Several interfering resonances

An illustrative application of the effective Hamiltonian approach is the interpretation of the (j-reversal effect [42] as the interference of three quasi-bound states (n = 3) decaying into a unique continuum [9]. The two functions are true narrow resonances of widths Fi and T2. The third quasi-bound state with much shorter lifetime (Fa Fi and F3 Fa) describes the relevant part of continuum and produces the large bumps (background) under the narrow resonances. 

The three-dimensional inner space is spanned by the resonances 1) and 

12) and by the quasi-bound state 3) describing the relevant part of the continuum. The matrix representation (lower part) of the effective Hamiltonian is written in the form 

E° (i = 1,2,3) are the zero-order energies of the quasi-bound states i) of partial widths Fa = 2tt Vf, V/s are the components of the coupling vector Va) (13). The index a was suppressed because there is only one decay channel. The V/s are assumed to be real and positive. To excite selectively the resonances the initial states are chosen successively as 

Another interesting application of the effective Hamiltonian explains the origin of the dips and peaks in photabsorption spectra. The model of spectrum incorporates into the inner space the relevant states of the continuum weakly interacting with the resonances [43]. This can be done by considering more than one decay channel. Such extension was discussed in detail in Ref. [8] and we sketch here only the principal idea. 

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The experimental determination of the reaction rate 12C(a, 7)lsO has been an important goal in nuclear astrophysics for several decades. Its cross section at the position of the Gamow window for a typical stellar temperature of 2.5 x 108K is comparable to that of weak interaction cross-sections. At those energies, this reaction is practically a non-resonant reaction and its cross-section is determined by the tails of interfering resonance and sub-threshold states [64]. The low cross section and the complexity of low energy contributions to the reaction rate makes a reliable prediction difficult [65,66]. 

Molecular absorption or light scatter can be corrected for by several methods. If the interfering salt composition is known, it may be possible simply to add the salt or salts to standards and make a direct comparison with calibration curves. It is relatively simple to measure the background absorbance. One way is to choose a nonresonance line from the lead hollow cathode lamp or another lamp that is not absorbed by lead and which occurs at least two bandpasses from the resonance... 

Resonance Raman spectrocopy can give the spectrum of the objective species only, even if the sample to be studied has a complex composition by selecting the excitation wavelength of laser light. Therefore, determination of the structure of adsorbed species from resonance Raman spectra can be more straightforward than in the assignment of IR spectra complicated with the presence of several adsorbed species and interfered with the absorption of clay mineral itself. 

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