Generalized Quantum Defect Theory Research Articles

Photoionization microscopy in terms of local-frame-transformation theory

Two-photon ionization of an alkali-metal atom in the presence of a uniform electric field is investigated using a standardized form of local frame transformation and generalized quantum defect theory. The relevant long-range quantum defect parameters in the combined Coulombic plus Stark potential is calculated with eigenchannel R-matrix theory applied in the downstream parabolic coordinate $\eta$. The present formulation permits us to express the corresponding microscopy observables in terms of the local frame transformation, and it gives a critical test of the accuracy of the Harmin-Fano theory permitting a scholastic investigation of the claims presented in Zhao {\it et al.} [Phys. Rev. A 86, 053413 (2012)].

Theory of dissociative recombination of a linear triatomic ion with permanent electric dipole moment: Study ofHCO+

We present a theoretical description of dissociative recombination of triatomic molecular ions having large permanent dipole moments. The study has been partly motivated by a discrepancy between experimental and theoretical cross-sections for dissociative recombination of the HCO$^+$ ion. The HCO$^{+}$ ion has a considerable permanent dipole moment ($D\approx$4 debye), which has not been taken explicitly into account in previous theoretical studies. In the present study, we include explicitly the effect of the permanent electric dipole on the dynamics of the incident electron using the generalized quantum defect theory, and we present the resulting cross section obtained. This is the first application of generalized quantum defect theory to the dissociative recombination of molecular ions.

R‐matrix quantum defects of molecular hydrogen

AbstractThe “Halfium” model, which combines the variational R‐matrix method with the methods of generalized quantum defect theory in prolate spheroidal coordinates, is illustrated for the 1Πu symmetry of molecular hydrogen. It is shown how the smooth behavior of the quantum defect matrices thus calculated permits the use of interpolation techniques that yield molecular potential energy curves, resonance positions and widths at minimal computational effort. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Permanent and transition dipole moments in CaF and CaCl

Permanent and transition dipole moments have been calculated for various states of CaF and CaCl by using an effective one-electron variational eigenchannel R-matrix approach combined with generalized quantum defect theory. The ion core dipole moment has been evaluated ab initio. The calculations reproduce the existing measurements involving the lowest states of these compounds to within about 5%. The calculations yield for the first time electronic one-photon transition moments for excitation of the higher Rydberg series members, from the A 2Π, C 2Π or D 2Σ+ intermediate states. Permanent dipole moments for the higher Rydberg states have also been evaluated. It is found that the dipolar ion core causes an “internal” Stark effect to appear, such that certain series are characterized by strong positive dipole moments and other series are characterized by strong negative dipole moments.

Onthe construction of basis functions for quantum defect theory in arbitraryfields

A numerical method is described for the evaluation of the regular andirregular basis functions used in quantum defect theory for arbitrarypotentials (generalized quantum defect theory). The method is related toMilne's phase-amplitude method and yields phase and amplitudeparameters which vary smoothly with energy and radius. It also permitsthe evaluation of these parameters for strongly closed channels, in theabsence of a classically accessible radial range.

The Electronic Structure of CaCl: Calculation by R Matrix and Generalized Quantum Defect Theory

The electronic spectrum of CaCl has been calculated using the variational eigenchannel R-matrix method combined with generalized multichannel quantum defect theory. The motion of the unpaired (Rydberg) electron is represented as a double scattering process on the closed-shell Ca++ and Cl− core ions. Electron penetration into Ca++ is taken into account as well as polarization effects. The partial saturation of the Cl− free-ion polarizability is evaluated on the basis of an ab initio calculation of the dipole and quadrupole moments of the CaCl+ ion core. The calculations reproduce the effective principal quantum numbers ν of the experimentally known states (including the ground state) to within ≈0.04. States with high-orbital angular momentum up to l = 6 are predicted.

The Rydberg spectrum of ArH and KrH: calculation by R –matrix and generalized quantum defect theory

The generalized ligand field approach developed recently by Arif and others for the description of the electronic structures of the alkaline earth halides is used to calculate the electronic spectr...

The Rydberg spectrum of CaF and BaF: Calculation by R-matrix and generalized quantum defect theory

R-matrix theory combined with generalized quantum defect theory is used to calculate the electronic spectrum of the CaF and BaF molecules from the ground state up near the ionization limit. The approach, an effective one-electron method similar in spirit to the ligand-field model of Rice, Martin, and Field [S. F. Rice, H. Martin, and R. W. Field, J. Chem. Phys. 82, 5023 (1985)] and to the electrostatic polarization model of Törring, Ernst, and Kändler [T. Törring, W. E. Ernst, J. Kändler, J. Chem. Phys. 90, 4927 (1989)] removes many of the limitations inherent in the previous work. The resulting level energies (effective principal quantum numbers) are in good agreement with the available experimental data and constitute the first quantitative theoretical calculation of the full electronic spectrum of CaF and BaF. Limitations and possible extensions of the theory are discussed, and quantum defects of high orbital angular momentum states are predicted.

Quantum state-selected photodissociation of K2(B 1Πu←X 1Σ+g): A case study of final state alignment in all-optical multiple resonance photodissociation

Polarized emission resulting from the quantum state-selected photodissociation of K2 through quasibound levels of the B 1Πu state has been studied experimentally by high-resolution all-optical triple resonance techniques, and theoretically by generalized quantum defect theory using the adiabatic/recoil model for the dissociation dynamics. Observation of alignment in the initial state (from the photopreparation steps) and in the photofragment (from the photodissociation step) provides detailed insight into the dynamical evolution. Excellent agreement between the theoretical calculations and the experimental results is shown.

Application of generalized quantum defect theory to van der Waals complex bound state calculations

Bound states of atom–diatom van der Waals complexes are calculated in the generalized quantum defect theory framework (GMQDT). Due to very strong interchannel couplings, the diabatic GMQDT formalism is extended in order to account for the strongly closed channels (associated with potential curves lying above the total energy E) in the asymptotic analysis of the wave function. An alternative GMQDT treatment combining diabatic and adiabatic representations is also presented. The influence of these strongly closed channels on the level positions and oscillator strengths is analyzed.

Studies of molecular Rydberg states by Schwinger variational-quantum defect methods: Application to molecular hydrogen

An ab initio electronic structure technique has been developed to study highly excited states of molecules by combining Schwinger variational methods of collision theory with generalized quantum defect theory. The technique exploits methods of scattering theory to study the region of highly excited Rydberg levels below and across ionization thresholds for molecules. The reaction matrix K, which describes the interaction of the Rydberg electron with the ionic core, is found at arbitrary negative electron energies by employing an unbounded Coulomb Green’s function in the Lippmann–Schwinger equation for the electronic wave function. Quantal conditions are imposed to obtain discrete molecular energy levels, associated Rydberg wave functions, and quantum defect functions, all as a function of the internuclear distance. Results within the static-exchange approximation for the 1,3Σ+u(1σgnσu) and 1,3Πu(1σgnπu) Rydberg states of H2, for n=2–20 and R=1.2–5.0 a0, are presented and discussed.

Application of generalized quantum defect theory to photodissociation processes: Predissociation of Ar-H2.

The application of generalized quantum-defect theory to photodissociation processes is described. The theory is of particular value when sharp resonance behavior is present in the photodissociation cross section. We show how the theory is capable of correctly predicting very sharp resonance features without the necessity of repeatedly solving systems of coupled differential equations at a very closely spaced sequence of energies. All the essential quantities occurring in the theory are smoothly varying functions of the energy despite the sharp resonances they predict.

A unified treatment of 2Π–2Π Rydberg–valence state interactions in NO

Generalized quantum defect theory is used to study the 2Π–2Π Rydberg–valence state perturbations in the NO molecule. The work is a generalization of the two-step quantum defect treatment used previously by Giusti-Suzor and Jungen for the calculation of competing preionization and predissociation processes in NO. The existing high-resolution spectroscopic data, mainly from Miescher and co-workers, are used to extract a set of quantum defect parameters relating to the pπ Rydberg channel associated with the NO+ X 1Σ+ state, and to determine potential energy curves for the B 2Π and L 2Π states as well as Rydberg–valence interaction parameters. Based on these parameters, the observed term values including rotational and spin–orbit effects are reproduced with a mean deviation of 4 cm−1 for all the 2Π levels from 45 500 to 71 600 cm−1 (i.e., to within 200 cm−1 of the dissociation limit). The fit is better than that previously obtained by Gallusser and Dressler in a vibronic perturbation approach, particularly for the levels near the dissociation limit. The set of parameters is used for the calculation of competing electronic predissociation and vibrational preionization of Rydberg levels lying above the dissociation limit and the v+=0 ionization limit. The resonance widths and energies measured recently by Anezaki et al. by a MPI double resonance technique are better reproduced by the present calculation than in the previous work of Giusti-Suzor and Jungen.