Resonance levels

Wender and Hershkowitz [237] used the sensitivity of the recoil-free fraction in tungsten Mossbauer spectroscopy to deduce the effect of irradiation of tungsten compounds by Coulomb excitation of the resonance levels (2 states of I82,i84,i8 y with 6 MeV a-particles. While no effect of irradiation on the/-factors could be observed for tungsten metal in agreement with [233], a decrease of/was measured for WC, W2B, W2B5, and WO3 after irradiation. 

The method of exchange-luminescence [46, 47] is based on the phenomenon of energy transfer from the metastable levels of EEPs to the resonance levels of atoms and molecules of de-exciter. The EEP concentration in this case is evaluated by the intensity of de-exciter luminescence. This technique features sensitivity up to-10 particle/cm, but its application is limited by flow system having a high flow velocity, with which the counterdiffusion phenomenon may be neglected. Moreover, this technique permits EEP concentration to be estimated only at a fixed point of the setup, a factor that interferes much with the survey of heterogeneous processes associated with taking measurements of EEP spatial distribution. 

It is assumed that upper and lower levels are separated by a gap of AE. If the lower level is occupied by N electrons the transition probability is P = N/AE, with a maximum of P = 1, which describes fully resonating levels. The probability of resonance within the highest multiplet level is always equal to one. The transferred energy from all affected levels to the topmost level is then calculated as... 

A good starting point for discussing chemisorption is the resonant level model. The substrate metal is jellium, implying that we look at metals without d-electrons, and the adsorbate is an atom. We focus on only two electron levels of the atom. Level 1 is occupied and has ionization potential / level 2 is empty and... 

Figure A.9 A potential energy diagram of an atom chemisorbed on the model metal jellium shows the broadening of the adsorbate orbitals in the resonant level model.

When the atom comes closer to the metal surface, the electron wave functions of the atom start to feel the charge density of the metal. The result is that the levels 1 and 2 broaden into so-called resonance levels, which have a Lorentzian shape. Strictly speaking, the broadened levels are no longer atomic states, but states of the combined system of atom plus metal, although they retain much of their atomic character. Figure A.9 illustrates the formation of broadened adsorbate... 

The resonant level model readily explains the change in work function associated with chemisorption. It is well known that alkali atoms such as potassium lower the work function of the substrate, whereas electronegative atoms such as chlorine increase the work function [2,8,19]. Figure A. 10 indicates that potassium charges positively and chlorine negatively when adsorbed on jellium. Remember that the surface contribution to the work function is caused by... 

Although the resonant level model successfully explains a few general aspects of chemisorption, it has nevertheless many shortcomings. The model gives no information on the electronic structure of the chemisorption bond it does not tell where the electrons are. Such information is obtained from a more refined model, called the density functional method. We will not explain how it works but merely give the results for the adsorption of Cl and Li on jellium, reported by Lang and Williams [20]. 

H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account, the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied anti-bonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden because of the rather weak interaction with the free electron cloud of the metal. 

Obviously, chemisorption on d-metals needs a different description than chemisorption on a jellium metal. With the d-metals we must think in terms of a surface molecule with new molecular orbitals made up from d-levels of the metal and the orbitals of the adsorbate. These new levels interact with the s-band of the metal, similarly to the resonant level model. We start with the adsorption of an atom, in which only one atomic orbital is involved in chemisorption. Once the principle is clear, it is not difficult to invoke more orbitals. 

The resonance level of the sodium atom is sometimes said to be 16960 cm-1 from the fundamental level. From this value calculate the corresponding wavelength and the energy of the transition associated with it. 

Perhaps the most pertinent observation to make at this point is that the process by which the molecule with energy spectrum hypothesized decays is simply a form of predissociation. There is one difference between the process we consider and the usual case of predissociation from a single zero-order molecular energy level. Because the exact resonant level is represented as a linear combination of the zero-order localized level, the... 

It is also possible [637] to bracket the donor triplet state by the proper choice of ligand, and a selective excitation of one of the resonance levels of Eu3+ ion can be effected. The fluorescence spectra of benzoyl-acetone and dibenzoylmethide complexes of Eu3+ show transitions from... 

We have seen earlier that Eu3+ possess two resonance levels, Do mid 5Z>i, from which fluorescence transitions to the J manifold of 1F takes place. The 5Do - 7Fo transition is strictly forbidden for regular octahedral symmetry but is observed in some complexes due to the lack of centro-symmetry. The intensity of the fluorescence transition is not directly dependent only on the amount of T 4f energy transfer, but mainly on the transition probabilities from a particular resonance level to the various J manifolds. However, the transition probabilities are sensitive functions depending on the ligand. A schematic representation of the... 

Figure 4.16 Hyperspherical potentials without the adiabatic correction term (full curves) for systems of unnatural parity e+He+(Pc) (left) and e+He+(D°) (right) converging to the asymptotic limits e+ + He+(n = 5-8) and He2+ + Ps(n = 2,3). The diabatic broken curves are for the He2+ + Ps configurations only see text. The vertical positions of the symbols He+(n) and Ps(n) on the right roughly indicate the asymptotic threshold energies. The calculated resonance levels are shown by horizontal bars, some of which are unexpected from the adiabatic potentials. Adapted from Ref. [66].

The obtained resonance levels are shown in Figure 4.16 by horizontal bars. We first pay attention to the three resonances lying just below the threshold Ps(n = 3), for each symmetry. The positions Er, = — ev and widths T ... 

V.L. Lyuboshitz, On collision duration in the presence of strong overlapping resonance levels, Phys. Lett. B 72 (1977) 41. 

The voltage-current curve is now asymmetric, a large step corresponds to the resonant level with inverted population. 

Crlm heat capacity from resonant level model Taf antiferromagnetic ordering temperature ... 

Fig. 12. Total heat capacity of a single crystal of PrFe4Pi2 vs. temperature in various applied magnetic fields (a) low fields and (b) high fields. The dashed fines in (b) correspond to the best fit of the heavy fermion state to die resonant level model (Crlm)-Cph is the estimate of die phonon contribution to the heat capacity (Aoki et al., 2002).

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