1. Positronium trapping at material surfaces
Bernardo Barbiellini
Northeastern University
Boston, Massachusetts

2. Content
Positron annihilation spectroscopy: new way to probe the surface of nanoparticles.
New theories of positron states at surfaces.
Formation of matter-antimatter molecules at surfaces.

3. Some applications of positron annihilation
Gamma-Ray Astrophysics
Positron Emission Tomography (PET)
Positron Annihilation Spectroscopy (PAS) in Material Science

4. Positron annihilation (Compton) Feynman diagram
The positron is the electron’s antimatter partner, which
can annihilates with an electron.
(space)‏
(time)‏
Essentially the same Feynman diagram describes the amplitude for positron annihilation and for Compton scattering.

5. Compton scattering
The Compton scattering has been used to study the quantum nature of the
hydrogen bond in ice.
E.D. Isaacs et al., PRL 82, 600 (1999).

6. Electron Momentum Density (EMD) and positron Lifetime
The emitted gamma photons carry detailed information
on the electron momentum distribution.
N(p) ~ ∑n | ∫ dr e -ip .r f+(r) yn(r) √g[r-( r)] | 2
The positron lifetime typically between ~100 ps and ~0.5 ns
(in absence of positronium formation) depends sensitively
on the local electron density at the annihilation site.
t -1 ≈ p re2 c ∫ dr- dr+ r+(r+) r-(r-) g[r-( r-)] d3(r- - r+)

7. Properties of the positron
Positrons are positively charged: high sensitivity to detect and identify atomic scale defects in matter.
Positrons have a magnetic moment: easy and direct imaging of the electronic structure of magnetic materials.

8. EMD for magnetic electrons in bilayer manganites : an example.
Calculations based on Density Functional Theory (DFT).
See Li et al., Phys. Rev. Lett. 93,
EMD projections: Occupation breaks & Wave-function effects are visible. .

9. Positron wave function
This density distribution (log-scale) in bilayer manganite show that
the positron selects particular regions of the sample.

10. Positron lifetime in bulk material
The GGA theory based onDFT [Barbiellini, M. J. Puska, T. Torsti and R. M. Nieminen,Phys. Rev. B 51, 7341 (1995)] gives excellent agreement with experiment.
GGA
LDA

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

12. 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.

13. 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.

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

15. Positronium formation at a surface of quartz
Positronium (Ps) is a strange sort of atom in which an electron and a positron orbit one another without a nucleus.
Positrons can pair up with electrons as Ps
at a surface of quartz and Ps can stick
to the surface.
Michael Schirber, Phys Rev. Focus 20, story 7

16. Ps-surface interaction potential
Repulsive
van der Waals z z0
vdW constant:
Where a(w) is Ps polarizability and e(w) is the bulk dielectric function.
zVW = z0
Surface position
Saniz, B. Barbiellini, P. M. Platzman, and A. J. Freeman,
PRL 99, , (2007); PRL 100, , (2008).

17. 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).

18. 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

19. Ps surface states
Ground state : eV
Excited state: eV

20. Molecular Ps Formation
Ps + Ps Ps2
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.

21. 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

22. 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.
These results also help guide researchers who aim to assemble larger collections of Ps into quantum state called a condensate (this is an important step toward the gamma ray laser).

23. Ps formation before annihilation

24. Gamma-ray laser
We could use the spontaneous annihilation of the BEC, and the subsequent outburst
of gamma-rays, to make a powerful laser.
As a result, there is a huge interest in the technology from energy researchers who believe
the lasers could be used to kick-start nuclear fusion in a reactor.