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by Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca

He: a superatom Superfluid helium Supersonic helium A surface superprobe Helium clusters Flying refrigerators From fountains to geygers Supersolid helium. by Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca. Helium: a brief biography of a superatom.

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by Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca

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  1. He: a superatom • Superfluid helium • Supersonic helium • A surface superprobe • Helium clusters • Flying refrigerators • From fountains to geygers • Supersolid helium by Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca

  2. Helium: a brief biography of a superatom - 18 Aug 1868 solar eclipse : Pierre Janssen 587.49 nm: Na? • 20 Oct 1868: Norman Lockyer same line (D3) in solar spectrum. • Proposal with Edward Frankland of a new atom: Helium! • 26 Mar 1895: William Ramsay looks for Ar in rocks but finds • something else; Lockyer and William Crookes confirm: Helium! • William F. Hillebrand (US) found it earlier but…. • later in 1895: Teodor Cleve & Abraham Langlet (Uppsala) • determine the atomic weight of He with great accuracy -1907: Ernest Rutherford & Thomas Royds prove that α rays are 4He nuclei Sir Ernest Rutherford

  3. Helium gets condensed • 1908: Heike Kamerlingh Onnes liquifies He, but attempts • to solidify He are unsuccesful • 1926: Kamerlingh’s student Willem Hendrik Keesom • succeeds in solidifying 4He at25 atm - 1938: Pyotr Leonidovich Kapitsa discovers superfluidity of 4He • 1969: Andreev & Lifshitz predict a superfluidity in solid 4He • ( supersolid) • 1972: Douglas D. Osheroff, D. M. Lee & R. C. Richardson • observe superfluidity in 3He as an effect of Cooper pairing • 2001: C. Cohen-Tannoudji et alobtain Bose-Einstein condensation in 4He*

  4. 4He: nuclear structure  Big Bang nucleosynthesis predicts an abundance of ~23% of 4He (by mass) This is due to: (a) helium-4 is very stable and most neutrons combine with protons to form 4He; (b) two 4He atoms cannot combine to form a stable atom: 8Be is unstable  Carbon can be produced within stars (triple-alpha process), thus making life possible

  5. Helium: a protected species Nearly all helium on Earth from radioactive decay (~0.0034 m3/km3/year): most helium comes from natural gas. Concentrations: • - in rocks: 8·10-9 • - in seawater: 4·10-12 • - in atmosphere: 5.2·10-6 Most helium in the Earth's atmosphere escapes into space due to its inertness and low mass. In a part of the upper atmosphere, He and other lighter gases are the most abundant elements. In 1958 John Bardeen and other influential scientists warned the Congress that all our helium would be gone by 1980. Congress reacted by spending $1 billion on a separation plant in Amarillo, Texas, and began stockpiling helium in empty gas wells.

  6. Thanks to the conservation measures, helium supplies were not exhausted by 1980. Still worldwide consumption of helium has increased by 5 to 10 % a year in the past decade. Presently it is about 100 million cubic metres, and is predicted to rise by 4 to 5 % a year. No one is claiming that we are in imminent danger of running out of helium--there should be at least 20 years supply left. However, new sources of the gas will have to be found to meet the ever-growing demand.  If not, God forbid, we may have to celebrate helium's 200th birthday in the year 2095--without any Mickey Mouse balloons.

  7. 4He vs 3He 3He: 0.000137% 4He: 99.999863% 3He hyperfine structure 3He nuclear magnetic resonance 3He spin-echo spectroscopy

  8. He: electronic structure I

  9. He: electronic structure II He*(23S) Refractive index of liquid He: 1.026 (!) Atomic radius: 0.31 Å VdW radius: 1.40 Å

  10. He: an ideal gas?  Van der Waals equation of state  Joule-Thomson effect  Thermal conductivity: 151.3·10-3W / mK (300 K)  Diffusivity in solids: ~3 times that of air; ~2/3 that of H2  Solubility in water: smaller than for any other gas

  11. He: a nobleman?  Helium in an electric glow discharge can form unstable compounds and molecular ions like HeNe, HgHe10, WHe2, He2+, He2++, HeH+, HeD+ and even He2 ….. or form otherwise a plasma  supersonic cluster beam deposition  Endohedral fullerenes (by heating under a high pressure of the gas): C60@He The neutral molecules formed are stable up to high temperatures.  If 3He is used, it can be readily observed by helium NMR spectroscopy: Fullerenes compounds, nanotubes, supramolecular compounds can be studied in this way. 3He sneaks into everywhere and tells about the electronic environment (a nobleman?)  The largest wdW cluster! 4He2 is a giant, > 50 Å wide! End of lecture 1

  12. Helium: the only substance which doesn’t freeze at absolute zero and normal pressure ordinary substances P. Kapitza (1938) Lee, Osheroff, Richardson

  13. log scale! from D. Vollhardt & P Wölfle 1990

  14. λ – line specific heat W. H. Keesom et al (1932)

  15. 4He solid vs. liquid II

  16. 4He: a quantum solid fighting against Heisenberg’s indetermination principle r0 pressure needed! in solid Helium unfavorable conditions: - attractive forces (Epot) are weak - bothm and r0 are small

  17. Classical (Maxwell-Boltzmann) statistics A B Quantum Bose-Einstein statistics A B 4He Quantum Fermi-Dirac statistics 3He A B Fermions (3He) also fight against Pauli’s esclusion principle!

  18. “Keesom and van den Ende (1930) observed quite accidentally that liquid helium II passed with very annoying ease through certain extremely small leaks which at a higher temperature were perfectly tight for liquid helium I and even for gaseous helium. ... the supersurface film H. Kamerlingh Onnes (1922) … This observation seemes to indicate an enormous drop of viscosity when liquid helium passes the λ-point.” Fritz London, Superfluids, Vol. II (John Wiley & Sons, New York 1954)

  19. a Helium fountain “At any rate the fountain effect experiments show that, in liquid helium, heat transfer and matter transfer are inseparably interconnected”. F. London, ibidem

  20. Two-fluid model of the superfluid state (L. Tisza) a normal (viscous) component with atoms having different excited-state velocities a superfluid component with all atoms having the same ground state velocity (BEC no dissipation  zero viscosity)

  21. simple ideas about Bose–Einstein condensation (BEC) density of states V,N

  22. total energy average energy per atom atom density condensation on the ground state

  23. BEC critical temperature & conditions de Broglie wavelength  2 x interatomic distance

  24. Micromégas, bien meilleur observateur que son nain, vit clairement que les atomes se parlaient … (Voltaire, Micromégas) de Broglie atoms “talk” each other if their average mean distance is smaller than their de Broglie wavelength but the boson attitudes are totally different from fermion attitudes….

  25. 3He condensation • (even L)(singlet) • = (odd L)(triplet) L = 0 S= 0 s-wave Cooper pair: unfavoured  L = 1 S = 1 p-wave Cooper pair: favoured  J = L + SJ= 0 (3P0), J = 1 (3P1), J = 2 (3P2) but spin-orbit interaction is below the mK range and can be neglected: 9-fold ~ degeneracy mixing of Sz = 1, 0,-1 states (like the ground state of ortho-H2 !) L = 2 S= 0 d-wave Cooper pair: less favoured 

  26. the superfluid phases of 3He B-phase: Balia-Werthamer state (isotropic gap (T))  = |> + 2-1/2[ |> + |>] + |> A-phase: Anderson-Brinkham-Morel “axial” state  = |> + |> anisotropic gap (k,T) = 0(T)[1 – (k·L)2]1/2 ^ ^ • a third phase (A1) is induced by a magnetic field with spin wavefunction • = |> a magnetic superfluid! End of lecture 2

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