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

2. Helium Droplets T 0 35 K P 0 20 bar Droplets are cooled by evaporation to =0.38 K ( 4 He), =0.15 K ( 3 He) Brink and Stringari, Z. Phys. D 15, 257 (1990), 257 (1990)

3. Some Microscopic Manifestations of Superfluidity 1. Free Rotations of Molecules 2. The Roton Gap (Phonon Wing) 3. 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. 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? OCS

6. Near UV Spectrum of the S 1 S 0 Transition of Glyoxal 2.Evidence for Superfluidity in Pure 4 He Droplets: Since IR absorption lines are so sharp, what about electronic transitions?

7. The Phase Diagram and Phonons in Liquid 4 He

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

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

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

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

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

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

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

15. Bose condensed Non-condensed

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

17. Aggregation of p-H 2 molecules around an OCS molecule inside a mixed 4 He/ 3 He droplet

19. (5-6 H 2 ) (3-4 H 2 ) (5-6 H 2 ) (3 H 2 )

20. Average Moments of Inertia I a I b I c 840 1590 1590 55 1590 1590 880 2500 2500 This is the first evidence for superfluidity of p-H 2

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 he-he pot The large zero point energy also affects the dimer The large zero-point energy makes liquid Helium the most tenuous of all liquids About 10 years ago it was not known whether the He dimer had a bound state

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 SiN x 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. 0 500100015002000 56 57 58 59 60 61 62 63 64 E f f e c t i v e S l i t W i d t h s [ n m ] e f f Particle Velocity v [m/s] Effective Slit Widths vs Particle Velocity He Atom versusHe Dimer Scattering length a = 2 = 97 A C =0.12 meV nm 3 3 He 2 Grisenti, Schöllkopf, Toennies Hegerfeldt, Köhler and Stoll Phys. Rev. Lett. 85 2284 (2000) =2.5 nm S eff 2003-07-02-T1-Schr. oo V (particle-wall) = 3 3 C X - = 52.0 + E b - ~ 4m 2 2 =1.2 10 K -3. 1 10 -3 K 104 A ° =1.110 -3 K 0.4 A Grisenti; Schöllkopf, Toennies, Hegerfeldt, Köhler and Stoll, Phys. Rev. Lett. 85 2284 (2000)

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

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

35. The Kr atom can pass through the middle of the molecule without its being affected The dimer is nearly invisible: magic! trim from J. P. Toennies 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: R. Guardiola,O. Kornilov, J. Navarro and J. P. Toennies, J. Chem Phys, 2006 Cluster Number Size N

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

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

40. 26

41. 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. To explain Magic numbers recall that clusters are formed in early hot stages of the expansion from J. P. Toennies

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

43. 2006 Thermalization via evaporation (DFT)

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

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

46. one-particle states

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

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

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

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