Lecture 5: Helium Droplets

1. Lecture 5: Helium Droplets Grebenev, Toennies & Vilesov Science 279, 2083 (1998)

2. Helium Droplets T0 ≤ 35 K P0 ≥ 20 bar Droplets are cooled by evaporation to =0.38 K (4He), =0.15 K (3He) Brink and Stringari, Z. Phys. D 15, 257 (1990) , 257 (1990)

3. Some Microscopic Manifestations of Superfluidity • Free Rotations of Molecules • The Roton Gap (Phonon Wing) • Anomalously Small Moments of Inertia How many atoms are needed for superfluidity? How will this number depend on the observed property?

4. Laser Depletion Spectroscopy

5. OCS Sharp spectral features indicate that the molecule rotates without friction The closer spacing of the lines indicates a factor 2.7 larger moment of inertia Is this a new microscopic manifestation of superfluidity?

6. 2.Evidence for Superfluidity in Pure 4He Droplets: Near UV Spectrum of the S1 S0 Transition of Glyoxal Since IR absorption lines are so sharp, what about electronic transitions?

7. The Phase Diagram and Phonons in Liquid 4He

8. The experimental sideband reflects the DOS of Elementary Excitations rotational lines

9. Two Methods Used to Produce Mixed 4He/3He Droplets Small 4He Clusters: N< 100 Large 4He Clusters: 100< N< 5000

10. Aggregation of 4He Atoms Around an OCS Molecule Inside a 3He Droplet 3He OCS surrounded by a cage of 4He

11. IR Spectra of OCS in 3He Droplets with Increasing Numbers of 4He Atoms ~ 60 He atoms are needed to restore free rotations: Number needed for superfluidity? Grebenev Toennies and Vilesov Science, 279, 2083 (1998)

12. The Appearance of a Phonon Wing Heralds the Opening up of the Roton Gap roton maxon Relative Depletion [%] Wavenumber [cm-1] According to this Criterium 90 4He Atoms are needed for Superfluidity! Pörtner, Toennies and Vilesov, in preparation

13. maxons: in both 4He and 3He rotons: in 4He only

14. Para-Hydrogen Has Long Been A Candidate for Superfluidity

15. Non-condensed Bose condensed

16. Decrease in the moment of inertia indicates superfluidity The reduced coordination In small droplets favors superfluid response cartoon H2 on OCS

17. Aggregation of p-H2 molecules around an OCS molecule inside a mixed 4He/3He droplet

19. (5-6 H2) (5-6 H2) (3-4 H2) (3 H2)

20. Average Moments of Inertia IaIb Ic 840 1590 1590 55 1590 1590 880 2500 2500 This is the first evidence for superfluidity of p-H2

21. In 1959 Migdal applied BCS theory (1957) to explain superfluidity in nuclei end of lecture 5

22. Lecture 6: Helium clusters

23. As a result it has a large zero point energy making it the most tenuous of all liquids  The large zero-point energy makes liquid Helium the most tenuous of all liquids  The large zero point energy also affects the dimer  About 10 years ago it was not known whether the He dimer had a bound state he-he pot

24. The diffraction angle is inversely prop. to N

25. Can discriminate against atoms with mass spectrometer set at mass 8 and larger from J. P. Toennies

26. Electron Microscope Picture of the SiNx Transmission Gratings Courtesy of Prof. H. Smith and Dr. Tim Savas, M. I. T.

27. from J. P. Toennies

28. At Low Source Temperatures New Diffraction Peaks Appear

29. from J. P. Toennies

30. Slit function from J. P. Toennies

32. Effective Slit Widths vs Particle Velocity He Atom versus He Dimer 64 C 3 - V (particle-wall) = 3 X 63 D S eff 3 C =0.12 meV nm =2.5 3 ] He 62 m nm n [ f f e s 61 h t d i W 60 t He i l 2 S e 59 v i t c e <R> = 52.0 + f f E 58 2 ~ E - 2 b 4m <R> 57 . -3 =1.2 10 K =1.1 10-3 K 56 o o 0 500 1000 1500 2000 Particle Velocity v [m/s] Scattering length a = 2 <R> = 97 A Grisenti, Schöllkopf, Toennies Hegerfeldt, Köhler and Stoll Phys. Rev. Lett. 85 2284 (2000) 2003-07-02-T1-Schr. 0.4 A 10-3 K 1 ° 104 A Grisenti; Schöllkopf, Toennies, Hegerfeldt, Köhler and Stoll, Phys. Rev. Lett. 85 2284 (2000)

33. The 4He dimer: the world‘s weakest bound and largest ground state molecule Since <R> is much greater than Rout the dimer is a classically forbidden molecule <R> A frail GIANT! High SR from J. P. Toennies

34. To Further Study the Dimer it is Interesting to Scatter from an Object Smaller than the Dimer: An Atom! A.Kalinin, O. Kornilov, L. Rusin, J. P. Toennies, and G. Vladimirov, Phys. Rev. Lett. 93, 163402 (2004)

35. from J. P. Toennies The Kr atom can pass through the middle of the molecule without its being affected The dimer is nearly invisible: magic! trim end of lecture 6

36. Cluster Magic Numbers

37. Recent highly accurate diffusion Monte Carlo (T=0) calculation rules out existence of magic numbers due to stabilities: Cluster Number Size N R. Guardiola,O. Kornilov, J. Navarro and J. P. Toennies, J. Chem Phys, 2006

38. Searching for Large 4He Clusters: 4HeN from J. P. Toennies He2+

39. Magic Numbers in Large 4He Clusters 2nd cl

40. 26

41. To explain Magic numbers recall that clusters are formed in early „hot“ stages of the expansion The K have sharp peaks whenever the N cluster has a new excited state. Then both Ξ and K will increase. But for the N+1 cluster both Ξ will be about the same and K will fall back. from J. P. Toennies

42. Single-particle excitation theory of evaporation and cluster stability evaporation probability Magic numbers!

43. Thermalization via evaporation (DFT) 2006

44. Binding energy per atom Barranco et al (2006)

45. Atomic radial distributions 4Hen 3Hen Barranco et al (2006)

46. one-particle states Barranco et al (2006)

47. 3He in 4Hen Barranco et al (2006)

48. 4He / 3He phase separation Barranco et al (2006)

49. Stable 4He + 3He mixed clusters Barranco et al (2006)

50. Electron bubbles in 4He droplets R 1.7 nm   0.48 dyn/cm E  0.26 eV