Transcript Slide 1

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
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
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
0
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.