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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 Ps2 production on the Quartz surface.
• A new criteria for Ps formation.
PAS can probe surfacesLow 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
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
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.
PAS has confirmed the Self-healing mechanism in CdSe QDs
Theory: optical gap properties explained by Se atoms outward relaxation.
Cd: BlueSe: Green
Puzder et al. ,Phys. Rev. Lett. 92, 217401 (2004).
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
0
z0
vdW constant:
Where is Ps polarizability and is the bulk dielectric function.
zVW = z0
Surface position
Bulk dielectric function
First-principles DFT for band structure: Full-potential linearized augmented plane wave (FLAPW).
We deduce
C=8.43 eV bohr3
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
Molecular Ps FormationPs + Ps Ps2
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.
D.B. Cassidy and A.P. Mills Jr., Nature 449, 195 (2007).
Langmuir-Hishelwood reaction
•2 Ps atoms bound to a surface•Effective Lennard-Jones potential•Collision → surface assisted recombination•DesorptionEnergy balance:
Ps2 binding energy: Eb=-0.44 eV
2×EPs > Eb => Ps + Ps → Ps2 + EK
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
Ps in Bulk quartz
Saito & Hyodo,PRL 90, 193401 (2003)
The self annihilationparametercan 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 different from 0 could be used a criteria for Ps formation. The parameter is connected tothe self annihilation parameter by a trigonometric formula.
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?