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 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.

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 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+)

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. Calculations based on Density Functional Theory (DFT). See Li et al., Phys. Rev. Lett. 93, 207206 EMD projections: Occupation breaks & Wave-function effects are visible. .

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 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

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

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 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, 096101, (2007); PRL 100, 019902, (2008).

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).

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 eV Excited state: -0.005 eV

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.

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

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 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.