Resonance scattering cross sections

Figure Bl.24.13. A thin film of LaCaMn03 on an LaA103 substrate is characterized for oxygen content with 3.05 MeV helium ions. The sharp peak in the backscattering signal at chaimel 160 is due to the resonance in the scattering cross section for oxygen. The solid line is a simulation that includes the resonance scattering cross section and was obtained with RUMP [3]. Data from E B Nyeanchi, National Accelerator Centre, Fame, South Africa.

Figure Bl.24.12. Elastic cross section of helium ions scattered from oxygen atoms. The pronounced peak in the spectrum around 3.04 MeV represents the resonance scattering cross section that is often used in detection...

Figure 1.13 Resonant scattering (cross sections and phase shifts). Plot of T(E)p and of the phase shift 3( ) determined from 5(E) as a function of the energy (79). (a) V = 0, (b) V = 0.2, and (c) V = 0.8. In the three cases the width of the zero-order resonance is r = 0.8 (arbitrary units).

Futamata, M., Maruyama, Y. and Ishikawa, M. (2003) Local electric field and scattering cross section of Ag nanopartides under surface plasmon resonance by finite difference time domain method. J. Phys. Chem. B, 107, 7607-7617. 

There is some disagreement in the literature as to the value of the (4He, H) elastic scattering cross section. Values differing by almost a factor of two have been reported, as reviewed by Paszti et al. (1986). The cross section is strongly non-Rutherford, but ab initio calculations have been reported that agree well with the trend of experimental data and could be used in simulation calculations (Tirira et al., 1990). The cross section for deuterium analysis has a resonance near a 4He+ energy of 2.15 MeV, which allows enhanced sensitivity. Detailed measurements of this cross section have been reported by Besenbacher et al. (1986). In practice, rather than calculate an experiment s calibration from first principles, calibration standards are usually used hydrogen-implanted silicon standard are the norm. 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Figure 3.15 (Heeger 1969, p. 306) shows the added resistivity due to iron-group impurities in gold. The low-temperature values, for which scattering cross-sections of order a2 occur (the unitarity limit ), include Kondo scattering. At room temperature, kBT is too great for most of the electrons near E to resonate...

The advances in this field are related with the development of the theory of configuration interaction between different excitation channels in nuclear physics including quantum superposition of states corresponding to different spatial locations for interpretation of resonances in nuclear scattering cross-section [7] related with the Fano configuration interaction theory for autoionization processes in atomic physics [8],... 

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. 

Scattering cross sections for chemical reactions may exhibit structure due to resonance or due to other dynamical effects such as interference or threshold phenomena. It is useful to have techniques that can identify resonance behavior in theoretical simulations and distinguish it from other sorts of dynamics [67]. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the subpicosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

It is very difficult to experimentally obtain the values of the scattering cross section. However, it is relatively easy to obtain the intensity of given normal mode k relative to that of another mode k. A simple expression relating the relative intensities has been derived for the special conditions of harmonic oscillators, no Duschinsky rotation, no change in normal mode frequencies, and pre-resonance (short time) condition spectra. Under these conditions the relative intensities of two modes is given by... 

Resonances in half and in full collisions have exactly the same origin, namely the temporary excitation of quasi-bound states at short or intermediate distances irrespective of how the complex was created. In full collisions one is essentially interested in the asymptotic behavior of the stationary wavefunction L(.E) in the limit R —> 00, i.e., the scattering matrix S with elements Sif as defined in (2.59). The S-matrix contains all the information necessary to construct scattering cross sections for a transition from state i to state /. In the case of a narrow and isolated resonance with energy Er and width hT the Breit- Wigner expression... 

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