Resonance state origin

Fig. 12a-c. Schematic representation of the effective potential Vejf and of different possibilities of localized and itinerant states for electrons of high 1 quantum number, a) The solid line d represents the periodic potential set-up by the cores R and R +i, which is a superimposition of central potential a dashed line). The dashed line b represents the centrifugal potential of kinetic origin 1(1 + l)/2 R in an atom, and c dashed line) the effective potential V f for an atom (compare Fig. 6) and full line) for a solid, b) Relative to two shapes of the effective potential Ve, two examples of localized state are given 1. resonant state 2. fully localized state. Notice that 1. is very near to Ep. h and t represent hopping and tunneling processes, c) A narrow band is formed (resonance band), pinning Ep 3. narrow band... 

Fig. 11. Energy diagram illustrating origin and configuration interaction of lowes exciton and charge resonance states of point group AC-...

Excimer may relax (i) by emission of characteristic structureless band shifted to about 6000 cm-1 to the red of the normal fluorescence, (ii) dissociate nonradiatively into original molecules, (iii) form a photodimer. Those systems which give rise to photodimers may not decay by excimer emission. The binoing energy for excimer formation is provided by interaction between charge transfer (CT) state A+A- A-A and charge resonance state AA s A A. 

A Fano profile was originally derived to interpret an asymmetrical spectral feature of autoionizing atoms [12], but it can also be identified in the electric spectrum of some simple molecules, which indirectly or directly dissociate. It has been known that a transition from an electronic ground state to a resonance state in the excited-state PES, formed through a mixing between zero-... 

In our original survey of the literature concerned with photoionization of benzene we inadvertently missed important contributions by J. C. Person220 and by Dibeler, Reese, and Krauss.230 Both of these studies provide evidence for an isotope effect in the photoionization of benzene, hence implying competition among the several decay channels available to the resonant state formed by photon absorption. 

In the previous sections, we introduced resonance states and discussed situations in which resonances can be observed. In this section, we address the question of the origin for the appearance of resonances, or in other words, the basic question is what can bring about the formation of metastable states. In a very general manner, it is common to classify resonances into two main groups shape-type resonances and Feshbach-type resonances. Although the classification is not unique and may depend on the chosen representation of the Hamiltonian [46, 47], it can be extremely helpful in understanding the physical mechanism that leads to the formation of the metastable state. 

Fig. 3. (a) The singlet states originating from Kekule and Dewar resonances in benzene. The marked points show the CASSCF computed values, the continuous and dashed lines corresponding to the fit with Hamiltonian of equation (14) (left side) (b) the geometry dependence of spin Hamiltonian parameters (right side). 

Irregular quantum systems, which dissociate in a statistical state-specific manner, cannot be analyzed in terms of progressions and the adiabatic picture becomes irrelevant. Nevertheless, the fluctuations have the same physical origin For each resonance state there is a unique distribution of the total excitation energy among the internal degrees of freedom and. 

For an interpretation of so-called shape-resonance state, an assumption of potential barrier surrounding the molecule was introduced. However, the origin of the potential barrier has not been clarified yet. DV-Xa calculation has also been applied to solve this problem. The theoretical and measured S and F K XANES spectra of SF molecule are compared in Fig. 15 and 16. In both cases, the agreements between theory and experiment are quite good. From the calculation, it is found that any potential barrier is not created and the excited MO states corresponding to the shape-resonance peaks are naturally generated by the molecular potential. 

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