A threshold law describes the dependence of a reaction yield near a reaction threshold. It is also a signature of the physical forces involved in the reaction, so the agreement of an observed threshold behavior with a threshold law or a departure from it can be a sensitive probe into how well the reaction physics is understood. A collaboration from Western Michigan University, the ALS, and Denison University has now shown that the threshold laws for inner-shell photodetachment of negative ions are not only obeyed but can extend over a much wider energy range than theory had predicted.

E. Wigner first derived the general threshold laws for the dissociation of a target into a pair of particles in 1948. In single-electron photodetachment of negative ions where the reaction products (a neutral atom and an electron) interact only in a short-range potential (proportional to 1/r⁴), the threshold behavior is governed by the centrifugal potential—the potential formed by the relative angular momentum of the products—and depends only on the energy (ε) and the relative angular momentum (l) of the particles through ε^l+1/2.

He⁺-production cross section for 1s photodetachment from He^– closely follows a Wigner p-wave (l = 1) threshold law (ε^3/2), despite significant post-collision interaction (PCI) effects. PCI appears only to effectively shift the observed threshold position (arrow) by about 25 meV from the theoretical position (vertical dashed line).

This form of the Wigner law has been observed in countless studies, most notably in photodetachment of an outer (valence) electron from negative ions. However, when an inner-shell electron is removed, the neutral atom formed is unstable and quickly emits a second electron (Auger decay). If one considers the final reaction products to be two electrons and a positive ion, the short-range potential threshold law would no longer apply. To investigate whether this is so, the group studied inner-shell photodetachment in two negative ions: He^– and S^–. The experimenters monitored the photodetachment by measuring the positive ion yield (He⁺, S⁺, S²⁺, and S³⁺) at the Ion-Photon Beamline on ALS Beamline 10.0.1.

The ground-state electron configuration of He^– is 1s2s2p. For inner-shell photodetachment, the 1s electron is removed. Since the electron gains one unit of angular momentum by absorbing the photon, the receding photoelectron has angular momentum l = 1 and, in absence of Auger decay, one would expect a p-wave threshold law: ε^3/2. In fact, the measured near-threshold cross section agrees very well with the p-wave law, except that it is shifted in energy by a significant amount—i.e., the Auger decay appears to mainly have the effect of requiring more energy for the photodetached electron to escape. This can be understood in the context of a post-collision interaction effect. Before the photoelectron can fully escape, there is a chance that an Auger process occurs and the fast Auger electron overtakes the slow photoelectron, thus causing the photoelectron to be attracted and possibly recaptured to the suddenly exposed positive core, so that the He⁺ signal is suppressed.

Post-collision interaction with recapture is responsible for shifting the observed He^– threshold energy. Shortly after the 1s electron in He^– is photodetached, the atom ejects a second electron in an Auger decay process (a). The high-energy Auger electron quickly overtakes the photoelectron (b) which then sees the exposed He nucleus (c) and can finally be recaptured (d) to form a neutral He atom (shown in an excited state), which does not contribute to the He⁺ signal monitored in these experiments.

To investigate the effect of the angular momentum l, photodetachment of the 2p electron from S^– was also studied. In this case the absorption of the photon will cause the photoelectron to leave with l = 1 ± 1 = 0 or 2, i.e., an s-wave or d-wave. The d-wave component has always been too weak to be observed, and the s-wave threshold law should be expected: ε^1/2. However, the group observed a change in threshold shape as the d-wave contribution grew.

Observed S²⁺ signal (S⁺ and S³⁺ production is similar) from the photodetachment of a 2p electron from S^–. The s-wave law (ε^1/2) is followed closely up to nearly 3 eV above the threshold (solid curve), after which the inclusion of the weak d-wave is necessary to extend the agreement (dashed curve). In the inset, the s-wave component has been subtracted from the data to make the d-wave law (ε^5/2) apparent. The departure beyond about 166 eV is likely due to the opening of additional detachment channels.

Furthermore, the wide energy range of agreement of the threshold law to the observed signal was unprecedented; the Wigner law has previously been observed to apply only some 0.01 to 0.1 eV above the threshold, compared to the nearly 3 eV in inner-shell photodetachment, a finding that is surprising and remains unexplained. Also surprising is that this range of agreement was further improved with the inclusion of a d-wave component to the fit. This is the first time a d-wave has been observed in this way.

Research conducted by R. C. Bilodeau (Western Michigan University and ALS); J.D. Bozek and G.D. Ackerman (ALS); N. D. Gibson and C.W. Walter (Denison University); I. Dumitriu and N. Berrah (Western Michigan University).

Research Funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.

Publications about this research: R.C. Bilodeau, J.D. Bozek, N.D. Gibson, C.W. Walter, G.D. Ackerman, I. Dumitriu, and N. Berrah, “Inner-shell photodetachment thresholds: Unexpected long-range validity of the Wigner law,” Phys. Rev. Lett. 95, 083001 (2005); R.C. Bilodeau, N.D. Gibson, J.D. Bozek, C.W. Walter, G.D. Ackerman, P. Andersson, J.G. Heredia, M. Perri, and N. Berrah, “High-charge-state formation following inner-shell photodetachment from S^–,” Phys. Rev. A 72, 050701(R) (2005); R.C. Bilodeau, J.D. Bozek, G.D. Ackerman, A. Aguilar, and N. Berrah, “Photodetachment of He^– near the 1s threshold: Absolute cross-section measurements and postcollision interactions,” Phys. Rev. A 73, 034701 (2006).