Results of ab initio R-matrix calculations S.N.Altunata et al,J.Chem.Phys.123,084319 (2005) indicate the presence of a broad shape resonance in electron-CaF~+ scattering for the ~2SIGMA~+ electronic symmetry near the ionization threshold.The properties of this shape resonance are analyzed using the adiabatic partial-wave expansion of the scattered electron wave function introduced by Le Dourneuf et al.J.Phys.B 15,L685 (1982).The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion.Mulliken's rule for the structure of the Rydberg state wave functions R.S.Mulliken,J.Am.Chem.Soc.86,3183 (1964) specifies that,except for an (n*)~(-3/2) amplitude scale factor,every excited state wave function within one Rydberg series is built on an innermost lobe that remains invariant in shape and nodal position as a function of the excitation energy.Mulliken's rule implies a weak energy dependence of the quantum defects for an unperturbed molecular Rydberg series,which is given by the Rydberg-Ritz formula.This zero-order picture is violated by a single ~2SIGMA~+ CaF Rydberg series at all Rydberg state energies (n* = 5->infinity,more so with increasing n*) below the ionization threshold,under the broad width of the shape resonance.Such a violation is diagnostic of a global "scarring" of the Rydberg spectrum,which is distinct from the more familiar local level perturbations.
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