Knowledge Bank

Results of \itshape{ab-initio }\upshape R-matrix calculations } indicate the presence of a broad shape resonance in electron-$CaF+$ scattering for the $2\Sigma +$ electronic symmetry near the ionization threshold. The properties of this shape resonance are analyzed using the adiabatic partial-wave expansion of the scattered electron wavefunction introduced by Le Dourneuf et. al. } The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion. Mulliken's rule for the structure of Rydberg state wavefunctions } specifies that, except for an $(n\ast )-3/2$ scale factor, every excited state wavefunction within a Rydberg series is build on an innermost lobe that remains invariant in shape and nodal position as a function of 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-prder picture is violated by a single $2\Sigma +$ $CaF$ Rydberg series at all Rydberg state energies ($n\ast \ge 5$, increasingly with $n\ast$) below the ionization threshold, under the broad width of the shape resonance. Such a violation is diagnostic of a \itshape global \upshape "scarring" of the Rydberg spectrum, which is distinct from more familiar \itshape local \upshape level perturbations.