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Physical Review A

Collisions of Rydberg atoms in an electric field: Calculations using hydrogenic wave functions in parabolic coordinates

A. P. Hickman

Published Jul 1, 1983• 18 citations

Abstract

The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms ($n=10, 15, \mathrm{and} 20$) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number $m$. The origin of this tendency is discussed.

DOI: 10.1103/physreva.28.111

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Journal of Physics B Atomic Molecular and Optical Physics•May 28, 1992•10 citations

The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms (

n=10, 15, \mathrm{and} 20

) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number

m

. The origin of this tendency is discussed.

Alignment and orientation effects in collisions of helium with Rydberg atoms due to the presence of static electric and magnetic fields are predicted. Analytical expressions are obtained for the cross sections of the state-to-state transitions within the manifold with the same principal quantum number. For moderate field-induced inelasticity, the curves of the cross sections vs the fields intensity show modulations that are explained in terms of the phase differences accumulated by the wave functions of the states involved in the collision. Due to the presence of the magnetic field, transitions involving inversion of high magnetic quantum numbers are dramatically quenched. The possibility of observing the predicted effects is discussed. The reported analytical cross sections are expected to help in the understanding of the results.

The influence of an external electric field on thermal collisions between a sodium atom excited in a ``circular'' Rydberg state (n=l+1=m+1=20) and a ground-state helium atom is studied numerically within the framework of the impulse approximation. The effect of the field is determined by using parabolic wave functions for the initial and final hydrogenic atomic states. The removal of degeneracy induced by the field appears to have no significant effect for fields in the range of 0--400 V/cm. However, the state-to-state transition cross sections are strongly dependent on the initial orientation as found in previous calculations without electric field.

We report on field induced inelasticity effects in state-to-state transitions caused by collisions of helium with Rydberg atoms in the presence of parallel static electric and magnetic fields. Due to the phases accumulated by the wavefunctions of the states involved into the collision events, the transition cross sections plotted as a function of the external fields exhibit modulations. When the relative velocity of the colliding atoms is high enough, these modulations are wiped out, while sizable modifications of the cross sections may take place due to the alteration of the wavefunctions' spatial localization. The possibility of using the field-assisted collisions as a probe giving information on localization of the Rydberg states is discussed.

State changing of high-Rydberg atoms by collisions with rare-gas atoms have been theoretically investigated using the free-electron model. The non-selective character of transitions arising from the short range of the interaction between the high-Rydberg atoms and the rare-gas atoms is found to be strongly modified in the following two cases. First, for the high-Rydberg atoms in the circular states with | m |= l ≃ n , it has been found that transitions take place overwhelmingly between the circular states. This propensity rule originates from a highly anisotropic electron-density distribution of the initial circular states. Second, for the high-Rydberg states with large quantum defects (modulo 1), suppression of the yield of the lower angular momentum states have been observed. This cancels out the fair enhancement of the production of the high-Rydberg states with small | m | seen for the hydrogenic case with small quantum defects. It leads to the m distribution of the final states apparently proportional to their statistical weight.

The influence of an applied electric field on state changing in collisions between laser-excited

\mathrm{Xe}(\mathrm{nf})

atoms and xenon target gas is described. The presence of the field results in marked changes in both the rate constant for collisional state changing and the final-state distribution. The changes can be generally understood in terms of energy-transfer arguments based on the "essentially-free" electron model, although the degree of spatial overlap between the wave functions associated with the initial and final states may also be important.

An experimental study of the depopulation and final-state distribution of Na 36s and 30p Rydberg states under Na + bombardment in the presence of electric fields up to 50 V cm -1 has been carried out. Incident energies E from 171 to 967 eV span the range from 0.6 to. 1.4 times the mean orbital speed of the excited electron in the initial state. Absolute depopulation cross sections of order 10 -8 cm 2 , believed accurate within 25%, are reported as functions of field and energy. sigma 36s is proportional to E -1 , but sigma 30p is nearly independent of energy. The distribution of final states was measured by selective field ionization. At weak fields for which the initial state is well separated from the nearest Stark manifold, final states are broadly distributed across the nearest manifolds. But for stronger fields that shift the initial state close to a Stark manifold the final states are strongly concentrated among the energetically closest manifold sublevels.