Fluorescence – a key to unravel (atomic) structure and dynamics

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 1885Johann Balmerdiscovered 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 Rydberggeneralized 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 1906Theodore Lyman discovered the first spectral line of the series whose members all lie in the UV region.

4. In 1913Niels 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 Enoccuring 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=mec2a2/2=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) n=1 n=2 n=3 n=4 n=5 n=6 Paschen, Brackett, Pfundt, Humphreys series of lines……..

5. 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 wavefunctionΨ most completely describes a physical system. • The electrons can only travel in certain classical orbits with certain energies Enoccuring 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=mec2a2/2=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)

6. Ionization ‘’continuum’’ Energy diagram of hydrogen atom. Energy levels with the same principal quantum number n=1,2,3… and different orbitalangular 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).

7. Helium atom =? Quantum flipper Energy 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

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

9. =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 eziF

11. It is interesting to see how the modern theory looks on old photographic plates: 1s6l → 1s2p F [kV/cm] l

12. 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 !

14. Doubly excited states of helium – a prototype of correlated system States accessible by single photon absorption from the ground state: Fluorescence decay n+=1/21/2 (2snp+2pns) n-=1/21/2 (2snp - 2pns) n0= 2pnd Nonradiative decay

15. 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

16. In 1963 Madden and Coldingrecorded 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 1992Domke 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.

18. 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 F=5 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->1s), Kb (3p->1s), La (3d->2p), Lb (4d->2p), etc, And are found at element specific energies. PIXE technique X-ray

22. x-ray detector l1 target 2d sinqB = Nl l2 beam q1 q2 crystal Energy dispersive detector Wavelength dispersive detector

23. 2p 2p 2s 2s 1s 1s Why better resolution is needed? The natural linewidthof 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.

24. →Cylindricaly bent crystal in Johansson geometry (RRowland=50 cm) Angular range: 300 – 650 crystalrefl. plane2d[Å]energyrange TlAP (001)25.9000.55 – 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 cooledBI CCD camera (ANDOR DX-438-BV), chip Marconi 555-20, 770x1152 pixels, pixel size 22,5 x 22,5mm2, CCI-010controler, readout frequency 1 MHz, 16bit AD conversion, High resolution x-ray spectrometer (HRXRS) at J. Stefan Institute →Spectrometeris enclosed in the1,6 x 1,3 x 0,3 m3stainless steel vacuum chamber with working pressure of 10-6 mbar.

25. 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 Kα doublet of S is mainly shifted due to chemical environment. The shape of Kβ line depends on the chemical environment Kavčič et al, 2004: proton impact excitation Spure Na2SO4 PbS ω0=2474 eV ω0=2474 eV ω0=2484 eV pseudoelastic peak

27. Argon 1s electron excitation/ionization This is x-ray absorption Spectrum around K-edge

28. 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.

29. 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)

30. Conclusions ①Observation of the total emitted photon yield, its angular, energy and/or temporal distribution, sometimes in coincidence with other emitted particlestells us about the structure and processes involved when the knowledge of QM is applied for interpretation. ② observables are sensitiveto 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.