## 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 (CaF blue light.

2 ), some examples of which contain traces of europium which serves as the fluorescent activator to emit 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  spectral line emissions of hydrogen atom: l In 1885 =B[n 2 /(n 2 Johann Balmer 2 2 discovered empirical equation to describe the )], B=346.56 nm, n>2.

 In 1888 Johannes Rydberg hydrogen atom: generalized Balmer formula to all transitions in 1/ l = R (1/m 2 -1/n 2 ), 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 E n occuring at certain distances r n 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=n

ћ

.

E n =-Z 2 R E /n 2 r n = a ћn 2 /(Zm e c) E n -E n’ =hν n=1 R E =m e c 2 a 2 /2=Rhc a =e 2 /(4 pe 0 )ћc =1/137.035999074(44), ≈Cos( p /137) Tan( p /137/29)/(29 p ) n=2 n=3 For n=1 and Z=1 we have r 1 =5.29 10 -11 m. (Bohr radius) and for hydrogen E ∞ =-R E =-13.6 eV, Rydberg energy (ionization threshold) Paschen, Brackett, Pfundt, Humphreys series of lines……..

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=Ze 2 /(4 pe 0 r): ’’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

V 12 = S i>j e 2 /(4 pe 0 r ij )

Ϟ Spin-orbit interaction

V SO = S i x i

l

i .s i and other relativistic corrections obtained from relativistic version of Schrödinger equation ( Dirac equation ).

Ionization ‘’continuum’’

Singly excited states

Photon 1 out Photon 2 out Photon 3 out Photon 4 out

## Quantum flipper

First ionization threshold @ 24.6 eV

e e Photon in

Spectrum Path 1s 2 – 1snp – 1s 2 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

S

i

i

### F

It is interesting to see how the modern theory looks on old photographic plates:

l

2

## 1s2p + photon-out

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 !

D oubly excited states of helium – a prototype of correlated system

States accessible by single photon absorption from the ground state:

n + =1/2 1/2 (2snp+2pns) n =1/2 1/2 2pns) (2snp n 0 = 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 conditional probability density x x x x x x

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. position 1 position 2 UV photons needle photon 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 – electric field is present. Even the

of these states was measured:

unless the

F=5 kV/cm, ∟ e 3 kV/cm

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 K a (2p->1s), K b (3p->1s), L a And are found at element specific energies. (3d->2p), L b (4d->2p), etc, PIXE technique

X-ray

Energy dispersive detector Wavelength dispersive detector target beam q 1 2d sin q B = N l x-ray detector l 1 l 2 crystal q 2

Why better resolution is needed?

1s 12000 10000 8000 6000 4000 2000 Si + 2 MeV protons 10000 1000 100 0 1.2

1.4

1.6

1.8

Energy [keV] 2.0

2.2

2.4

The

natural linewidth

of x-ray lines G is of the order of 1 eV. The width is inversely proportional to the core-hole state t = ћ / G

of the which is of the order of 10 -15 s = 1 fs. 10 1.70

K

a 1.75

1.80

Energy [keV] 2p 2s

K

b 1.85

2p 2s 1s 1.90

### High resolution x-ray spectrometer (HRXRS) at J. Stefan Institute

→ Cylindricaly bent crystal in Johansson geometry (R Rowland Angular range:

30 0 – 65 0

crystal refl. plane 2d[Å] energy range

TlAP Quartz Si (001) (110) (111)

=50 cm)

25.900

0.55 – 0.95 keV (1.1 – 1.9 keV) 8.5096 1.6 – 2.9 keV (3.2 - 5.8 keV) 6.271

2.2 – 4.0 keV

→ Diffracted photons are detected by the CCD camera (pixel size 22.5 x 22.5 mm 2 ) Thermoelectricaly cooled BI CCD camera (ANDOR DX-438-BV), chip Marconi 555-20, 770x1152 pixels, pixel size 22,5 x 22,5 mm 2 , CCI-010 controler, readout frequency 1 MHz, 16bit AD conversion, → Spectrometer is enclosed in the chamber 1,6 x 1,3 x 0,3 m 3 with working pressure of 10 -6 mbar.

stainless steel vacuum

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

Kavčič et al, 2004: proton impact excitation Kα doublet of S is mainly shifted due to chemical environment.

The shape of Kβ line depends on the chemical environment 2000 1000 pseudoelastic peak S pure ω 0 =2474 eV 3000 2000 1000 0 0 100 200 300 400 pixel 500 600 700 PbS ω 0 =2474 eV 0 0 100 200 300 400 pixel 500 600 700 6000 4000 2000 Na 2 SO 4 ω 0 =2484 eV 0 0 100 200 300 400 pixel 500 600 700

Argon 1s electron excitation/ionization

3.5

Ar [1s3p]

3.0

2.5

2.0

1.5

3220 3225 3230

1.0

0.5

0.0

3200 This is x-ray absorption Spectrum around K-edge 3210 3220 Energy [eV] 3230 3240

Why even better experimental resolution than the natural linewidth is useful?

L a 1,2 line (L 3 – M 4,5 )

Na 2 MoO 4 (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 Eexc= 2535 eV L a 2 L a 1 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!

L b 2,15 line (L 3 – N 4,5 )

## 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.