Positronium trapping at

material surfaces

Bernardo Barbiellini

Northeastern University

Boston, Massachusetts

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.

Some applications of positron annihilation

• Gamma-Ray Astrophysics• Positron Emission Tomography (PET)• Positron Annihilation Spectroscopy (PAS)

in Material Science

Positron annihilation (Compton) Feynman diagram

(space)

(time)

The positron is the electron’s antimatter partner, whichcan annihilates with an electron.

Essentially the same Feynman diagram describes the amplitude for positron annihilation and for Compton scattering.

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).

Electron Momentum Density (EMD) and positron Lifetime

p) ~ ∑n | ∫ dr e -ip .r (r) n(r) √[( r)] | 2

-1 ≈ re2 c ∫ dr dr+ (r+) (r) [( r)] r - r+)

The emitted gamma photons carry detailed information on the electron momentum distribution.

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.

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.

EMD for magnetic electrons in bilayer manganites : an example.

EMD projections: Occupation breaks & Wave-function effects are visible.

.

Calculations based on Density Functional Theory (DFT).See Li et al., Phys. Rev. Lett. 93, 207206

Positron wave function

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

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

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

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

Ps-surface interaction potential

Repulsive van der Waals z

0

z0

Saniz, B. Barbiellini, P. M. Platzman, and A. J. Freeman, PRL 99, 096101, (2007); PRL 100, 019902, (2008).

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

Ps surface states

Ground state : -0.112 eVExcited state: -0.005 eV

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

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).

Ps formation before annihilation

Gamma-ray 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.

We could use the spontaneous annihilation of the BEC, and the subsequent outburst of gamma-rays, to make a powerful laser.