Effect of a virtual state near ans-wave threshold: Absolute Li photodetachment cross sections near the Li (22P) threshold

Abstract

Absolute cross sections for Li photodetachment have been measured near the Li(22P)+as channel threshold. The energy dependence deviates rapidly from normal Wigner-cusp behavior on each side of threshold. From an analysis of the total cross sections in terms of a two-channel scattering theory that includes the effects of a virtual state, a parametric expression has been derived which accurately describes the energy dependence. A least-squares fit of the data yields the position of the virtual state (55+10 meV below 22P), the phase shift at the Li(22P) +as threshold (1. 4+0.1 rad), and the electron affinity of Li (6&7.3 +0.7 meV).The threshold behavior of scattering and excitation cross sections has been a subject of extensive theoretical and experimental studies for more than three decades in the fields of atomic, nuclear, and elementary-particle physics. However, only with the recent development of high-resolution laser-photodetachment methods have experimental studies begun to disclose the strong effects that neighboring resonances can have on the threshold behavior. It is therefore of experimental usefulness as well as theoretical importance to understand, describe, and predict these effects. Similar to the resonance phenomena in other short-range potential scattering systems (atom-atom, neutron-nucleus, etc.), ' electron scattering and photodetachment resonances are of three types. In the electron-atom (molecule) systems they are caused by the short-range attractive (correlation energy) forces that commonly exist in the collision complex at energies near the thresholds of excited-state channels. If the correlation potential is sufficiently strong that the compound state is "bound" below the continuum of the excited state channel, it is a "bound, " "closed-channel, " or "Feshbach" resonance. If the attractive potential is not quite strong enough to form. a bound resonance, a "virtual state" can exist for an s-wave channel, or a "shape" resonance can exist if l~1. The scattering phase shift changes rapidly and passes through (n+ 2)rr as the total energy passes through the levels of bound and shape resonances, but it does not quite reach (n+ T)n. in the case of a virtual state.In his treatment Wigner3 showed that in the neighborhood of a threshold the cross section is, apart from a constant, the same function of energy regardless of the excitation mechanism so long as the long-range interaction of the product particles is the same. Thus, photodetachment threshold behavior is the same as that of electron scattering for the same final state, and studies by photodetachment have the advantages of high-energy resolution and the definition of the final-state spin and angular momentum.Dramatic interference effects due to Feshbach resonances were first observed by Patterson et al. 4 in the photodetachment of K, Cs, and Rb just below the thresholds of the first excited neutral product channels. Lee applied multichannel reaction-matrix theory to develop a ten-parameter expression which was capable of fitting the Cs result...

Isotope shift in the electron affinity of lithium

“…The most accurate experimental 7 Li EA is likely the results of 4984.90͑17͒ cm −1 reported by Haeffler et al 8 However, the uncertainty of 0.17 cm −1 is still too high to allow distinction between the EAs of 6 Li and 7 Li. Thus, as the results of this work will show, the theoretical calculations are significantly more accurate in this case than the available experimental results.…”

“…Even though there have been experiments concerning the EA of 7 Li, [4][5][6][7][8] there have been no reports on the measurement of the 6 Li electron affinity. The most accurate experimental 7 Li EA is likely the results of 4984.90͑17͒ cm −1 reported by Haeffler et al 8 However, the uncertainty of 0.17 cm −1 is still too high to allow distinction between the EAs of 6 Li and 7 Li.…”

“…Thus, as the results of this work will show, the theoretical calculations are significantly more accurate in this case than the available experimental results. These calculations will hopefully challenge the experiment to remeasure the 7 Li EA more accurately and to find a way for performing a similar measurement for 6 Li. The lithium EA has been a subject of numerous theoretical calculations.…”

“…10 The maximum number of Gaussians used in the calculations was 7000. In the present work we increase this number to 10 000 and, in addition to 7 Li − / 7 Li calculations, we also performed 6 Li − / 6 Li to determine the isotope shift of the lithium electron affinity. The increase in the number of basis functions resulted in generating virtually exact ͑i.e., basis-set error free͒ nonrelativistic energies for all studied systems.…”

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Very accurate electron affinity ͑EA͒ calculations of 6 Li and 7 Li ͑and ϱ Li͒ have been performed using explicitly correlated Gaussian functions and a variational approach that explicitly includes the nuclear motion in the calculations ͑i.e., the approach that does not assume the Born-Oppenheimer approximation͒. The leading relativistic and quantum electrodynamics corrections to the electron affinities were also calculated.

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