Quantum Oscillations in the Shape of Pressure-Broadened Atomic Lines

Abstract

Oscillatory or bandlike structure is predicted to occur in the wings of pressure‐broadened atomic lines when the interaction potential between the emitting atom M* and the perturbing atom A is deeply attractive compared to $\mathrm{kT}$ and the interaction in the final state is repulsive. The oscillations in intensity arise from quantum effects and are associated with the nodal structure of the continuum wavefunction which describes the dissociated state of the diatomic molecule (A + M*). The number of maxima in the line shape is a measure of the number of bound states which can be supported in the potential while the amplitude and resolution of the oscillations depend on the long‐range behavior of the potential. The bandlike structure, which may extend over thousands of cm⁻¹ on the long‐wavelength side of the atomic emission line, is resolvable as long as $\text{kT\hspace{0.17em}<\hspace{0.17em}∼\hspace{0.17em}1\hspace{0.17em}/\hspace{0.17em}10}$ the vibrational quantum ${\mathrm{\hslash \omega }}_e$ of the AM* molecule. This is a generalization of similar bandlike structure which has been calculated and observed to occur in the collision‐induced radiation of helium metastable atoms and which is merely a special case of pressure broadening involving forbidden lines. Specific calculations are presented for the broadening of the hydrogen Lyman‐α line by H(1s), and the visible absorption spectra of H(1s) in the presence of free protons. The quantum theory of line shape which is employed here was first developed by Jablonski but then neglected due to difficulties involved in evaluating essentially the band strength for continuum–continuum transitions of diatomic molecules. Jablonski introduced the WKB and other approximations into his theory which reduced it to the classical statistical theory. These approximations are compared to exact quantum‐mechanical calculations. The WKB approximation is shown to be quite valid in the special case of attractive–replusive transitions, but Jablonski then improperly averaged over those very quantum oscillations of interest here. This structure offers a unique and extremely sensitive method of studying interaction potentials involving excited states of atoms.