Coulomb potentials electron emission

Here the quantity U is an effective potential that contains three contributions the kinetic energy for the radial movement of the electrons (in the coordinate a), a centrifugal potential energy, and the Coulomb potential energy — C(a, 12)/R of the system. In the present context of double photoionization it is this Coulomb energy which determines the features of two-electron emission (in atomic units) ... 

Exotic atoms are produced by stopping a beam of negatively charged particles like muons, pions, or antiprotons in a target, where they are captured in the Coulomb potential of the atoms at high principal quantum numbers n. These systems deexcite mainly by fast Auger emission of electrons in the upper part of the atomic cascade and more and more by X-radiation for lower-lying states. 

Shakeup represents a fundamental many-body effect that takes place in optical transitions in many-electron systems. In such systems, an absorption or emission of light is accompanied by electronic excitations in the final state of the transition. The most notable shakeup effect is the Anderson orthogonality catastrophe [5] in the electron gas when the initial and final states of the transition have very small overlap due to the readjustment of the Fermi sea electrons in order to screen the Coulomb potential of pho-toexcited core hole. Shakeup is especially efficient when the optical hole is immobilized, and therefore it was widely studied in conjunction with the Fermi edge singularity (FES) in metals [6-8] and doped semiconductor quantum wells [9-15]. Comprehensive reviews of FES and related issues can be found in Refs. [16,17]. 

It is known (Chap. A) that Koopmans theorem is not vahd for the wavefunctions and eigenvalues of strongly bound states in an atom or in the cores of a solid, i.e. for those states which are a solution of the Schrodinger (or Dirac) equation in a central potential. In them the ejection (or the emission) of one-electron in the electron system means a strong change in Coulomb and exchange interactions, with the consequent modification of the energy scheme as well as of the electronic wavefunction, in contradiction to Koopmans theorem. 

Because of its lower electron affinity, Te sites trap holes which can then coulombically bind an electron in or near the conduction band to form an exciton. Subsequent radiative collapse of this exciton leads to emission (10,11,12,13). In the context of the PEC, emission thus serves as a probe of electron-hole (e -h" ) pair recombination which competes with e - h+ pair separation leading to photocurrent. Except for intensity, the emitted spectral distribution is found to be independent of the presence and/or composition of polychalcogenide electrolyte, excitation wavelength (Ar ion laser lines, 457.9-514.5 nm) and intensity (<30 mW/cnZ), and applied potential (-0.3V vs. SCE to open circuit) (6,1,8,9). 

Figure 2. Thermodynamic cycles for evaluating the free energy changes AG°et associated with the intramolecular photoinduced electron transfer processes in system 13 in its oxidized (a) and reduced (b) form. The quantity, the spectroscopic energy, is obtained from the emission spectrum the E values, electrode potentials associated with the given redox change, can be determined through voltammetry experiments. The Coulombic term (e /er) has been considered negligible under the present circumstances.

The BSFs in GaN do not introduce localized states in the band gap, but can be considered as a thin zinc-blend (ZB) layer embedded in the wurtzite (W) matrix. The theory predicts that this polytypic QW has a type 11 band alignment with a conduction band offset of about 270 meV [55]. The D1 emission can be described as a recombination of electrons confined in the ZB region with holes residing in the W barrier. At low temperatures, the holes are expected to be localized in a triangular potential notch formed in the barrier because of the discontinuity of the spontaneous polarization across the ZB-W interface [55]. Thus, the emission occurs between separately localized but closely spaced electrons and holes. At higher temperatures, the holes become delocalized and the emission is attributed to a recombination between electrons still localized in ZB QW and holes are attracted to them by Coulomb interaction. This... 

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