1. Positronium in Quartz: Surface and Bulk Bernardo Barbiellini Northeastern University Boston, Massachusetts

2. Outline Positron surface states. Why they are useful? Ps interaction with a Quartz surface: the potential calculation by first-principles. The mechanism of the Ps 2 production on the Quartz surface. A new criteria for Ps formation.

3. PAS can probe surfaces Low energy (~10ev) positron in. Implantation, thermalization, diffusion, encountering the surface Positron trapped in surface state Annihilation of surface state positron with an electron 10 -12 - 10 -11 sec 10 -10 sec

4. Experiments reveal surface states The theory for positron surface states is still in its infancy. We have recently solved the case for a quartz surface.

5. PAS a new probe for Nanoparticles CdSe nanoparticles [Eijt et al., Nat. Mat. 5, 23 (2006) ]‏ The PAS provides a powerful tool to determine the composition of the surface region of NPs.

6. PAS has confirmed the Self-healing mechanism in CdSe QDs Theory: optical gap properties explained by Se atoms outward relaxation. Cd: Blue Se: Green Puzder et al., Phys. Rev. Lett. 92, 217401 (2004).

7. Positronium formation at a surface of quartz Positrons can pair up with electrons as Ps at a surface of quartz and Ps can stick to the surface. Saniz, B. Barbiellini, P. M. Platzman, and A. J. Freeman, PRL 99, 096101, (2007); PRL 100, 019902, (2008). Michael Schirber, Phys Rev. Focus 20, story 7

8. Ps-surface interaction potential Repulsivevan der Waals z 0 z0z0 vdW constant:  Where  is Ps polarizability and  is the bulk dielectric function. z VW = z 0 Surface position

9. Bulk dielectric function  First-principles DFT for band structure: Full-potential linearized augmented plane wave (FLAPW). We deduce C=8.43 eV bohr 3

10. Charge density exponential decay at the surface z 0 =0.95 a.u. 1/l =2.06 a.u. k c = 1/l The repulsive part of the potential is given by

11. Ps surface states Ground state : -0.112 eVExcited state: -0.005 eV

12. Molecular Ps Formation Ps + Ps Ps 2 Gas phase reaction - inefficient More efficient channel on surfaces Once two positroniums are trapped on a surface, they can easily combine to form a dipositronium molecule. The mechanism is analogous to H 2 formation on dust grain surfaces in space. D.B. Cassidy and A.P. Mills Jr., Nature 449, 195 (2007).

13. Langmuir-Hishelwood reaction 2 Ps atoms bound to a surface Effective Lennard-Jones potential Collision → surface assisted recombination Desorption Energy balance: Ps 2 binding energy: E b =-0.44 eV 2×E Ps > E b => Ps + Ps → Ps 2 + E K

14. Nature of the Ps at the surface At the surface the Ps has two well defined spin states. Para-Ps (S=0) with  ~125 (ps) Ortho-Ps (S=1) with  ~10 (ns) In which conditions there is a transition from a spin mixture state with only one lifetime component to well defined spin states having two markedly different lifetimes components ? Total Spin

15. 2D-ACAR in bulk quartz These peaks are a manifestation of Ps delocalzation (Bloch wave).

16. Ps in Bulk quartz Saito & Hyodo, PRL 90, 193401 (2003) The self annihilation  parameter  can be seen as an order parameter associate to positron formation. The ortho-Ps lifetime is about 300 ps much shorter that the corresponding lifetime at the surface: important pickoff effect due to high electron density.

17. Ps wavefunction The existence coherent state catacterized parameter different from 0 could be used a criteria for Ps formation. The parameter  is connected to  the self annihilation parameter  by a trigonometric formula. 

18. Conclusion The PAS has recently provided a powerful technique to determine the composition of the surface region of nanoparticles (solar cells). We are still exploring the fascinating theory of positrons and Ps states at surfaces and in the bulk. Could the Ps formation and in particular the self- annihilation parameter  described by a coherent state?

19. Barbiellini Theory effort DFT Spectroscopy RIXS X-ray Compton Positron Annihilation Hsin Lin Ray Wang Peter Mijnarends Wael Al-SawaiSusmita Basak QMC Dan Nissenbaum Collaborators: A. Bansil and R.S. Markiewicz