Fluorescence

1
Fluorescence a key to unravel (atomic)
structure and dynamics
2

• What is a fluorescence?
• Wiki emission of light by a substance that has
  absorbed light or other electromagnetic radiation
  of a different wavelength.
• The name coined by George Gabriel Stokes in 1852
  to denote the general appearance of a solution
  of sulphate of quinine and similar media. In
  fact, the name is derived from mineral fluorite
  (CaF2), some examples of which contain traces of
  europium which serves as the fluorescent
  activator to emit blue light.
• We use word fluorescence in a more general way as
  a relaxation of the (quantum) system by photon
  emission.

Photon in
Photon out
3

• Fluorescence played important role in development
  of QM.
• 
  
• 410
  nm 434 486
  
  656 nm
• ? In 1885 Johann Balmer discovered empirical
  equation to describe the spectral line emissions
  of hydrogen atom
• lBn2/(n2-22), B346.56 nm, ngt2.
• ?In 1888 Johannes Rydberg generalized Balmer
  formula to all transitions in hydrogen atom
• 1/lR(1/m2-1/n2), R10973731.57 m-1, ngtm
• ? What about fluorescence transitions back to the
  ground state (n1)? In 1906 Theodore Lyman
  discovered the first spectral line of the series
  whose members all lie in the UV region.

4

• In 1913 Niels Bohr introduced the model of an
  atom that explained (among others) the Rydberg
  formula
• The electrons can only travel in certain
  classical orbits with certain energies En
  occuring at certain distances rn from the
  nucleus. Energy of emitted light is given as a
  difference of energies of stationary orbits
  selected by the quantization rule for angular
  momentum Ln?.
• En-Z2RE/n2
  
• rna?n2/(Zmec)
• En-Enh?
• REmec2 a2/2Rhc
• ae2/(4pe0)?c
• 1/137.035999074(44),
• Cos(p/137) Tan(p/137/29)/(29 p)
• For n1 and Z1 we have r15.29 10-11 m.
• (Bohr radius)
• and for hydrogen E8-RE-13.6 eV,
• Rydberg energy (ionization threshold)

n1
n2
n3
n4
n5
n6
Paschen, Brackett, Pfundt, Humphreys series of
lines..
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• In 1926 Schrödinger equation was formulated by
  Erwin Schrödinger. It describes how the quantum
  state of a physical system changes in time.
• Bohr stationary orbitals are described by
• wavefunctions whose spatial part is
• obtained by solving the time independent
• Schrodinger equation
• with the Coulomb potential VZe2/(4pe0r)
• Orbitals are replaced by eigenfunctions of
• Hamiltonian operator HTV and orbital
• energies with corresponding eigenenergies
• Of H. The wavefunction ? most completely
• describes a physical system.

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Ionization continuum

• Energy diagram of hydrogen atom.
• Energy levels with the same principal
• quantum number n1,2,3 and different
• orbital angular momentum l0,1,2,n-1
• are degenerate (have the same energy).
• In other atoms and also in hydrogen,
• this is not true anymore when other
• (realistic) contributions to electron
• energy are included into H
• ? Electron-electron interaction
• V12Sigtj e2/(4pe0rij)
• ? Spin-orbit interaction
• VSOSi xi li.si
• and other relativistic corrections obtained
• from relativistic version of Schrödinger
• equation (Dirac equation).

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Helium atom ? Quantum flipper
Energy
First ionization threshold _at_ 24.6 eV
Singly excited states
Photon 1 out
Photon 2 out
Photon 3 out
Photon 4 out
e-
e-
Photon in
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Spectrum
Path 1s2 1snp 1s2 is the most probable.
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1s21p
What about inserting He atom in a constant DC
electric field F and study emission processes
there?
Such kind of measurement enabled
characterization of Stark effect in He and
provided a definitive test of the QM treatment
given by Schrödinger. Ann. Phys. 80, 437, 1926
The atomic wavefunctions are changed under field
influence the new states ? are eigenstates
of a new Hamiltonian H obtained from the
field-free Hamiltonian H by adding an
electron-field interaction energy
H H - Si ezi F
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It is interesting to see how the modern theory
looks on old photographic plates

1s6l ? 1s2p
F kV/cm
l
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1s2 photon-in ? 1s6l ? 1s2p photon-out
Fixed!
Recorded at different field values
13
Simulated photographic plate new details
are seen avoided crossings effects are expected
to cause sharp variation in fluorescence yield.
To be measured !
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Doubly excited states of helium a prototype of
correlated system
States accessible by single photon absorption
from the ground state
Fluorescence decay
n1/21/2 (2snp2pns) n-1/21/2 (2snp - 2pns) n0
2pnd
Nonradiative decay
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Doubly excited states are correlated the
probability to find one electron at certain place
depends on the position of the other electron
?(1,2) ? ?(2)?(1)
X nucleus position electron position
conditional probability density
x
x
x
x
x
x
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In 1963 Madden and Colding recorded the first
photoabsorption spectrum of Helium in the region
of doubly excited states. They used synchrotron
light as a probe. Only one series was detected
at that time n. In 1992 Domke et al recorded
a high resolution photoionization spectrum of the
same region. The members of all three types of
series were seen, although with much different
intensities.
17
Although the fluorescence decay probability of
doubly excited states is relatively low in terms
of its absolute value, the fluorescence spectra
have brought to light many new details about
these states in the last 10 years. In
fluorescence the singlet lines have comparable
intensities and their profiles are not smeared
out as in photoionization spectra. Excitation of
triplet doubly excited states via spin-orbit
interaction was identified by efficient detection
of triplet metastable state 1s2s.
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What about doubly excited states in the electric
field?
For strong dc fields the first spectra are
reported in 2003 and cover the limited region
of doubly excited states. Detected He ions
formed by nonradiative decay.
Harries et al, PRL90 133002
19
The fluorescence spectra of this region are
predicted to look like this
F ? e
F II e
.but nobody has tried to measure this beautiful
spectra yet.
20
The fluorescence spectrum uncovered some even
parity doubly excited states of Helium that
cannot be excited from the ground state by one
photon absorption unless the electric field is
present. Even the lifetime of these states was
measured
3 kV/cm
F5 kV/cm, ? e
21
We turn now to X-ray fluorescence emission of
X-rays during target relaxation. How we do this
with high resolution? X-rays are emitted when
most tightly bound electrons are removed from
their orbitals and inner-shell vacancies are
created. These are subsequently filled by close
electrons and energy is released in the form of
an x-ray photon. The lines are sorted into Ka
(2p-gt1s), Kb (3p-gt1s), La (3d-gt2p), Lb (4d-gt2p),
etc, And are found at element specific energies.
PIXE technique
X-ray
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Energy dispersive detector
Wavelength dispersive detector
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Why better resolution is needed?
The natural linewidth of x-ray lines G is of the
order of 1 eV. The width is inversely
proportional to the lifetime of the core-hole
state t ? /G which is of the order of 10-15 s
1 fs.
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High resolution x-ray spectrometer (HRXRS) at J.
Stefan Institute
? Spectrometer is enclosed in the 1,6 x 1,3 x 0,3
m3 stainless steel vacuum chamber with working
pressure of 10-6 mbar.
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The spectrometer may use ion beam or photon beam
as a target probe. It is heavy, but robust for
the transportation.
26
Sulphur in different solid state compounds
Ka doublet of S is mainly shifted due to
chemical environment. The shape of Kß line
depends on the chemical environment
Kavcic et al, 2004 proton impact excitation
Spure
Na2SO4
PbS
?02474 eV
?02474 eV
?02484 eV
pseudoelastic peak
27
Argon 1s electron excitation/ionization
This is x-ray absorption Spectrum around K-edge
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Why even better experimental resolution than the
natural linewidth is useful?
La1,2 line (L3 M4,5)
Na2MoO4 (tetrahedral)

• Measurements of compounds
• with 4d-transition elements.
• On account of experimental resolution that is
  better than the natural linewidth, the resolution
  of XANES spectra can be improved.

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The resonant x-ray photon in photon out
technique (RIXS) allows to select events that
deposit only a few eV of energy deep inside the
bulk!
Lb2,15 line (L3 N4,5)
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Conclusions

• ? Observation of the total emitted photon
  yield, its angular, energy and/or temporal
  distribution, sometimes in coincidence with other
  emitted particles tells us about the structure
  and processes involved when the knowledge of QM
  is applied for interpretation.
• ? observables are sensitive to details of
  excitation, atomic structure, the local (chemical
  environment), long-range order and existence and
  speed of other relaxation channels. In some
  cases photon in photon out technique may
  improve the results of the classical approach of
  structure analysis like photoabsorption.
• ? Evidently, photon in photon out is
  extremely suitable to study targets in external
  fields.
• ? Further development of intense light
  sources like Free Electron Lasers and of more
  sensitive and efficient instrumentation will
  enhance the opportunities to obtain important new
  research results.