Width levels

The bandpass of the incoming radiation has already been considered in connection with the monochromatization of synchrotron radiation, Section 1.4, and the finite resolution of the electron spectrometer, introduced in Section 1.5 (equ. (1.49)), will be taken up again in Section 4.2.2. Therefore, only the level width rn o- and the explanation of its origin will be discussed here. Then how the three contributions, characterized by Bm, Tn/j and A sp, form the observed photoline with its width fwhmexp, by convolution procedures will be discussed. Finally, the results are applied to the quantitative analysis of the linewidth obtained for the Is photoline in neon. 

The two decay mechanisms of interest in the following discussion are radiative 

If F(E,E a), integrated over all energies E, is normalized to unit area, i.e, 

This result describes quantitatively the energy distribution of the decaying nij hole-state. The function is symmetric in E around En(j. For E = E (j it has a maximum, and its fwhm value is given by En(j which is called the natural or inherent level width because it originates from the decaying hole-state which is inherent to the atom. As an example, a compilation of level widths r in neon is given in Table 2.2. Because of the replacement made in the derivation of equ. (2.18b) for xn(, one has (in atomic units) 

With rn( only the total decay rate or, equivalently, the total level width of an inner-shell hole-state has been considered so far. In general, the system has different decay branches. In many cases these branches can be classified as radiative (fluorescence) or non-radiative (Auger or autoionizing) transitions, and even further, by specifying within each group individual decay branches to different final ionic states. (Combinations of radiative and non-radiative transitions are also possible in which a photon is emitted and simultaneously an electron is excited/ ejected. These processes are termed radiative Auger decay (see [Abe75]).) As a result, the total transition rate Pnr and, hence, the total level width is composed of sums over partial values  

---

Further, the electron level of adsorbed particles differs from that of isolated adsorbate i>articles in vacuum as shown in Fig. 5-5, this electron level of the adsorbate particle shifts in the course of adsorption by a magnitude equivalent to the adsorption energy of the particles [Gomer-Swanson, 1963]. In the illustration of Fig. 5-5, the electron level of adsorbate particles is reduced in accordance with the potential energy curve of adsorption towards its lowest level at the plane of adsorption where the level width is broadened. In the case in which the allowed electron energy level of adsorbed particles, such as elumo and ehcmio, approaches the Fermi level, ep, of the adsorbent metal, an electron transfer occurs between... 

More recently, Mies and Kraus have presented a quantum mechanical theory of the unimolecular decay of activated molecules.13 Because of the similarity between this process and autoionization they used the Fano theory of resonant scattering.2 Their theory provides a detailed description of the relationships between level widths, matrix elements coupling discrete levels to the translational continuum, and the rate of fragmentation of the molecule. 

By analogy, the energy uncertainty associated with a given state, AE, through the Heisenberg uncertainty principle can be obtained from the lifetime contributed by each decay mode. If we use the definition AE = T, the level width, then we can express F in terms of the partial widths for each decay mode T, such that... 

The half-life and the abundance (in bold face from [7]) are shown followed by their units "%" symbol in the case of abundance) which are followed by the uncertainty, in italics,in the last significant figures. For example, 8.1 s 10 means 8.1 1,0 s. For some very short-lived nuclei, level widths rather than half-lives are given, There also, the width is followed by unite e.g., eV, keV, or MeV) which are followed by the uncertainty in italics, if known, As stated above when a limit or an approximate value is given it is based on systematics (sy), mostly from [5]. A in this field indicates that T is not known, For 2p and 2e decay only the lowest value of their several limits e.g., for Ov or 2v, etc.) is given,... 

The presence of an outer open shell in an atom, even if this shell does not participate in the transitions under consideration, influences the X-ray radiation spectrum. Interaction of the vacancy with the open shell, particularly in the final state when the vacancy is not in a deep shell, splits the levels of the core. Depending on level widths and relative strength of various intra-atomic interactions, this multiplet splitting leads to broadening of diagram lines, their asymmetry, the occurrence of satellites, or splitting of the spectrum into large numbers of lines. 

At strong coupling to the leads and the finite level width the master equation approach can no longer be used, and we apply alternatively the nonequilibrium Green function technique which have been recently developed to treat vibronic effects in a perturbative or self-consistent way in the cases of weak and intermediate electron-vibron interaction [113-130]. 

Assume that a noninteracting nanosystem is coupled weakly to a thermal bath (in addition to the leads). The effect of the thermal bath is to break phase coherence of the electron inside the system during some time Tph, called decoherence or phase-breaking time. rph is an important time-scale in the theory, it should be compared with the so-called tunneling time - the characteristic time for the electron to go from the nanosystem to the lead, which can be estimated as an inverse level-width function / 1. So that the criteria of sequential tunneling is... 

Using the level-width function (below without spin polarization of the leads)... 

We should stress once more that this formula is valid for finite voltage. Therefore, the voltage dependence of the level-width functions is important. 

Table 2.2. Natural level widths in neon (see, for example, [Kra79f).

Before these partial quantities are discussed further, an important comment has to be made unlike the partial transition rates, the partial level widths have no direct physical meaning, because even for a selected decay branch it is always the total level width which determines the natural energy broadening. The partial level width is only a measure of the partial transition rate. Both aspects can be inferred from the Lorentzian distribution attached to a selected decay branch, e.g., Auger decay, which is given by... 

Figure 2.7 Theoretical level widths for K-shell ionization as a function of the atomic number. The total level width T is the sum of two contributions that come from radiative (fluorescence) decay, TR, and non-radiative (Auger) decay, TA. From [Kra79].

Figure 2.10 Neon Is photoline obtained with monochromatized A1 Ka radiation. The solid line is a fit to the experimental data given by the points. The observed fwhm value of 0.39 eV is indicated. From this value the level width T(ls) = 0.27(2) eV can be obtained (see text). For T(ls) see [SMB76] for the ionization (binding) energy see also [PNS82]. Reprinted from J. Electron Spectrosc. Relat. Phenom. 2, Gelius et al. 405 (1973) with kind permission of Elsevier Science - NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The...

Energies and natural level widths for resonance excitation Doubly-excited states in He ... 

---