Resonance scattering theory

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

A type of molecular resonance scattering can also occur from the formation of short-lived negative ions due to electron capture by molecules on surfrices. While this is frequently observed for molecules in the gas phase, it is not so important for chemisorbed molecules on metal surfaces because of extremely rapid quenching (electron transfer to the substrate) of the negative ion. Observations have been made for this scattering mechanism in several chemisorbed systems and in phys-isorbed layers, with the effects usually observed as smaU deviations of the cross section for inelastic scattering from that predicted from dipole scattering theory. 

Fig. 3. The normalized excitation functions in A2 versus collision energy for the two isotopic channels for the F+HD reaction. The solid line is the result of quantum scattering theory using the SW-PES. The QCT simulations from Ref. 71 are plotted for comparison. The experiment, shown with points, is normalized to theory by a single scaling factor for both channels. Also shown in (a) is the theoretical decomposition of the excitation function into direct and resonant contributions using the J-shifting procedure.

Blume, M., in Resonance Anomalous X-ray Scattering. Theory and Applications, G. Materlik,... 

The volume dependence of the d band width is expected from a simple approximation within resonant scattering theory (Heine (1967)) to behave as... 

A further factor which affects the shape of a resonance line is the transport of resonance radiation through the. parent gas. Milne s early theory of self-absorption by the imprisonment of resonance radiation has been revised by Holstein (3) and Bichermau (4), taking into account the incoherent scattering of resonance photons. Furthermore, Walsh (" ) has extended the imprisonment lifetime calculation for cases where Doppler and collision broadening of the resonance line are simultaneously present, and in addition this author has examined the complications caused by the, hfs. The line shape, linewidth, and other properties of self-absorbed lines hare been discussed recently bv Tako (6), who summarizes the various effects of self-absorption as follows ... 

The shape resonances have been described by Feshbach in elastic scattering cross-section for the processes of neutron capture and nuclear fission [7] in the cloudy crystal ball model of nuclear reactions. These scattering theory is dealing with configuration interaction in multi-channel processes involving states with different spatial locations. Therefore these resonances can be called also Feshbach shape resonances. These resonances are a clear well established manifestation of the non locality of quantum mechanics and appear in many fields of physics and chemistry [8,192] such as the molecular association and dissociation processes. 

Figure 14.9 Resonant Cu KL23L23 Auger spectra excited from Cu metal foil using near-threshold- and sub-threshold-energy X-ray photons [25]. The energies of the photons related to the K-absorption threshold are indicated. Dots experimental data corrected for inelastic electron scattering solid line calculated spectra using the resonant X-ray scattering theory and the DV-Xa cluster MO model.

We can apply the uncertainty principle, which is an approximate scattering theory, to a resonant state. Corresponding to the uncertainty Tr in energy it has an uncertainty Xy in time, given by... 

The time spectrum of the scattered electron in this limit has the shape g-Frf/fi jjjg lifetime of the compound electron—target system in the resonant state is Xr. We have derived the same result for a detailed scattering theory that we knew already from the uncertainty principle. The uncertainty relation (4.146) becomes an exact equality (4.167) if Tr is the full width at half maximum and Xr is the lifetime. 

While we have developed the theory of wave-packet scattering and resonances in the context of potential scattering of electrons it is easy to generalise. In particular there is no reason why the scattered particle should not be a photon. In this case the wave packet does not spread and the formalism is valid for general values of 3. Wave packets are known whose widths correspond to a lifetime of order lO s, which is easily resolved with nanosecond electronics. Such wave packets arise in the photon decay of many atomic states. The time spectrum of detected photons is given by (r,t)p for X < 0. We see from (4.166) that this involves an interference between a term whose lifetime is h/3 and one whose lifetime is Xr. The resulting time oscillations have been observed experimentally. They are called quantum beats. 

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