Resonance partial widths

The quantities define the resonance partial width of the adsorbate level due to the tip (t) and to the substrate (s) within an Anderson model, and Paisp) is the local density of substrate states on the adsorbate at the Fermi energy. The factor determines the adsorbate energy level rise due to non-adiabatic coupling. The relaxation/excitation rates at zero... 

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

The quantities y4 are related to the partial widths of the resonance according to... 

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

The form displayed in eq. (2-40) implies that the ratios of the amplitudes for scattering into different exit channels are independent of the entrance channel. This, of course, will only be true if the resonance is long lived, so that memory of the initial state can be lost. Note that Aga is a symmetric function, which is a consequence of time-reversal invariance. Note also that, within the approximations used, the phase shift associated with a given channel is just the elastic scattering phase shift for that channel. Finally, the partial widths are proportional to the probability of decay from channel fi. Equation (2-41) is, then, merely a statement that the total probability of decay from channel is the sum of the probabilities of decay into individual channels. 

Conversely, a coherent superposition of continuum states with a population closely reproducing an isolated peak in the density of states, which corresponds to a resonance, can be built in such a way to give rise to a localized state. From this localized state, there will be an outward probability density flux, i.e., it will have a finite lifetime. In the limit of a resonance position far from any ionization threshold and a narrow energy width, the decay rate will be exponential with the rate constant T/ft. The decay is to all the available open channels, in proportion to their partial widths. 

If a resonance Is not narrow, then the partial widths may still be defined in terms of the residue at the pole, but Equation 4 is no longer valid (92,93,107). Branching probabilities are now defined by... 

The reaction probabilities that determine some of the E g and the adiabatic partial widths are nonzero only because of tunneling. We have considered two semiclassical methods to calculate the resonance energy and tunneling probabilities, namely the primitive WKB method (140), which simply quantizes the phase Integral for motion in the well of the adiabatic potential, and a uniform semiclassical method (168,169), which... 

Nonadiabatic Feshbach calculations. Using the reaction-path Hamiltonian and invoking an adiabatic separation of the reaction coordinate from all other coordinates, resonance energies and adiabatic partial widths are obtained by neglecting all off-diagonal terms of the Hamiltonian. The most important... 

Partial widths. In Table II a compilation of adiabatic and nonadiabatic partial widths is given for the same resonances. 

Total resonance widths. The total resonance widths are compiled in Table III. The reactlon-path-Hamiltonian (RPH) method denotes using the SCSA method for adiabatic partial widths and the Feshbach golden-rule method for nonadlabatic partial widths and summing these to obtain the total width. 

Hence the resonance width Is a sum of partial widths Into the several arrangement channels. 

V = 1 and 2, with the higher resonance appreciably wider. Partial widths are also shown In Table I. 

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