Universal shape function for the double ionization cross section of negative ions by electron impact

It is shown that recently measured cross sections for double ionization of negative ions (H−, O−, and C−) possess a universal shape when plotted in suitable dimensionless units. The shape can be represented with a simple analytical function, following the same principles as it has been done in establishing a universal shape function for single ionization [Rost and Pattard 1997 Phys. Rev. A 55 R5]. Thereby, it is demonstrated that direct double ionization dominates the cross section for the targets considered. PACS numbers: 34.50, 34.80, 82.30 In a complex ion such as O− double ionization can proceed along different paths utilizing intermediate excited (autoionizing) states. How important are these indirect processes in comparison with direct double ionization (DDI) to describe total cross sections for double ionization (DI) of negative ions by electron impact? A calculation of a cross section from DDI processes alone compared to the experimental results could answer this question. However, neither such a calculation nor a full calculation exists for the published experimental cross sections involving the target ions H− [1] and O−, C− [2]. Given this situation we have developed an alternative theoretical approach which has been applied successfully to the single ionization of atoms [3] and positively charged ions [4]. For these species we have established the existence and analytical form of a universal shape function for the cross section. In contrast to well known semi-empirical formulae (e.g. the Lotz formula [5]) our shape function uses the analytically known form of the cross section at high and low energies. Moreover, and this is crucial, the universal shape emerges only if the energy is measured from the ionization threshold I of the respective process, i.e. E ≥ 0. (Usually, the energy is given in terms of the impact energy E + I). The shape function itself is parameter free. It can be directly compared to the experimental cross section if the latter is plotted in dimensionless coordinates where the cross section y is written in terms of its maximum value y = σ/σM and the energy is expressed in a scale which corresponds to the energy EM where the maximum cross section appears, x = E/EM . In practice, these two quantities σM and EM may be viewed as fitting parameters and determined by a fit of the data to σ(E) = σMf(E/EM ) (1) Letter to the Editor 2 Table 1. Scaling parameters EM , σM with uncertainties obtained by fitting the experimental cross sections from figure 2 with (1). target EM (eV) σM (10 cm) H− 36.0±0.6 0.935±0.008 O− 100.3±0.6 5.33 ±0.02 C− 57.0±1.0 7.44 ±0.07 where the shape function is given by