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.

We use word fluorescence in a more general way as a relaxation of the (quantum) system by photon emission.

Photon in Photon out

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

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. (Bohr radius)

and for hydrogen E∞=-RE=-13.6 eV, Rydberg energy (ionization threshold)

Paschen, Brackett, Pfundt, Humphreys series of lines……..

n=1

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 bywavefunctions whose spatial part is obtained by solving the time independentSchrodinger equation

with the Coulomb potential V=Ze2/(4pe0r):

’’Orbitals’’ are replaced by eigenfunctions ofHamiltonian operator H=T+V and orbital energies with corresponding eigenenergies Of H. The wavefunction Ψ most completelydescribes a physical system.

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)

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. (Bohr radius)and for hydrogen E∞=-RE=-13.6 eV, Rydberg energy (ionization threshold)

Energy diagram of hydrogen atom.Energy levels with the same principalquantum number n=1,2,3… and different orbital angular momentum l=0,1,2,…n-1are 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 obtainedfrom relativistic version of Schrödinger equation (Dirac equation).

Ionization ‘’continuum’’

Photon 1 out

Photon in

Photon 2 out

Photon 3 out

Photon 4 out

Helium atom =?Quantum flipper

e- e-

First ionization threshold @ 24.6 eV

Singly excited states

Ener

gy

Spectrum

Path 1s2 – 1snp – 1s2 is the most probable.

=1s21p

What about inserting He atom in aconstant DC electric field F and studyemission processes there?

Such kind of measurement enabled characterization of Stark effect in He and provided a definitive test of the QMtreatment given by Schrödinger.Ann. Phys. 80, 437, 1926

The atomic wavefunctions are changedunder field influence – the new states Ψ ‘ are eigenstates of a new HamiltonianH’ obtained from the field-free HamiltonianH by adding an electron-field interaction energy:

H’= H - Si ezi F

l

F[kV/cm]

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

1s6l → 1s2p

1s2 + photon-in 1s6l 1s2p + photon-out

Fixed!Recorded atdifferent fieldvalues

Simulated ‘’photographic plate’’ – new details are seen – avoided crossings effectsare expected to cause sharp variation in fluorescence yield.

To be measured !

n+=1/21/2 (2snp+2pns)

n-=1/21/2 (2snp - 2pns)

n0= 2pnd

Doubly excited states of helium – a prototype of correlated system

States accessible by single photonabsorption from the ground state:

Fluorescence decay

Nonradiativedecay

Doubly excited states are correlated – the probability to find one electron at certainplace depends on the position of the other electron: Ψ(1,2) Ψ(2)Ψ(1)

xx

x

x x

x

X nucleus position electron position conditional probability density

In 1963 Madden and Colding recorded the first photoabsorption spectrum of Helium in the region ofdoubly 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 profilesare not smeared out as in photoionizationspectra.Excitation of triplet doubly excited states via spin-orbit interaction was identified by efficient detection of triplet metastable state 1s2s.

position 1

needle

photonbeam

U V photons

position 2

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 bynonradiative decay.

Harries et al, PRL90 133002

The fluorescence spectra of this region are predicted to look like this:

….but nobody has tried to measure this beautiful spectra yet.

F ∟ e

F II e

F=5 kV/cm, ∟ e

3 kV/cm

The fluorescence spectrum uncovered some even parity doubly excited states of Heliumthat 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:

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 theirorbitals and inner-shell vacancies are created. These are subsequently filled byclose 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.

X-ray

PIXE technique

q2q1

2d sinqB = Nl

target

crystal

x-ray detector

beam

l1

l2

Energy dispersive detector

Wavelength dispersive detector

1.2 1.4 1.6 1.8 2.0 2.2 2.40

2000

4000

6000

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Yie

ld [

coun

ts]

Energy [keV]

Si + 2 MeV protons

1.70 1.75 1.80 1.85 1.90

10

100

1000

10000

K

Yie

ldEnergy [keV]

K

1s

2s

2p

1s

2s

2p

Why better resolution is needed?

The natural linewidth of x-raylines G is of the order of 1 eV. The width isinversely proportional to the lifetime of thecore-hole state t= ћ /G which is of the orderof 10-15 s = 1 fs.

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] energy rangeTlAP (001) 25.900 0.55 – 0.95 keV (1.1 – 1.9 keV)Quartz (110) 8.5096 1.6 – 2.9 keV (3.2 - 5.8 keV)Si (111) 6.271 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, 16bit AD conversion,

→ 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.

0 100 200 300 400 500 600 7000

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arb

. u

nits

pixel0 100 200 300 400 500 600 700

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arb

. u

nits

pixel0 100 200 300 400 500 600 700

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nits

pixel

Kavčič et al, 2004:proton impact excitation

Spure PbS Na2SO4

Kα doublet of S is mainly shifted due to chemical environment.

The shape of Kβ line depends on the chemical environment

ω0=2474 eV ω0=2474 eV ω0=2484 eV

Sulphur in different solid state compounds

pseudoelastic peak

3220 3225 3230

3200 3210 3220 3230 32400.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

[1s3p]

D

Energy [eV]

Ar

Argon 1s electron excitation/ionization

This is x-ray absorption Spectrum around K-edge

Na2MoO4 (tetrahedral)

2284 2288 2292 2296 2300

X-ray energy [eV]

Eexc= 2525.75 eV

2284 2288 2292 2296 2300

L2

Eexc= 2535 eV

X-ray energy [eV]

L1

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.

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

La1,2 line (L3 – M4,5)

Lb2,15 line (L3 – N4,5)

The resonant x-ray photon in – photon out technique (RIXS) allows to select eventsthat deposit only a few eV of energy deep inside the bulk!

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.