Photoemission matrix element

F. Pforte, A. Gerlach, A. Goldmann, R. Matzdorf, J. Braun, A. Postnikov, Wave-vector-dependent symmetry analysis of a photoemission matrix element the quasi-one-dimensional model system Cu(110)(2 x 1)0. Phys. Rev. B 63(16), 165405 (2001)... 

In order to understand how photoemission spectra relate to the electronic band structure and elementary excitation spectra of surfaces, we need to return to the discussion of the photoemission matrix element (Section 3.2.2.1.3) and of what is different when valence electronic states are involved. These states are characterized... 

The two processes that contribute to the photoemission current are the direct emission from the adsorbate orbital into a plane wave final state /) and the indirect emission from the adatom orbital via backscattering from the substrate lattice. Formally both effects are taken into account by replacing the matrix element of Eq. (14) by... 

Synchrotron-radiation and x-ray photoemission studies of the valence states of condensed phase-pure Cm showed seventeen distinct molecular features extending 23 cV below the highest occupied molecular states with intensity variations due to matrix-element effects involving both cluster and free-electron-like final states. Pseudopotential calculations established the origin of these features, and comparison with experiment was excellent. The sharp C Is main line indicated a single species, and the nine satellite structures were due to shakeup and plasmon features. The 1.9-eV feature reflected transitions to the lowest unoccupied molecular level of the excited state. 

The XPS measurements included observations of N and S core level shifts which yielded values for the number of charged-transferred electrons of about 0.4. This is compared with our recent XPS data on a related compound, Se N., yielding a charge transfer of 0.3 e only. One of the major observations from both XPS and UPS was that of low photoemissive yields near the Fermi level. Our calculations of the photoemissive response tensor, D (E,hv), show that this low yield near Ep is primarily a result of dipole matrix element energy dependence. 

The various forms of photoelectron spectroscopy presently available permit a straightforward determination of occupied and unoccupied surface states. The most comprehensive and authoritative collection of reviews is in the book edited by Feuerbacher et al. [44], while Ertl and Kiippers [15] also provide useful information. Here, we will only attempt to summarize how the principal versions of the technique can be used in the determination of surface electronic structure. In this context the crucial factor is that photoemission spectra represent a direct manifestation of the initial and final density of states of the emitting system. Because selection rules (matrix element effects) can be involved in the transition, the state densities may not always correspond to those derived from the band structure, but in practice there is frequently a rather close correspondence. 

In the following it will be reported on a straightforward method to provide information about the dipole matrix elements and phase shifts being essential for the theoretical description of the photoemission process in a relatively simple way and with a pronounced accuracy [2]. This can be achieved by means of photoelectron spectroscopy with linearly polarized light using the ability of a continuous rotation of the electric field vector. The method is exemplarily demonstrated at the system hydrogen on Gd(0001)/W(l 10) which possesses a pronounced adsorbate induced state. 

In the case of valence band photoemission, the atomic model cannot directly be applied to the numerical estimation of the effect, but rather for a qualitative consideration only. For valence bands, the initial state is no longer described by a single spinor spherical harmonic as it was done in [32] but it can be expanded for a certain k value in a series of spherical harmonics [44] due to their completeness. This procedure will influence the values of the state multipoles and the dipole matrix elements in Eq. 5.6, but the general Eqs. 5.5 and 5.7 will remain unchanged. In particular, they should correcdy describe the dependence of MDAD on the angle of photon incidence. 

In this context it is noted that Kildal [2] proposed the energy spectrum of the conduction electrons in non-linear optical materials under the assumptions of isotropic momentum matrix element and isotropic spin-orbit splitting, respectively, although the anisotropies of the aforementioned band parameters are the significant physical features of this compound. Besides, III-V optoelectronic compounds find extensive application in distributed feedback lasers and infrared photodetectors. In what follows, we study the photoemission in quantum confined CdGeAs2 on the basis of a newly formulated electron... 

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