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Positronium in Quartz: Surface and Bulk

Bernardo Barbiellini Northeastern University Boston, Massachusetts. Positronium in Quartz: Surface and Bulk. Outline. Positron surface states. Why they are useful? Ps interaction with a Quartz surface: the potential calculation by first-principles.

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Positronium in Quartz: Surface and Bulk

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

  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 Ps2 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 10-12 - 10-11 sec Positron trapped in surface state 10-10 sec Annihilation of surface state positron with an electron

  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 Puzder et al. , Phys. Rev. Lett. 92, 217401 (2004). Cd: Blue Se: Green Theory: optical gap properties explained by Se atoms outward relaxation.

  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 Repulsive van der Waals z z0 0 vdW constant: zVW = z0 Surface position Where a(w)is Ps polarizability and e(w) is the bulk dielectric function.

  9. Bulk dielectric function e(w) We deduce C=8.43 eV bohr3 First-principles DFT for band structure: Full-potential linearized augmented plane wave (FLAPW).

  10. Charge density exponential decay at the surface z0=0.95 a.u. 1/l =2.06 a.u. kc= 1/l The repulsive part of the potential is given by

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

  12. Ps + Ps Ps2 Molecular Ps Formation D.B. Cassidy and A.P. Mills Jr., Nature 449, 195 (2007). 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 H2 formation on dust grain surfaces in space.

  13. Langmuir-Hishelwood reaction • 2 Ps atoms bound to a surface • Effective Lennard-Jones potential • Collision → surface assisted recombination • Desorption Energy balance: Ps2 binding energy: Eb=-0.44 eV 2×EPs > Eb => Ps + Ps → Ps2 + EK

  14. Nature of the Ps at the surface • At the surface the Ps has two well defined spin states. • Para-Ps (S=0) with t~125 (ps) • Ortho-Ps (S=1) with t~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 annihilationparameter k 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 l different from 0 could be used a criteria for Ps formation. The parameter l is connected tothe self annihilation parameter k by a trigonometric formula. k

  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 k described by a coherent state?

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

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