Quantum defect theory (QDT) is concerned with the properties of an electron in the field of a positive ion and, in particular, with expressing those properties in terms of analytical functions of the energy. It provides a unified theory of bound states, including series perturbations, autoionisation and electron-ion scattering, both elastic and inelastic. The main emphasis of the review is on the foundations of the theory. Properties of Coulomb functions are discussed in some detail and outline sketches are given of relevant topics in collision theory and radiative theory. One-channel and many-channel QDT are discussed separately. Applications to the following problems are considered: resonances, atomic collision calculations, systems with two energy levels of the ion core, helium, other rare gases, alkaline earths and other atomic systems, molecular hydrogen, dielectronic recombination.

https://iopscience.iop.org/article/10.1088/0034-4885/46/2/002/pdf

Quantum defect theory

This paper studies the impact of ambiguity and ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitudes toward ambiguity are heterogeneous across the population, just as attitudes toward risk are heterogeneous across the population, but that heterogeneity of attitudes toward ambiguity has different implications than heterogeneity of attitudes toward risk. In particular, when some state probabilities are not known, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This suggests a different cross-section of portfolio choices, a wider range of state price/probability ratios and different rankings of state price/probability ratios than would be predicted if state probabilities were known. Experiments confirm all of these suggestions. Our findings contradict the claim that investors who have cognitive biases do not affect prices because they are infra-marginal: ambiguity averse investors have an indirect effect on prices because they change the per-capita amount of risk that is to be shared among the marginal investors. Our experimental data also suggest a positive correlation between risk aversion and ambiguity aversion that might explain the “value effect” in historical data.

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Theory and Experiment

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

The concept behind active thermochemical tables (ATcT) is presented. As opposed to traditional sequential thermochemistry, ATcT provides reliable, accurate, and internally consistent thermochemistry by utilizing the thermochemical network (TN) approach. This involves, inter alia, a statistical analysis of thermochemically relevant determinations that define the TN, made possible by redundancies in the TN, such as competing measurements and alternate network pathways that interrelate the various chemical species. The statistical analysis produces a self-consistent TN, from which the optimal thermochemical values are obtained by simultaneous solution in error-weighted space, thus allowing optimal use of all of the knowledge present in the TN. ATcT offers a number of additional features that are not present nor possible in the traditional approach. With ATcT, new knowledge can be painlessly propagated through all affected thermochemical values. ATcT also allows hypothesis testing and evaluation, as well as d...

Introduction to Active Thermochemical Tables: Several “Key” Enthalpies of Formation Revisited†

It is shown that under the usual conditions of zero‐electron‐kinetic‐energy, pulsed field ionization (ZEKE–PFI) spectroscopy the lifetimes of very high‐lying Rydberg states are increased by at least approximately the factor n (in addition to the expected factor of n3), the principal quantum number, due to strong l mixing by the Stark effect. Additional factors may increase lifetimes by still another factor of approximately n. Pulsed field ionization under typical conditions is shown as likely to be predominantly diabatic and the effect on resolution is assessed. Factors affecting rotational line intensities are also discussed.

Factors affecting lifetimes and resolution of Rydberg states observed in zero-electron-kinetic-energy spectroscopy

Multichannel quantum defect theory (MQDT) is applied to the treatment of electron motion in molecular Rydberg states and its coupling to the vibrational and rotational motions of the nuclei. The full rovibronic Hamiltonian is taken into account and the theory formulated in terms of parameters which relate to the standard Born–Oppenheimer (BO) theory. The development is an extension of Seaton’s quantum defect theory and relies on Fano’s frame transformation method. MQDT is not restricted to the BO approximation, but includes the so‐called adiabatic corrections and nonadiabatic effects (i.e., vibronic coupling and rotational l uncoupling), however strong, without requiring the explicit evaluation of the interactions between individual levels. The general formalism can be simplified for the H2 and D2 molecules in the range below or near the ionization threshold and for vibrational excitation well below the dissociation energy. The only input data required are the potential energy curve of the ion core in its...

Rovibronic interactions in the photoabsorption spectrum of molecular hydrogen and deuterium: An application of multichannel quantum defect methods

The multichannel quantum defect theory of dissociative recombination is reviewed and adapted to treat simultaneous vibrational preionization and electronic predissociation in NO. The photoionization, photodissociation, and photoabsorption cross sections of NO corresponding to 2Π excited states are computed in the range from the N(2D)+O(3P) dissociation limit up beyond the second vibrational level of NO+(X 1Σ+). The calculations are based on the 2Π Rydberg and valence state potential curves and Rydberg‐valence state interaction energies extracted by Gallusser and Dressler from the high‐resolution spectroscopic data of Miescher and co‐workers. These data pertain to the discrete range and furnish precise information on numerous spectral perturbations involving levels of the npπ Rydberg series and the B and L valence states. The calculated cross section profiles reproduce with reasonable accuracy the observed absorption and photoionization curves, and in particular the widths of the Rydberg resonances. The co...

Theoretical study of competing photoionization and photodissociation processes in the NO molecule

Publisher Summary This chapter discusses the molecular applications of quantum defect theory. Quantum defect theory provides a unified description of discrete and continuous spectra in terms of the same parameters pertaining to the physics at short range. It accounts for the Rydberg structures as well as for their decay into the continuum. This decay is called preionization (or autoionization), or predissociation if the continuum is associated with nuclear rather than with electronic motion. It displays two molecular spectra exhibiting striking effects due to both preionization and predissociation. Both spectra result from photoexcitation of nitric oxide and they cover the same wavelength region. The upper spectrum is a recording of the ion current resulting after excitation just above the ionization threshold. The small peaks superimposed on the flat continuum are Rydberg structures whose presence reveals the occurrence of preionization. The lower trace is an absorption spectrum taken under comparable experimental resolution. The significant different appearance of the two spectra reveals that a second decay channel, corresponding to production of neutral atomic fragments, must also interfere. Moreover, the different appearance of the Rydberg peaks in the two spectra indicates that predissociation is strong and competes with preionization.

Molecular Applications of Quantum Defect Theory

Multichannel quantum defect theory is adapted to treat simultaneous rotational and vibrational preionization in H2. The strongly preionized spectrum between the N+=0 and N+=2 rotational thresholds of photoionization of H2X1Σg+(J″=0, v″=0) to produce H2+X2Σg+(N+, v+=0) is computed as example and good agreement is obtained with the photoionization data of Dehmer and Chupka.

Calculation of rotational–vibrational preionization in H2 by multichannel quantum defect theory

Multichannel quantum defect theory has been used to calculate the effect of vibrational preionization on the total and partial oscillator strength distributions and photoelectron angular distribution in H2 for excitation between 790 and 760 A. The total oscillator‐strength distribution obtained agrees well with the high‐resolution photoionization data of Dehmer and Chupka. The partial oscillator strength resonance profiles are predicted to have different shapes in different vibrational ionization channels, while their widths change little with channel. The preionization resonances are also predicted to affect the angular distribution asymmetry parameters b over a broader range than they affect the oscillator strength distribution. The gross features of the preionization resonances are discussed in terms of approximate solutions of the MQD equations.

Calculation of vibrational preionization in H2 by multichannel quantum defect theory: Total and partial cross sections and photoelectron angular distributions

Ch. Jungen

Papers

Rovibronic interactions in the photoabsorption spectrum of molecular hydrogen and deuterium: An application of multichannel quantum defect methods

Theoretical study of competing photoionization and photodissociation processes in the NO molecule

Molecular Applications of Quantum Defect Theory

Calculation of rotational–vibrational preionization in H2 by multichannel quantum defect theory

Calculation of vibrational preionization in H2 by multichannel quantum defect theory: Total and partial cross sections and photoelectron angular distributions