Proceedings of the Dalgarno Celebratory Symposium

The following sections are included:

• PREFACE

• CONTENTS

Various landmarks in the evolution of Alexander Dalgarno from a gifted mathematician to becoming the acknowledged Father of Molecular Astrophysics are noted. His researches in basic atomic and molecular physics, aeronomy (the study of the upper atmosphere) and astrophysics are highlighted.

The main ideas and results of dipole response theory are summarized, and the application of pseudospectral methods are discussed. Recent progress in high precision variational methods for helium and lithium are summarized and applied to the calculation of isotope shifts as a means to determine the nuclear charge radius of halo nuclei.

The elastic approximation, developed by Dalgarno for the calculation of spin exchange cross sections, is extended to predict the cross sections for spin flipping transitions induced by the anisotropic magnetic coupling between two hydrogen atoms.

Following the establishment of quantum mechanics around 80 years ago, many formulae that describe how atoms and molecules interact with each other and with external electromagnetic fields were derived. While such formulae provide prescriptions for calculating atomic and molecular properties many of them are inconvenient to evaluate because of the need to calculate the sums of a, large, often infinite, number of expressions constructed from various matrix elements and excitation energies. Alex Dalgarno through his major work in perturbation theory pioneered the method, now standard, in which these sums are calculated from the solutions of finite numbers of differential equations. This article is a brief summary of the method and its use.

Dispersion coefficients C₆ can be calculated from the dynamic polarizabilities of the interacting monomers at imaginary frequencies. This article describes a linear response time dependent density functional approach that has been recently developed for evaluating these polarizabilities. Using a spherical tensor expansion, both the isotropic and anisotropic components of the C₆ coefficient can be obtained for a set of molecular states. Isotropic C₆ coefficients for the interactions between a pair of transition metals are presented.

It is indeed a pleasure to start our symposium celebrating Alec Dalgarno with the topic of astrochemistry. This subject, so intimately connected to radioastronomy, continues to provide new molecular species in a variety of astronomical sources, molecular clouds, circumstellar shells, and planetary nebula. A currently maintained catalog is online.¹ The majority of species observed are not commercially available stable gas-phase species. Thus their laboratory production and the production of their rotational spectra is a most significant challenge. There is a pressure to make observations at increasingly higher frequencies, for reasons of higher signal strength. This further challenges the laboratory astrophysicist. For semi-rigid species the rotational energy may be well expressed in powers of angular momentum by three rotational constants (quadratic) and five centrifugal distortion constants (quartic).² Thus a quite finite number of rotational transitions, at frequently convenient laboratory frequencies, allows the reasonably accurate estimation of the higher frequency spectrum. For larger molecules, especially those with large amplitude motions such as internal rotation or low frequency bending motions, the semi-rigid model is likely inadequate and a more complete laboratory spectrum is essential for reliable carrier identification…

An overview of some developments in astrochemistry over the last 40 years is given, with special emphasis on topics that Alex Dalgarno has opened up (which is nearly all of astrochemistry!). The development of astrochemistry into an integral part of modern astrophysics is illustrated with recent examples. The bright future of astrochemistry is discussed in the light of new observational facilities and the need for continued studies of basic molecular processes under interstellar conditions is emphasized.

The emission from atoms and molecules provide our best probes into astronomical environments. Observations of atomic and molecular lines provide information on the abundance of species, the gas temperature and density. When combined with astrochemical models one may infer ionization rates along with heating and cooling rates. This paper will review a few examples of using atoms and molecules as probes. Most of the examples are selected from work done in collaboration with Alex Dalgarno.

The negative hydrogen ion H^- plays an important role in the continuum opacity of late-type stars and in the kinetics of low-metallicity gas. We review the H^- photodetachment cross section along with other processes involving H^-. We address H^- in early Universe chemistry, the role of oscillator-strength sum-rules in constraining its continuum cross section, and the influence of auto-detaching resonances on the efficiency of H^- photodestruction in the reioniza-tion era.

Alex Dalgarno has introduced many of the themes that define current research in astrochemistry. Variations on these themes will continue to be played out well into the future. Clear and unambiguous tests of theories of formation of interstellar molecules remain elusive; however, the understanding of fluorine chemistry appears to offer one success story. The predicted chemical activity in X-ray dominated regions and in shock waves is being studied with increasingly sensitive observations. Molecules whose chemistry and internal excitation are strongly coupled are especially valuable. In some cases, observations of these reactive species can provide probes of specific chemical rates in interstellar gas. Superthermal OH observed in a shock front appears to offer special diagnostic value. Even cosmologists have recognized that chemistry plays an important role in the early evolution of matter in the Universe around the epoch of recombination. The hydrogen molecule is being used to test cosmological theories of dark matter.

In a cartoon in a well known French mountain climbing series, an Alpine guide is climbing an impossibly sheer granite needle. He has his hand on the tiny platform at the top of the needle, and says to his roped-up companion below, "Ah, the joy of touching virgin rock." The climber cannot see—but the reader can—looking down from above, that the climber's hand is almost touching a sardine can…

In 1986 Alex Dalgarno published a paper entitled Is Interstellar Chemistry Useful?¹ By the middle 1970s, and perhaps even earlier, Alex had hoped that astronomical molecules would prove to: possess significant diagnostic utility; control many of the environments in which they exist; stimulate a wide variety of physicists and chemists who are at least as fascinated by the mechanisms forming and removing the molecules as by astronomy. His own research efforts have contributed greatly to the realization of that hope. This paper contains a few examples of: how molecules are used to diagnose large-scale dynamics in astronomical sources including star forming regions and supernovae; the ways in which molecular processes control the evolution of astronomical objects such as dense cores destined to become stars and very evolved giant stars; theoretical and laboratory investigations that elucidate the processes producing and removing astronomical molecules and allow their detection.

Atomic, molecular, and optical processes play fundamental roles in regulating the evolution of star-forming regions in galaxies, and of accreting black holes in galaxy nuclei. I present a discussion of the essential physics and chemistry of interstellar photon-dominated regions (PDRs) and X-ray dominated regions (XDRs). In such regions, intense radiation fields determine the atomic and molecular compositions of dense interstellar gas, and control the resulting observable spectroscopic emissions and absorptions.

The Infrared Spectrograph onboard the Spitzer Space Telescope has proven to be a powerful tool for the study of astrophysical molecules, particularly in interstellar regions where the gas has been heated by shock waves. Recent observations – which have provided valuable information about the simple hydrides H₂, HD, H₂O and OH – are reviewed here.

In this work I propose that the large abundances of CH⁺ and observed in the diffuse interstellar medium may have a common origin, and I identify the driving agent in the dissipation of turbulence. Results of the present model are consistent with the observational constraints along the line of sight towards ζ Persei, and may be extended to other diffuse lines of sight.

Alex Dalgarno saved my career.

I entered the Graduate School at Harvard in the Chemistry Department in September of 1973 from the University of Michigan, where I had (unfortunately) majored in Chemistry. Chemistry is considered a "laboratory science" but I had no talent in the laboratory. I had merely fallen in love with the ideal gas law in high school, and I had stubbornly allowed this to determine my course of studies, most of which had nothing to do with the ideal gas law, and much of which was focused on laboratory studies…

This chapter provides a brief summary of the overall role of atomic and molecular (ATM) processes in solar system environments and a few examples of Alex Dalgarno's contributions. The bulk of the chapter is devoted to the role of ion-neutral collisional processes at comet Halley and at Saturn's satellites Enceladus and Titan.

The energy relaxation of fast atoms moving in a thermal bath gas is explored theoretically. We found that two time scales characterize the equilibration, one a short time, in which the isotropic energy distribution profile relaxes to a Maxwellian shape at some intermediate effective temperature, and the second, a longer time in which the relaxation preserves a Maxwellian distribution and its effective temperature decreases continuously to the bath gas temperature. It is shown that the formation and preservation of a Maxwellian distribution does not depend on the projectile to bath gas atom mass ratio, contrary to predictions of the hard-sphere model. This two-stage behavior is universal. It arises due to the dominance of small angle scattering and small energy transfer in the collisions of neutral particles and reflects a fundamental property of long-range atomic forces. The Boltzmann equation is solved numerically for nitrogen in He and in Ar. The solutions are in close agreement with the experimental measurements of the evolving Doppler profiles of emission from excited initially energetic N atoms traversing bath gases of helium and argon. Our investigation provides the first experimental and theoretical evidence of the formation and preservation of hot Maxwell distributions with a time-dependent effective temperature in actual atomic gases.

Charge-exchange collisions between heavy solar wind ions and neutral atoms and molecules are considered as the mechanism to explain some astrophysical observations of X-ray and EUV emissions. Theoretical and experimental data on the charge-exchange emission spectra are reviewed. Physical characteristics of heliospheric sources of the charge-exchange X-rays are discussed. Modeling of X-ray and EUV spectra observed from different heliospheric objects is described in detail. Satellite observational data obtained with the Chandra and XMM-Newton X-ray telescopes are compared with our theoretical predictions. Contribution of the charge-exchange mechanism to the observed diffuse soft. X-ray background is determined and the computed photon spectra are compared with the results of recent observations. X-ray diagnostics of the solar Wind composition and velocity are considered. Examples of a determination of the solar wind ion composition from cometary and planetary X-ray spectra are presented.

In many research areas, including long range potentials and ultracold collisions, Alex Dalgarno has been a pioneer and a leader. His work is well integrated within a tradition, he has been very supportive of young people or colleagues and has given good advice. The community should be grateful to him for the structuration achievement through the creation of ITAMP and the organization of many workshops.

Photoassociation of ultracold atoms has been used to determine interaction potentials and to extract scattering lengths with great precision, which we discuss here in the context of lithium. We also describe a recent experiment where saturation in the rate of photoassociation of an atomic BEC was observed.

One of the many important contributions of Alex Dalgarno to Atomic, Molecular, and Optical (AMO) Physics relates to his work on ultracold physics. After a brief review of his early work on photoassociation (PA) of ultracold atoms and the formation of ultracold molecules, a short description of new results using Feshbach Optimized Photoassociation (FOPA) will be given. This research points to Alex's influence on the work now performed in my group at UConn.

We describe a quantum theory of atomic and molecular collisions in the presence of external electromagnetic fields based on the fully uncoupled space-fixed basis representation of the scattering wave functions. The fully uncoupled basis leads to simple expressions for the matrix elements of the Hamiltonian providing all operators of fine and hyperfine interactions as well as the operators describing interatomic and intermolecular interactions are represented as direct products of spherical tensors defined in the laboratory-fixed coordinate system. We present a general expression for the electrostatic interaction operator of two atoms in arbitrary electronic states in terms of uncoupled products of space-fixed spherical tensors and describe recent studies of molecular collisions in external fields.

Recent years have witnessed exciting advances in the development of novel methods to cool and trap molecules and collisions and interactions involving ultracold atoms and molecules have become topics of considerable experimental and theoretical interest. In this article, we provide an overview of recent theoretical investigations of inelastic and reactive collisions in atomic and molecular samples at cold and ultracold temperatures.

Progress in calculations on the hyperfine structure (hfs) of the hydrogen molecular ion is summarized taking a long view with emphases on Alex Dalgarno's contributions and also on some recent developments.

The chemistry of individual molecular clouds in nearby galaxies is found to be correlated with large scale galactic structure, as revealed by principal component analysis. The high spatial resolutions of millimeter and submillimeter interferometers can resolve the complexity and confusion in other galaxies by isolating areas of common physical conditions.

The research program known as Atomtronics aims to create one-to-one analogs of electronic components and devices with ultracold atoms trapped in periodic potentials. Such an analogy can be realized with reservoirs of neutral, ultracold atoms connected to optical lattices. Due to their highly tunable band structure, the lattices can be tailored to create resonances between certain states of the system. This allows atomic transport through specific dynamical pathways of the system, while minimizing transport through others.

In this presentation, a quantum master equation approach is outlined for treating the problem of two or more reservoirs of ultracold atoms, with arbitrary chemical potentials, connected to optical lattice configurations. The formalism is quite general and readily lends itself to the theoretical study of transport phenomena in open atomic systems.

This theoretical approach is applied to atomtronic systems, demonstrating how certain custom lattices can mimic the behavior of the electronic semiconductor diode, field effect-transistor, and bipolar junction transistor (BJT). Logic elements, such as AND and OR gates are constructed by taking two atomtronic BJTs and combining them in a manner similar to that of conventional electronics. This is promising since it is possible that we may join basic atomtronic components to construct elementary logic devices in a fully quantum mechanical system.

Experimental approaches to implementing ideas from quantum information science focus on developing well-understood physical systems that have only a few quantum bits. I will discuss potential applications of these quantum systems, including high-resolution magnetic field sensing and simulating quantum mechanical models from condensed matter physics. By relying upon proven technologies, we can take full advantage of the tremendous experimental advances in preparing, controlling, and measuring isolated mesoscopic and atomic systems made over the past decade.

The following sections are included:

• Introduction

• The TAMOC Community and the NRC Reports, 1984-1987

• Some Relevant NSF Activities Prior to September 1987

• NSF September 1987-October 1988, A Chronology

• Further Comments

• References

The following sections are included:

• Introduction

• The First Five Years

• The Second Five Years

• The Third Five Years

• Present

At this 3-day symposium, we have all come together to honor the scientific contributions of a remarkable scientist, Professor Alex Dalgarno. Because Alex's scientific reach has been so broad, many of us may know only a small slice of the science that Alex has impacted. For instance, if you are an astrophysicist, you may be aware of the important work Alex has done in molecular astrophysics, early Universe chemistry, or on the origin of cometary x-rays, but you may not be aware of his seminal work in atomic and molecular scattering theory, or his work on long-range forces, or his exceptional contributions to the understanding of atomic and molecular processes in the terrestrial ionosphere and thermosphere…

It is an honor to be invited to speak at this special symposium to honor a truly extraordinary scientist, mentor, colleague and human being, Alex Dalgarno.