Positronium trapping at material surfaces

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Positronium trapping at material surfaces

• Bernardo Barbiellini
• Northeastern University
• Boston, Massachusetts

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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.

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Some applications of positron annihilation

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

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Positron annihilation (Compton) Feynman diagram
The positron is the electrons 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.
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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).
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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) vgr-(
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-) gr-(
r-) d3(r- - r)
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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.

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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. .
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Positron wave function
This density distribution (log-scale) in bilayer
manganite show that the positron selects
particular regions of the sample.
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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
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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
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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.
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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.
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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.
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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
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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).
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Bulk dielectric function e(w)
We deduce C8.43 eV bohr3
First-principles DFT for band structure
Full-potential linearized augmented plane wave
(FLAPW).
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Charge density exponential decay at the surface
z00.95 a.u. 1/l 2.06 a.u. kc 1/l
The repulsive part of the potential is given by
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Ps surface states
Ground state -0.112 eV
Excited state -0.005 eV
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Molecular Ps Formation
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.
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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

• 2EPs gt Eb gt Ps Ps ? Ps2 EK

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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).

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Ps formation before annihilation
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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.