Showing papers in "Advances in atomic and molecular physics in 1969"

Flowing Afterglow Measurements of Ion-Neutral Reactions

Abstract: Publisher Summary This chapter describes the experimental and analytical techniques that have been developed for flowing afterglow applications to the quantitative study of ion–neutral reaction processes. Most other techniques for the measurement of ion–molecule reaction rate constants are inherently unsuited for the examination of an ion reacting with a neutral where the neutral has the lower ionization potential, and sufficient data for this generalization did not exist prior to the flowing afterglow results. Charge transfer reactions of negative ions have sometimes been useful in establishing relative electron affinities of molecules, which are often difficult to measure. Positive ion charge-transfer reactions have, on occasion, been useful in establishing relative ionization potentials of molecules, generally known or better measured in more direct ways. The dc discharge had other advantages over the microwave discharge as well. Its geometrical configuration was more compatible with the detailed flow analysis, and it was more easily incorporated in metal flow tubes, which were soon found to be advantageous.

Radiofrequency Spectroscopy of Stored Ions II: Spectroscopy

Abstract: Publisher Summary This chapter focuses on manipulation and investigation of stored ions using radiofrequency spectroscopy (rf). When a charge moves between arbitrarily shaped grounded electrodes, the distribution of field lines originates at the charge and ends on various electrodes changes. This must be accompanied by a change in the surface charges on a given electrode at which these field lines end, and consequently result in currents to and from the electrode. The high-inductance coil connecting the cap electrodes to form the tuned detection circuit acts as a choke to the trapping frequency and because of the finite capacity between the caps and the ring, the electrode usually held at a high rf voltage causes undesirable voltages at Ω to appear at the cap. The trapping rf voltages at Ω and the dc bias are applied to the ring electrode. The capacity of the other cap electrode in this configuration to ground is about 36 pF for the major trap. At the expense of an increase of this capacity by one-third, a low impedance path to ground for the trapping frequency is provided.

The Calculation of Atomic Transition Probabilities

Abstract: Publisher Summary This chapter presents the calculation of atomic transition probabilities. Measurements of lifetimes proceed by exciting the atoms of interest either optically or by electron impact and studying the subsequent decay by one of a variety of techniques. In favorable circumstances, accuracy for the lifetime of better than 10% is frequently possible. In non-relativistic quantum mechanics, the calculation of the dipole matrix element can be carried out exactly only for the one-electron problem. For any more complex atom, it will be necessary to employ approximate wavefunctions to describe the upper and lower states of the transition. In practice, calculations are frequently made using both length and velocity matrix elements, agreement being interpreted as a favorable sign, although it is clear that this is not a guarantee of accuracy. The wavefunction will now become some linear combination of single configuration wavefunctions of the same total space and spin symmetry. The important perturbers have been generally supposed to be the terms of energy close to the term of interest.

Relativistic Z-Dependent Corrections to Atomic Energy Levels

Abstract: Publisher Summary A non-relativistic perturbation calculation of atomic energy levels with a sum of single-electron hydrogenic Hamiltonians as unperturbed Hamiltonian and the electrostatic interaction of the electrons as perturbation operator results in an expansion of the non-relativistic energy in inverse powers of the nuclear charge Z. The diagonalization leads to a single energy in which the energy contributions from the various orders are inseparably combined. In the variational screening theory, each orbital is assigned a screening parameter derived from a variation principle. The programs written in the chapter allow for the introduction of screening parameters into the calculation of the radial integrals. The elementary screening method does not involve any new calculation of the radial integrals using screened wavefunctions. Instead the energy is given by a simple screened formula in which the screening parameter is determined from an unscreened first-order calculation. If the irreducible tensor operators are products of one-electron operators, then the whole matrix element can be written as a linear combination of products of radial integrals times reduced matrix elements of one-electron operators between one-electron states times recoupling coefficients.

The Meaning of Collision Broadening of Spectral Lines: The Classical-Oscillator Analog*

Abstract: Publisher Summary The idea of a sudden interruption of the oscillation by a strong collision originates from the works of Michelson and Lorentz in the earliest days of pressure-broadening theory. The oscillation need not be completely interrupted by collisions to damp the radiation. One usually uses quantum theory for the description of internal states of molecules in such calculations. The treatment of the collision problem, having to deal with the many channels of molecular collisions, is very cumbersome, in spite of the many simplifying assumptions ordinarily introduced. It may be necessary to introduce a few quantum-mechanical modifications, utilizing the correspondence principle. An interesting analogy to the case of sense-reverting collisions, discussed in the chapter, is encountered in an application of the linear rotor model to the problem of line overlapping in vibration–rotation spectra. If only the internal state of the oscillator is affected by collisions, then the internal and translational motions may be treated independently and the resulting shape of an isolated line is a convolution of a Gaussian and a Lorentzian shape.

The Spectra of Molecular Solids

Abstract: Publisher Summary This chapter focuses on the spectra of molecular solids, explaining intensities of intra-molecular vibrational spectra The original incentive to the development of the field of infrared spectroscopy of molecular crystals was twofold On one hand, it seemed promising to study the absorption spectra of single-oriented crystals in polarized light to obtain information helpful for the assignment of intra-molecular vibrations Because the molecules in the crystal are rigidly fixed in space, it was thought that it should be possible to relate the results of polarized light investigations to the symmetry of the vibration observed The vibrational exciton theory was based on the electronic exciton theory of molecular solids In this case, the first attempts at quantitative calculations were made for an intermolecular potential that was expanded in a multipole series retaining the first term, the dipole–dipole term It is concluded that for intense infrared transitions, the splitting energies observed are to a large degree accounted for by the dipole interaction approximation

Experiments with Merging Beams

Abstract: Publisher Summary This chapter focuses on the merging beams (mb) technique that consists of two beams traveling in the same direction along a common axis. The technique can be used to investigate ion–neutral, ion–ion, neutral–neutral, and electron–ion reactions. It should be noted that the states of the mb reactants are unknown. If excited states did exist, cross sections for ground state reactants could be obtained, in principle, by applying corrections to the quoted values. The potential on the collision chamber permitted discrimination between ions created by charge transfer within the chamber and those created outside. It also accurately defined the length of the interaction region. The mutual neutralization experiments are fine examples of the use of merging beams for obtaining measurements that could not be made by other techniques. The merged beams then passed through an electric field between a set of condenser plates. Charged particles were eliminated by this field. After passage through a second collimating hole, the resultant neutral beams entered the interaction region.

Tables of One- and Two-Particle Coefficients of Fractional Parentage for Configurations SλS′μpq

Abstract: Publisher Summary Single-particle coefficients of fractional parentage (cfp) have effected a great simplification in calculations of matrix elements of one- and two-particle operators for both discrete and continuum states Many-particle cfp spanning more than one equivalence set assume a special utility when atomic Eigen-functions are introduced in which correlation or configuration mixing effects are included in this chapter. Parentage expansions achieve anti-symmetry by sums over intermediate terms rather than by permutations of coordinates or labels. Coefficients that work entirely within sets of equivalent orbitals have a number of special properties. In the evaluation of the matrix element of an operator, it is convenient to identify as coparent that wavefunction upon which the operator acts. Ordinarily the coparent contains fewer orbitals than the preparent. Adjective cfp can be partitioned. The first part is a product of substantive cfp, each of which detaches one or more orbitals from a set of equivalent orbitals. The second part is the unitary re-coupling transformation coefficient that relocates and recouples the detached orbitals, and it is expressible in terms of 3nj coefficients together with various weights and phases. The remaining part consists of a transposition phase, found by counting the intervals through which the orbitals have been moved and a combination of multinomial coefficients appropriate to the symmetry divisions that have occurred.