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

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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 2 ), 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

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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: =B[n 2 /(n 2 -2 2 )], B=346.56 nm, n>2. In 1888 Johannes Rydberg generalized Balmer formula to all transitions in hydrogen atom: 1/ =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.

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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=nћ. E n =-Z 2 R E /n 2 r n = ћn 2 /(Zm e c) E n -E n =hν R E =m e c 2 /2=Rhc =e 2 /(4 0 )ћc =1/137.035999074(44), Cos( /137) Tan( /137/29)/(29 ) 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=1 n=2 n=3 n=4 n=5 n=6

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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 V=Ze 2 /(4 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. 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=nћ. E n =-Z 2 R E /n 2 r n = ћn 2 /(Zm e c) R E =m e c 2 /2=Rhc =e 2 /(4 0 )ћc =1/137.035999074(44), Cos( /137) Tan( /137/29)/(29 ) 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)

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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 = i>j e 2 /(4 0 r ij ) Ϟ Spin-orbit interaction V SO = i i l i.s i and other relativistic corrections obtained from relativistic version of Schrödinger equation (Dirac equation). Ionization continuum

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Photon 1 out Photon in Photon 2 out Photon 3 out Photon 4 out Helium atom =? Quantum flipper e- First ionization threshold @ 24.6 eV Singly excited states Energy

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Spectrum Path 1s 2 – 1snp – 1s 2 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 Ψ are eigenstates of a new Hamiltonian H obtained from the field-free Hamiltonian H by adding an electron-field interaction energy: H= H - i ez i F

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

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1s 2 + photon-in 1s6l 1s2p + photon-out Fixed! Recorded at different field values

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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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n + =1/2 1/2 (2snp+2pns) n - =1/2 1/2 (2snp - 2pns) n 0 = 2pnd D oubly excited states of helium – a prototype of correlated system States accessible by single photon absorption from the ground state: Fluorescence decay 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: Ψ(1,2) Ψ(2)Ψ(1) x x x x x x X nucleus position electron position conditional probability density

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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.

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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

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The fluorescence spectra of this region are predicted to look like this: ….but nobody has tried to measure this beautiful spectra yet. F F II

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F=5 kV/cm, 3 kV/cm 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:

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

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

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1s 2s 2p 1s 2s 2p Why better resolution is needed? The natural linewidth of x-ray lines is of the order of 1 eV. The width is inversely proportional to the lifetime of the core-hole state = ћ / 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 Cylindricaly bent crystal in Johansson geometry (R Rowland =50 cm) Angular range: 30 0 – 65 0 crystal refl. plane 2d[Å] energy range TlAP (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 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 1,6 x 1,3 x 0,3 m 3 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.

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Kavčič et al, 2004: proton impact excitation S pure PbS Na 2 SO 4 Kα doublet of S is mainly shifted due to chemical environment. The shape of Kβ line depends on the chemical environment ω 0 =2474 eV ω 0 =2484 eV Sulphur in different solid state compounds pseudoelastic peak

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

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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. Why even better experimental resolution than the natural linewidth is useful? L 1,2 line (L 3 – M 4,5 )

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L 2,15 line (L 3 – N 4,5 ) 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!

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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.

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