C. E. Burkhardt

Classical view of the properties of Rydberg atoms: Application of the correspondence principle

The properties of Rydberg atoms are contrasted with those of hydrogen atoms using both classical and quantal points of view. It is shown that, classically, the effects of the ionic core of the Rydberg atom produce a precession of the otherwise Keplerian elliptical orbit of the excited electron, and that this precession is responsible for the nonhydrogenic properties. Using the correspondence principle, classical properties are then related to quantum mechanical properties by correlating the precession frequency with the quantum defect δl. The linear and quadratic Stark effects are also discussed and it is shown that a negative polarizability of the atom is a consequence of a positive ∂δl/∂l. In the Appendix, the ‘‘gravitational defect’’ associated with the precession of the perihelion of the Keplerian orbit of the planet Mercury is presented.

Classical view of the Stark effect in hydrogen atoms

The unique properties of the hydrogen atom, especially those that result from the dynamic symmetry of the 1/r potential, are presented from both classical and quantal points of view. Using these properties as a starting point, the response of a classical hydrogen atom, an electron executing a Keplerian ellipse about a proton, to a weak electric field is described. Because the field is weak, the elliptical orbit may be treated as a dynamical element itself, variations in its shape and orientation depicting the classical Stark effect. The behavior of this orbit is then correlated with the quantum mechanical description of the first‐order Stark effect in hydrogen, a subject that is included in most introductory courses in quantum mechanics.

Electronic energy transfer in near‐resonant electron capture collisions of H+2 with metal atoms: Radiative and nonradiative transitions

Modes of energy disposal in electron capture of H+2 with metal atoms (Cs, K, Mg, and Zn) for ion velocities in the range 3–7×107 cm/s are examined using combined optical and beam scattering techniques. Radiative and nonradiative transitions are observed for processes occurring under near resonant conditions. The following branching sequences are identified: Branching ratios are dependent on the vibrational state and the nuclear separation (Franck–Condon factors) of the H+2 ion at the time of electron capture. The branching ratio decreases for the (triplet)/(singlet) formation for H2 produced from reactions of vibrationally relaxed H+2 ion with K or Cs. Under conditions of H+2 ion relaxation, the kinetic energy of scattered atomic hydrogen following radiative decay from 3Σ+g state of H2 increases, implying a shift in the 3Σ+g→3Σ+u continuum toward longer wavelengths. The results also show that, at these velocities, the reations occur under near‐resonant conditions with vertical transitions.

Vibration-rotation coupling in a Morse oscillator

The Morse function is invaluable for describing the vibrational motion of diatomic molecules. The time independent Schrodinger equation can be solved in closed form for this potential only if molecular rotation is ignored or if the rotation is isolated from the vibrational motion by approximating it as a rigid rotor. To find the dependence of the energy eigenvalues on the vibrational and rotational state to a level of approximation that includes vibrational-rotational coupling, a higher level of approximation than the rigid rotor model is required. We present a method that can be understood by undergraduates, thus making the Morse potential a more useful example. The method yields results that are identical to those presented by Morse, but in a more elementary way.

Energy partitioning in He2+/K collisions

Final state distributions and state‐specific reaction cross sections for 1.5–6 keV He2+/K collisions have been determined from data acquired using both neutralized ion beam spectroscopy and direct observation of luminescence from decay of excited collision products. While several minor reaction channels can be identified, it is found that near‐resonant processes yielding He2(a 3Σu+) and He2(A 1Σu+) are predominant. These major channels, both of which have cross sections in excess of 100 A2, lead to substantial production of energetic metastable molecules and VUV continuum radiation extending from about 750 to 850 A.

Atomic polarizabilities: Quantal and classical perspectives

The mechanism by which an external electric field induces in an atom an electric dipole moment is discussed from classical and quantal points of view. It is shown that the expressions for the atomic polarizability α derived from each of these viewpoints are, to the same level of approximation, identical. The classical perspective is, however, more intuitive and provides a more insightful picture. The presentation is at the undergraduate level.

Coherent states composed of Stark eigenfunctions of the hydrogen atom

It is well known that for the nonrelativistic hydrogen atom it is possible to separate the Schrodinger equation in parabolic as well as spherical coordinates. The eigenfunctions obtained in these coordinate systems are each a suitable basis set in the absence of an electric field, but only the parabolic states, the Stark eigenfunctions, retain their character in the presence of a weak field. The properties of coherent superpositions of these Stark states are investigated and the motion of the resulting wave packet described. It is shown that a properly constituted superposition will mimic classical motion. It is also shown that the constant energy separation between adjacent Stark states of a given principal quantum number leads to periodic motion. In general, they split into distinct “clumps” of probability, but revive to form a single packet after each period. It is, however, possible to construct a packet that maintains its shape for all time.

State mixing in collisions involving highly excited barium atoms

Using two‐step laser excitation it is shown that the state distributions of highly excited barium atoms are substantially altered by inelastic collisions with barium atoms. For ‘‘pure’’ Rydberg states the initially produced ns or nd eigenstates are rapidly mixed with nearly degenerate n‘l’ states. For initially produced states that may be viewed as admixtures of Rydberg and doubly excited independent electron eigenstates, collisions convert the distribution to one with nearly pure, albeit state‐mixed, Rydberg character. Broadening of the absorption profiles of the highly excited states is also observed.

Photoionization of Rydberg atoms very near threshold

Abstract Experiments in which photoionization of atoms in high-lying states is investigated are described. Some of the technical difficulties encountered and means of eliminating them are discussed. A method of diagnosing the presence of stray electric fields and of eliminating these fields is also presented.

Production of Atomic Rydberg States in Optical Collisions

The advent of tunable lasers has provided the means to study many processes of fundamental importance in atomic and molecular physics. Among the phenomena of current interest are “laser-assisted” or “laser-induced” collisional processes[1]. In this context these terms refer to processes which result in atomic or molecular final states that are only accessible to irradiated systems undergoing collisional interaction[2];