Positronium in Quartz Surface and Bulk Bernardo Barbiellini
Positronium in Quartz: Surface and Bulk Bernardo Barbiellini Northeastern University Boston, Massachusetts
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.
PAS can probe surfaces Low energy (~10 ev) 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
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.
PAS a new probe for Nanoparticles Cd. Se 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.
PAS has confirmed the Self-healing mechanism in Cd. Se QDs Cd: Blue Se: Green Puzder et al. , Phys. Rev. Lett. 92, 217401 (2004). Theory: optical gap properties explained by Se atoms outward relaxation.
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
Ps-surface interaction potential Repulsive van der Waals z z 0 0 vd. W constant: Where a(w) is Ps polarizability and e(w) is the bulk dielectric function. z. VW = z 0 Surface position
Bulk dielectric function e(w) We deduce C=8. 43 e. V bohr 3 First-principles DFT for band structure: Full-potential linearized augmented plane wave (FLAPW).
Charge density exponential decay at the surface z 0=0. 95 a. u. 1/l =2. 06 a. u. kc= 1/l The repulsive part of the potential is given by
Ps surface states Ground state : -0. 112 e. V Excited state: -0. 005 e. V
Molecular Ps Formation Ps + Ps Ps 2 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 H 2 formation on dust grain surfaces in space.
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: Eb=-0. 44 e. V 2×EPs > Eb => Ps + Ps → Ps 2 + EK
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
2 D-ACAR in bulk quartz These peaks are a manifestation of Ps delocalzation (Bloch wave).
Ps in Bulk quartz Saito & Hyodo, PRL 90, 193401 (2003) The self annihilation parameter 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.
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 to the self annihilation parameter k by a trigonometric formula. k
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 selfannihilation parameter k described by a coherent state?
Barbiellini Theory effort DFT QMC Hsin Lin Ray Wang Dan Nissenbaum Spectroscopy RIXS Wael Al-Sawai X-ray Compton Susmita Basak Collaborators: A. Bansil and R. S. Markiewicz Positron Annihilation Peter Mijnarends
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