c = µ n B H Ω k ≈ 10 −3 K. (11.32) This finding is in agreement with the measurement data. The fact that the nuclear moments can be arranged in parallel or antiparallel to each other is consistent with the presence of the respective phases of superfluid helium-3. Concluding this approach permits to explain the mechanism of superfluidity in liquid helium. In this way, the quantitative estimations of main parameters of the liquid helium and its transition to the superfluid state were obtained. It was established that the phenomenon of superfluidity as well as the phenomenon of superconductivity is based on the physical mechanism of the ordering of zero-point oscillations. Science Publishing Group 117

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