Quantum defect theory of dipole and vibronic mixing in Rydberg states of CaF

Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg-Stark states by resonance-enhanced two-colour two-photon excitation from the X 2Π1/2 (v'' = 0, J'' = 3/2) ground state, through the A 2Σ+ (v' = 0, N' = 0, J' = 1/2) intermediate state. These excited molecules were decelerated from 795 ms-1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg-Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N+= 0, 1, and 2 rotational states of NO+. For the range of Rydberg states studied, the measured decay times of between 200 μs and 400 μs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.

Analysis of vibrational autoionization of CaF Rydberg states

We report calculations of vibrational autoionization rates of CaF Rydberg states, based on the results of a global multi-channel quantum defect theory (MQDT) fit. Our goal is to use intuitive physical models to interpret and extend the results from the MQDT calculations and, in particular, to characterize the physical mechanisms for the interaction between the Rydberg electron and the ion-core. The calculations indicate that, among the six strongly l-mixed core-penetrating (CP) Rydberg series of CaF, the n.36 p^Π Rydberg series has the fastest Δv = 1 vibrational autoionization rate, which is at least four times larger than that for the other CP Rydberg series, in agreement with experimental results. We first demonstrate that the rotational level dependence of the vibrational autoionization rate of the n.36 p^Π series is satisfactorily explained by l-uncoupling interactions, which differ for the positive and negative Kronig symmetry levels. Next, we interpret the relative vibrational autoionization rates of all six CP Rydberg series in the context of a valence-precursor (VP) model. The VP model is a consequence of Mulliken's rule, which states that the innermost lobe of the Rydberg wavefunction remains invariant in both the nodal position and shape for members of the same Rydberg series. The electronic properties of the six VP states, which are the terminus states (lowest-n) of each of the six CP Rydberg series, are further characterized in terms of a ligand-field model, providing insight into the intimate relationship between the Rydberg electron density in the ion-core region and the vibrational autoionization rate.

Determination of the Spin-Rotation Fine Structure of He_{2}^{+}

Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He_{2}^{+} ion in the X ^{2}Σ_{u}^{+} state. The fine-structure splittings of the v^{+}=0, N^{+}=1, 3, and 5 levels of He_{2}^{+} are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He_{2} from the a ^{3}Σ_{u}^{+} metastable state.

Broad shape resonance effects in CaF Rydberg states

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 (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 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*)(-32) 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 (2)Sigma(+) 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.

Properties of nearly one-electron molecules. II. Application to the Rydberg spectrum of CaF

The ab initio K matrix method described in the preceding paper (Part I) is applied to the Rydberg electronic structure of calcium monofluoride. The spectroscopic quantum defects for the 2Sigma+, 2Pi, 2Delta, and 2Phi states of CaF are computed using the effective potential of Arif et al. [M. Arif, Ch. Jungen, and A. L. Roche, J. Chem. Phys. 106, 4102 (1997)]. Satisfactory agreement with the experimental values is obtained. The eigenquantum defects obtained from the reaction matrix for the CaF++e- system are found to be strongly energy dependent. The analysis shows that the main features of the energy-dependent structure in the eigenphases are a consequence of a broad molecular shape resonance. Partial-l (orbital angular momentum) characters of two interacting collision eigenchannels vary rapidly as a function of increasing collision energy. This prominent variation leads to interference structure in the intensities for transitions into the ionization continuum, manifesting nodal points in the total ionization cross section in the continuum above the shape resonance. The usefulness of this structure in the ionization cross section as a direct probe of the l-character of the bound state is discussed. In addition, ab initio results for the photoelectron angular distribution and the anisotropy parameter are presented. These computed results are susceptible to direct experimental verification.

Properties of nearly one-electron molecules. I. An iterative Green function approach to calculating the reaction matrix

An ab initio R-matrix method for determining the molecular reaction matrix of scattering theory is introduced. The method makes use of a principal-value Green function to compute the collision channel wave functions for the scattered electron, in combination with the Kohn variational scheme for the evaluation of R-matrix eigenvalues on a spherical boundary surface at short range. This technique permits the size of the bounded volume in the variational calculation to be reduced, making the computations fast and efficient. The reaction matrix is determined in a form that minimizes its energy dependence. Thus the procedure does not require modification or an increase in the computational effort to study the electronic structure and dynamics in Rydberg molecules with extremely polar ion cores. The analysis is specialized to examine the bound-state and free-electron scattering properties of nearly one-electron molecular systems, which are characterized by a Rydberg/scattering electron incident on a closed-shell ion core. However, it is shown that the treatment is compatible with all-electron/ab initio representations of open-shell and nonlinear polyatomic ion cores, emphasizing its generality. The introduced approach is used to calculate the electronic spectrum of the calcium monofluoride molecule, which has the extremely polar (Ca+2F-)+e- closed-shell ion-core configuration. The calculation utilizes an effective single-electron potential determined by M. Arif, C. Jungen, and A. L. Roche [J. Chem. Phys. 106, 4102 (1997)] previously. Close agreement with experimental data is obtained. The results demonstrate the practical utility of this method as a viable alternative to the standard variational approaches.