The Dancing Wu Li Masters. Gary Zukav.
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Physics of Atoms and Molecules. Cynthia C. Dreams Of A Final Theory. Steven Weinberg. Franco Strocchi. Water: A Very Short Introduction. John Finney. Nuclear Physics. John Lilley. Frank Close. Atoms in the Family. Laura Fermi. David Chapple. Richard Rhodes. Your review has been submitted successfully. Experiment and theory evidence a new pathway for correlated two-electron release from many-body compounds following collective excitation by a single photon. Results from a full ab initio implementation for C 60 fullerene are in line with experimental observations. The findings endorse the correlated two-electron photoemission as a powerful tool to access electronic correlation in complex systems.
A sample absorbing a single ultraviolet photon may emit a single electron having energy and momentum distributions that reflect the spectral properties of the material 1. It is also possible, though usually less probable, that two electrons escape. For few-electron atoms, it is established 2 that the Coulomb repulsion plays a key role. A possible scenario is that the photon is absorbed by one bound electron that approaches the other electron while undergoing multiple scattering from the residual ion or the other electron.
Springer Series on Atomic, Optical, and Plasma Physics | James Babb | Springer
Mediated by electron-electron Coulomb interaction, the two electrons exchange momentum while leaving the sample and interacting mutually and with the residual ion, in principle to infinite distances. This physical picture, often referred to as knock-out mechanism, dominates for photon energies close to double ionization threshold, whereas for larger photon energies different processes e. When detecting the two electrons in coincidence called double photoemission DPE spectroscopy 4 , 5 , 6 , depending on the selected energies and angles, one may zoom into some of these processes, albeit with restrictions imposed by symmetry 2 , 7.
The situation changes with a growing number of electrons in the system. The effective electron-electron interaction is not even known a priori as it is determined by the dynamic behavior of its active surrounding, meaning that the e—e interaction builds up during the photoexcitation process. Thereby, dimensionality is a key factor 8. In fact, for electronic systems strongly confined to one dimension e. As DPE experiments are available for weakly and moderately correlated surfaces and bulk materials e.
A possible scenario of DPE is that the photon excites one electron which senses its environment for accessible scattering channels elastic, phononic, magnonic, etc.
DPE at a fixed incident photon energy via the selection of the energy sharing and relative angles between the two escaping electrons zooms into those channels, where electron-electron e—e interaction is operational. The focus here is on e—e interaction mediated by charge density fluctuations in confined geometry. On the other hand, electronic correlations are at the heart of diverse fundamental phenomena such as superconductivity and plasmon formation which underlines the relevance of the information encoded in the DPE spectra.
Theoretically, the treatment of two-particle correlations is a central problem in many-body physics 13 , 14 , 15 , For the electron gas in particular, focus was put on two aspects affecting the two-particle interaction. Exploiting the tunability of synchrotron radiation, DPE cf. Charge-density fluctuations play the key role for the correlation hereby.
The latter is compared to our calculations of the joint density of states JDOS shaded blue line. A standard single photoemission SPE theory usually relies on the hole spectral density, which accommodates so-called intrinsic energy losses, and the optical matrix elements. Plasmon-mediated processes are typical for extrinsic losses. These refer to all scattering events which the photoelectron undergoes before detection Formulating a theory for SPE valid for all types of electronic systems, proved to be an involved task. The perturbation theory for the transition dipole, as employed for atoms or molecules 25 is in principle able to incorporate both electron-electron scattering processes and also collective effects One may also attempt at a direct diagrammatic expansion of the observable photocurrent, as was put forward in ref.
A formal theory of DPE entails the use of many-body perturbation theory MBPT for two-particle propagators 15 and is thus even more involved. Based on the direct diagrammatic approach for the observable coincidence yield 28 we present here the first fully ab initio implementation for DPE accompanied by charge density fluctuations and compare with the first experiments of this kind on C Our approach is applicable to complex atoms such as Xe possessing strong collective resonances 29 , as well. The emerging physical picture is illustrated in Fig. It is already clear at this stage that DPE is qualitatively different from SPE in that, a it delivers information on e—e interaction mediated by charge-density fluctuations, and b as these plasmonic excitations are triggered by an electron a multitude of modes, e.
In Fig. The Auger process, which one might expect to be comparable to DPE when plotting as a function of the binding energy, can be interpreted in terms of the joint density of states JDOS as determined by the convolution of the density of occupied states of the neutral system, , and that of the ionized molecule, ,.
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Our ab initio calculations in Fig. For plasmon-mediated DPE the situation is different. As inferred from Fig. Which mode is active and what is its multipolar nature is set by the momentum balance that in turn points to the momentum region of the involved plasmons. The full ab initio calculations of multipolar plasmons in C 60 in ref. The electron pair coincidence yield is calculated following the derivation in the supplementary information.
From Fig. As expected from the scheme in Fig. We write the effective e-e interaction in the form. The Lehmann representation of the response function is expressible as. The static part in eq. The two-electron coincidence yield, averaged over the initial orientations of C 60 , reads.
Here, is the partial single-ionization cross section for a photoelectron with energy. The momenta of the two photoelectrons are denoted by k 1 and k 2. The sum over n runs over all occupied states of the singly ionized molecule and is the corresponding spectral function. Inspecting eq. Overall energy conservation follows from the restrictions i , ii , and iii. The equal energy-sharing case has been chosen by the experience on atoms, where this represents the case where the effects of the correlation and symmetry play a dominant role. Further tests see supplementary information show that, in contrast to the Auger process [ Fig.
Curves have been normalized to each others at one point. Coincidence yield resolved with respect to plasmon modes d , and multipolarity e. In particular, the plasmon giving rise to the emission of the second electron at stage iii needs to provide sufficient energy to promote a certain initial state of the molecule [ Fig.
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This confirms the picture outlined above. Our theory permits also to selectively include different plasmonic modes in the calculation. On the contrary, the electron scattering as in EELS transfers a finite momentum meaning that SS and AS plasmons with any multipolarity can be excited 30 , 33 , In agreement with this Fig.
Similarly, SS dipolar plasmon transitions play only a minor role, while the multipolar plasmons are responsible to a large extent for the coincidence yield [ Fig. All these facets endorse that DPE mediated by charge-density fluctuations as the predominant channel for e-e correlations represents a new facet to the information what is extractable from SPE and Auger spectra. To summarize, an ab initio scheme for this process has been implemented with results in line with the first DPE experiment resolved with respect to the electron pair energies. We identified the dominant pathway as the following: a valence electron absorbs the photon and rescatters inelastically from multipolar collective modes that mediate the coherent emission of a second electron.
The dwell time for this quasi-resonant scattering may be accessed by attosecond time-delay experiments For plasmon-assisted DPE the average electronic density plays a decisive role. For metals the plasmonic energies which can be estimated using a classical expression with r s being the Wigner-Seitz radius are too low for plasmons to lead to a direct electron emission, although these modes may likely contribute to the loss channel for DPE. Thus, energy- and angle resolved DPE experiments open the opportunity to explore different regimes of electronic correlation, including Coulombic scattering, local field effects and dynamical screening.
The larger turntable rotates in the same plane and its seven analyzers can be used to measure the angular distribution of the correlated electrons.
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At variance with previous works 44 , 45 , 46 where the di-cation yield was measured versus photon energy, here the energy spectrum of the C 60 di-cation states is reconstructed by detection of photoelectron-photoelectron pairs in coincidence as the photon energy is scanned. In order to improve the statistical accuracy of the experimental results, the coincidence signals were added up, after a careful energy calibration of the non-coincidence spectra independently collected by the ten analyzers.
The C 60 source is collinear with the photon beam 47 , which passes through the hollow core of the source before interacting with the molecular beam and ending up on the photodiode. Six apertures drilled into the closure piece of the crucible and pointing to the interaction region increase the molecule density therein. The full derivation is presented in the supplementary information.
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