### Fluorescence * a key to unravel (atomic) structure and dynamics

```Fluorescence – a key to unravel
(atomic) structure and dynamics
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.
Photon in
Photon out
We use word fluorescence in a more general way as a relaxation of the
(quantum) system by photon emission.
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:
l=B[n2/(n2-22)], B=346.56 nm, n>2.
In 1888 Johannes Rydberg generalized Balmer formula to all transitions in
hydrogen atom:
1/l=R(1/m2-1/n2), R=10973731.57 m-1, n>m
 What about fluorescence transitions back to the ground state (n=1)? In
1906 Theodore Lyman discovered the first spectral line of the series whose
members all lie in the UV region.
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 L=nћ.
En=-Z2RE/n2
rn=aћn2/(Zmec)
En-En’=hν
n=1
RE=mec2 a2/2=Rhc
a=e2/(4pe0)ћc
=1/137.035999074(44),
≈Cos(p/137) Tan(p/137/29)/(29 p)
For n=1 and Z=1 we have r1=5.29 10-11 m.
and for hydrogen E∞=-RE=-13.6 eV,
Rydberg energy (ionization threshold)
Paschen, Brackett, Pfundt, Humphreys series of lines……..
n=2
n=3
n=4
n=5
n=6
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 V=Ze2/(4pe0r):
’’Orbitals’’ are replaced by eigenfunctions of
Hamiltonian operator H=T+V and orbital
energies with corresponding eigenenergies
Of H. The wavefunction Ψ most completely
describes a physical system.
Energy diagram of hydrogen atom.
Energy levels with the same principal
quantum number n=1,2,3… and different
orbital angular momentum l=0,1,2,…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:
Ϟ Electron-electron interaction
V12=Si>j e2/(4pe0rij)
Ϟ Spin-orbit interaction
VSO=Si xi li.si
and other relativistic corrections obtained
from relativistic version of Schrödinger
equation (Dirac equation).
Ionization ‘’continuum’’
First ionization threshold @ 24.6 eV
Singly excited states
Photon 1 out
Photon 2 out
Photon 3 out
Photon 4 out
e-
e-
Photon in
Energy
Helium atom =?
Quantum flipper
Spectrum
Path 1s2 – 1snp – 1s2 is the most probable.
=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
Ψ ‘ 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
It is interesting to see how the modern theory looks on old photographic plates:
1s6l → 1s2p
F
[kV/cm]
l
1s2 + photon-in  1s6l  1s2p + photon-out
Fixed!
Recorded at
different field
values
Simulated ‘’photographic plate’’ – new details are seen – avoided crossings effects
are expected to cause sharp variation in fluorescence yield.
To be measured !
Doubly excited states of helium – a prototype of correlated system
States accessible by single photon
absorption from the ground state:
Fluorescence +
1/2 (2snp+2pns)
n
=1/2
decay
decay
n-=1/21/2 (2snp - 2pns)
n0= 2pnd
Doubly excited states are correlated – the probability to find one electron at certain
place depends on the position of the other electron: Ψ(1,2)  Ψ(2)Ψ(1)
X nucleus position
electron position
x
x
x
x
x
x
conditional probability density
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.
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.
p o sitio n 1
p o sitio n 2
U V p h o to n s
n e e d le
p h o to n
beam
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
Harries et al, PRL90 133002
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.
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
F=5 kV/cm, ∟ e
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->1s), Kb (3p->1s), La (3d->2p), Lb (4d->2p), etc,
And are found at element specific energies.
PIXE technique
X-ray
Energy dispersive detector
x-ray detector
Wavelength dispersive detector
l1
target
l2
2d sinqB = Nl
beam
q1
q2
crystal
Why better resolution is needed?
12000
Ka
Si + 2 MeV protons
10000
8000
Yield
Yield [counts]
10000
6000
4000
1000
Kb
100
2000
0
1.2
10
1.4
1.6
1.8
2.0
2.2
2.4
1.70
1.75
Energy [keV]
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= ћ /G which is of the order
of 10-15 s = 1 fs.
1.80
1.85
1.90
Energy [keV]
2p
2p
2s
2s
1s
1s
High resolution x-ray spectrometer (HRXRS) at J. Stefan Institute
→ Cylindricaly bent crystal in Johansson geometry (RRowland =50 cm)
Angular range: 300 – 650
crystal
refl. plane
2d[Å]
TlAP
(001)
25.900
Quartz
(110)
8.5096
Si
(111)
6.271
energy range
0.55 – 0.95 keV (1.1 – 1.9 keV)
1.6 – 2.9 keV (3.2 - 5.8 keV)
2.2 – 4.0 keV
→ Diffracted photons are detected by the CCD camera (pixel size 22.5 x 22.5 mm2 )
Thermoelectricaly cooled BI CCD camera (ANDOR DX-438-BV), chip Marconi 555-20,
770x1152 pixels, pixel size 22,5 x 22,5 mm2, CCI-010 controler, readout frequency 1 MHz,
→ 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.
The spectrometer may use ion beam or photon beam as a target probe.
It is heavy, but robust for the transportation.
Sulphur in different solid state compounds
Kα doublet of S is mainly shifted due to
chemical environment.
Kavčič et al, 2004:
proton impact excitation
The shape of Kβ line depends on the
chemical environment
Spure
ω0=2474 eV
Na2SO4
PbS
3000
6000
ω0=2474 eV
ω0=2484 eV
4000
arb. units
2000
pseudoelastic
peak
arb. units
arb. units
2000
1000
2000
1000
0
0
0
100
200
300
400
pixel
500
600
700
0
0
100
200
300
400
pixel
500
600
700
0
100
200
300
400
pixel
500
600
700
Argon 1s electron excitation/ionization
3.5
Ar
[1s3p]
3.0
2.5
D
2.0
3220
3225
3230
1.5
1.0
This is x-ray absorption
Spectrum around K-edge
0.5
0.0
3200
3210
3220
Energy [eV]
3230
3240
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.
Eexc= 2525.75 eV
La1
Eexc= 2535 eV
La2
2284
2288
2292
X-ray energy [eV]
2296
2300
2284
2288
2292
X-ray energy [eV]
2296
2300
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)
Conclusions
① 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.
② 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.
③ Evidently, photon in – photon out is extremely suitable to study targets in
external fields.
④ 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.
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