Richard P. Leavitt

Crystal‐field analysis of triply ionized rare earth ions in lanthanum trifluoride

Previously reported spectra of nine triply ionized lanthanides in LaF3 are analyzed by using a parametrized C2 crystal‐field Hamiltonian. Initial crystal‐field parameters Bnm in the fitting procedure were obtained from point charge lattice sums Anm using previously derived ρn, where Bnm=ρnAnm. The largest rms deviation of theory from experiment was 18.1 cm−1 (Pr3+), and the smallest was 2.1 cm−1 (Ho3+). The resulting Bnm were used to obtain a smoothed set of crystal field parameters for the entire lanthanide series whose largest rms deviation was 20.8 cm−1 (Pr3+) and whose smallest was 3.5 cm−1 (Ho3+).

Pressure broadening and shifting in microwave and infrared spectra of molecules of arbitrary symmetry: An irreducible tensor approach

Contributions to the interruption function S(b) used in semiclassical perturbation approaches to impact broadening and shifting of microwave and infrared molecular gas spectra are derived by irreducible tensor methods for molecules of arbitrary symmetry. Results are given explicitly for long‐range intermolecular interactions: up to R−5 for the electrostatic interactions and to R−7 for the induction and dispersion interactions. A new contribution to S(b) is found that has no counterpart for the case of two interacting linear molecules; all other terms are appropriate generalizations of the linear molecules case. For the three cases of asymmetric tops, symmetric tops, and linear molecules, group‐theoretical arguments are given that simplify the computation of certain reduced matrix elements that occur in the theory. Results are given in detail for the case in which both radiating and perturbing molecules are linear, and errors in the published literature concerning the contributions to S(b) in this case are...

On the role of certain rotational invariants in crystal‐field theory

We examine a perturbation scheme in which the effect of the crystal‐field Hamiltonian in mixing free‐ion states is represented in second order by an effective operator acting only on the free‐ion state under consideration. The shifts in the centers of gravity of the free‐ion levels caused by J mixing is derived in terms of three parameters s2, s4, s6, which are quadratic rotational invariants. The second moment of the Stark levels corresponding to a particular free‐ion state is described by these same parameters in the absence of J mixing. Using Ho3+ as an example, we show how these parameters can be extracted from experimental data in a simple manner and how they can be used to correct the data for J‐mixing effects.

Crystal‐field analysis of triply ionized lanthanides in Cs2NaLnCl6

Optical spectra of the elpasolite hexachloride compounds Cs2NaLnCl6, where Ln represents one of the lanthanide ions, are analyzed with a crystal‐field Hamiltonian of Oh symmetry. Crystal‐field parameters, Bnm, are found that minimize the rms deviation between calculated and experimental energy levels for Ln=Ce, Pr, Nd, Eu, and Tb. A set of ’’smoothed’’ Bnm is found for the lanthanide series that predicts the spectroscopic properties of the remaining eight lanthanide ions. Predicted energy levels and g values are compared with available experimental data for all the lanthanides except Pm and Gd, and magnetic dipole intensities are computed.

Cutoff‐free theory of impact broadening and shifting in microwave and infrared gas spectra

A cutoff‐free impact theory of pressure broadening and shifting of rotation and rotation–vibration spectra in gases is derived. The theory is based on the ATC (Anderson–Tsao–Curnutte) theoretical framework and uses a linked‐cluster theorem for degenerate states to obtain a form for the interruption function S(b) in which the dependence on the interaction potential is exponential. S(b) is bounded for 0⩽b⩽∞, allowing integrals over the impact parameter b to be performed without resort to a cutoff. Earlier impact theory results are shown to be limiting cases of our result. Results for broadening cross sections are obtained for certain ideal cases and compared to corresponding ATC results.

An irreducible tensor method of deriving the long‐range anisotropic interactions between molecules of arbitrary symmetry

The long‐range, anisotropic interaction energy between two molecules of arbitrary symmetry is derived to second order in perturbation theory by using irreducible tensor methods. The resultant formulas can be used to express the interaction energy to any desired power of R, the separation of the two molecules. Group‐theoretical arguments are used to reduce the number of independent parameters in the theory and to determine which parameters are nonzero in particular molecular point groups. The theory is illustrated by being applied to the case of two linear molecules, and the interaction energy is given explicitly for linear molecules up to R−5 for the electrostatic (first‐order) interactions and to R−7 for the induction and dispersion (second‐order) interactions. Certain discrepancies in the published literature concerning the induction and dispersion interactions of two linear molecules are clarified.

Crystal‐field analysis of triply ionized rare earth ions in lanthanum trifluoride. II. Intensity calculations

Implementation of the Judd–Ofelt theory of induced electric dipole transitions is considered for rare‐earth ions in LaF3. Parameters in the theory are derived a priori. Calculations of the multiplet‐to‐multiplet line strengths, lifetimes, branching ratios, and line‐to‐line squared matrix elements are performed between all the energy levels considered for the triply ionized lanthanides Ce3+ through Yb3+. Magnetic dipole calculations are also performed. The g factors for all the lanthanides with an odd number of f electrons are given. Calculated Judd–Ofelt intensity parameters and radiative lifetimes compare reasonably well with experiment.

Optical spectra, energy levels, and crystal‐field analysis of tripositive rare‐earth ions in Y2O3. IV. C3i sites

We report an analysis of new and previously existing optical absorption and fluorescence data, far‐infrared data, and electronic Raman scattering data for Eu3+, Dy3+, and Er3+ in the C3i sites of Y2O3 and R2O3, where R=a rare earth. Our previous analysis of C2‐site spectra yields an effective point‐charge model for the host lattice that allows initial estimates to be calculated for the C3i‐site crystal‐field parameters Bkm. Best‐fit values of B20, B40, and B43 are obtained for Eu, and best‐fit values of all Bkm allowed by symmetry are obtained for Dy and Er. The best‐fit Bkm are in relatively poor agreement with the model; in particular, B20 has the opposite sign from and B44 is much smaller than the model predictions. From the best‐fit Bkm we obtain phenomenological crystal‐field components Akm, from which we predict Bkm and C3i ‐site energy levels for the ground states of Tb3+, Ho3+, Tm3+, and Yb3+. While the effective point‐charge model is apparently too crude to make accurate, quantitative, a priori p...

The orotron–A free‐electron laser using the Smith‐Purcell effect

A theory of operation of the orotron is described in which the electromagnetic field present in the open resonator of the device bunches the electron beam; this bunching leads to coherent oscillation. Theoretical results at 75 GHz are discussed.

Optical spectra, energy levels, and crystal‐field analysis of tripositive rare‐earth ions in Y2O3. III. Intensities and g values for C2 sites

We report measurements of the oscillator strengths between the Stark‐split ground level and numerous excited Stark levels of Nd3+, Sm3+, Er3+, and Tm3+ in the C2 sites of Y2O3. Experimental results are compared with calculations based on the Judd–Ofelt theory of induced electric‐dipole transitions, which uses the odd‐parity terms in the crystal‐field interaction (determined via an effective point‐charge model). We also compare our theoretical results with previous measurements of manifold‐to‐manifold oscillator strengths, excited‐state lifetimes, and Judd–Ofelt intensity parameters. Magnetic‐dipole contributions to the intensities are included as well. Calculated ground‐state g values for all the rare earths with an odd number of f electrons are reported. Comparison of theoretical and experimental results indicates that good agreement is obtained in most cases.