Resonance position and width

Known values of f render Eq. (80), plotted semilogarithmically, quite useful in grouping resonances into series, in clarifying which decoupled channels they belong to, i.e., by which potential they are mainly supported, and in extending the series to obtain the resonance positions and widths of still uncalculated higher members, often more accurately than even elaborate scattering calculations. 

T. Brage, C.F. Fischer, G. Miecznikt, Non-variational, spline-Galerkin calculations of resonance positions and widths, and photodetachment and photo-ionization cross sections for H and He, J. Phys. B At. Mol. Opt. Phys. 25 (1992) 5289. 

To answer this question, we eomputed the resonance positions and widths of HCO 41] and HN2,[42] using both doubled and undoubled autocorrelation funetions obtained from the damped Chebyshev propagation. The results indieated tiiat the enforeed doubling of the autocorrelation function yields no appreeiable differenees in both positions and widths of the narrow resonances when compared with those obtained from a directly calculated autocorrelation function. The differences are plotted in Fig. 1 for the low-lying resonances of HN2. The largest differences are for resonanees with widths on the order of a few hundred wave numbers.[42]... 

Of these direct approaches the complex coordinate method is the most rigorous one. In principle it yields the exact energies of the poles of the scattering matrix, which. Ignoring the background contribution to the scattering, gives the resonance position and width. 

V. Ryaboy and N. Moiseyev, V. A. Mandelshtam, and H. S. Taylor, Resonance positions and widths by complex scaling and modified stabilization methods van der Waals complex NelCl, J. Chem. Phys. 101 5611 (1994). 

Table 8,2. Resonance Positions and Widths for the H—C—C- H + C=C Model Alkyl System...

An interesting problem of behaviour of the resonance levels along isoelec-tronic sequences can be investigated by the Z-dependent perturbation theory. Manning and Sanders (32,33) combined the complex rotation method with the Z-dependent perturbation theory. Expansion of the complex eigenvalue corresponding to the resonance as a power series in simultaneously yields values of both the resonance position and width for all members of an isoelectronic sequence. 

Manning and Sanders (33) used the Z-dependent perturbation theory combined with the complex rotation method to calculate the resonance position and width for the 2s2p autoionizing states of all members of the helium isoelectronic sequence. 

The success of the cSTO-MG and cSTO-NreG sets means that the resonance energy can be computed by using only real primitive basis functions and analytically continued to the complex energy plane by the complex contraction coefficients. This is good news for computational efficiency. In the cmrent computation, cSTO-NrG can be used to compute the resonance position and width because the Feshbach resonance of H2 is very narrow however, it seems difficult to treat more broad resonance with the cSTO-MG set. 

Resonance Positions and Widths for Collinear Reactions. DIVAH energies and widths determined by variable phase mediod. 

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