Resonance cross section

The detected yield is a function of the concentration of the element being profiled, the resonance cross section, the detector efficiency, and dE/dx. To be specific. 

Mossbauer nuclei per square centimetre, the Debye-Waller factor/a of the absorber material, and the resonance cross-section Gq of the Mossbauer isotope. For a multiline spectrum, the result must be split into separate values for each line, which are obtained by weighting t with the relative transition probability of each line. 

N. Moiseyev, Israel J. Chem., 31, 311 (1991). Resonances, Cross Sections and Partial Widths... 

Figure 4.1 Fano profile of resonance cross sections normalized by the maximum cross section. The shape parameter q = — cotSb is assumed to be a constant independent of energy E. In actual processes, its dependence on E can alter the profile significantly. The background phase shift 8b is indicated in the parentheses below each value of q.

The approach we follow here is based on a many-body theory of reactive scattering (1 ). Other approaches have been reviewed in the literature (14). For example, several of the available results on resonances have been obtained in wave-mechanical approaches that propagate and match wavefunctlons (15.16) or expand them in functions of suitable coordinates (17). Another approach which promises to provide accurate resonance cross sections is that of channel-coupling-array equations, also recently reviewed (18). The Feshbach theory of resonances has also been recently applied to molecular reactions (19. ). 

Fig. 1. Dependence of total cross-sections on the interaction energy for neutrons (top panel) and charged particles (bottom panel). Note the presence of resonances (narrow or broad) superimposed on a slowly varying non-resonant cross-section (after [13])...

Despite a very considerable amount of effort to improve the quality of such calculations, they represents a formidable challenge, and the accuracy is only of the order of 20-30%. Currently, the RPAE remains the most intellectually consistent and successful theory for the ab initio calculation of giant resonance cross sections. 

An example of the oxygen resonance cross section is shown in figure B 1.24.12 which displays the cross section versus energy [19]. The resonance that occurs at 3.04 MeV shows a strong peak. This results in a peak... 

All that remains now is to relate the relative line intensities to the total absorption intensity. The equations for the resonant cross-section of a single peak in Section 1 are still basically valid except that the term for each hyper-fine line must additionally contain the appropriate... 

The chromophoric character of the conjugated bonds leads to a similar resonance enhancement for the Raman lines in the various systems. This is shown in Fig.lO. The similarity of the experimental results allows to interprete the data in terms of the Albrecht theory for conjugated systems . The resonance cross-section for poly(acetylene) is for the long chain part of the Raman line. The observed resonance enhancement for C 0 is more than a factor of 50. In this case the lowest two allowed optical transitions hu to t g and hg+Qg to [Pg.364]

Figure 10. Resonance cross-section for the bond alternation mode Raman line in poly(acetylene) (PA), potassium reduced carbyne (CA) and fuUerene (Ceo)- The cross-section is in arbitrary units. The full drawn lines are as calculated from the A-term in the Albrecht theory. The dashed line is a guide line for the eye.

The 2.56 MeV resonance is not shown in the alpha particle transitions to other low states of Li , including the ground state. This can be explained if the 3.58 MeV state is identified as the first T = 1 state of Li , since then the resonant state of at 8.89 MeV would also be predominantly T = l, and a break-up to T = 0 states, such as Li + a or Be + d would be forbidden, except in so far as mixing of wave functions occurs in the compound state or isotopic spin impurity exists in the wave functions of the T — Q nuclei concerned. The conservation of isotopic spin in the Be ( a) reaction has been especially discussed by Malm and Inglis. The magnitude of the resonant cross section is used by Mackin to predict that / 2 for the 8.89 MeV state of B , and the observed width of the... 

This expression contains various (so-called Fano) parameters that are specific for the resonance the peak position Ejt, its width F, the shape factor q, the background non-resonant cross section cTo, and the mixing parameter p. ... 

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