BROAD SHAPE RESONANCE EFFECTS IN CaF RYDBERG STATES

SERHAN N. ALTUNATA, \underline{STEPHEN L. COY}, AND ROBERT W. FIELD, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139.

Results of ab-initio R-matrix calculations ^{a} indicate the presence of a broad shape resonance in electron-CaF^{+} scattering for the ^{2}Σ^{+} 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. ^{b} 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 ^{c} specifies that, except for an (n^{∗})^{−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}Σ^{+} CaF Rydberg series at all Rydberg state energies (n^{∗} ≥ 5, increasingly with 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 more familiar local level perturbations.

aAltunata et. al. J. Chem. Phys. 123, 084319(2005).

bLe Dourneuf et. al. J. Phys. B, 15, L685(1982)

cR.S. Mulliken, J. Am. Chem. Soc. 86, 3183(1964).