One − electron capture

Below about 1 keV/amu HeII(np → 1s) line emission from np states with n ≥ 3 becomes negligible in comparison to the Lyman-α emission [10, 23]. In figure 3, (left panel) the present HeII(2p→1s) line emission cross sections are seen to present a smooth extension of previous data towards lower energies. The theoretical results by Saha et al.

[24] are in good agreement with the data, except maybe just above 1 keV/amu where they exhibit a small local maximum, which is not observed in the data.

By means of translational energy spectroscopy (TES) Hodgkinson et al. [25] deter-mined cross sections for capture into He¹⁺(n= 2), i.e. the sum of capture into the degen-erate He¹⁺(2s) and He¹⁺(2p) states. In the energy range in which the TES experiments were performed (0.5–2 keV/amu), the cross section for capture into the 2s state is small as compared to the cross section for capture into 2p [23, 26]. Therefore, at least by and large the TES measurements should yield cross sections similar to our HeII(np→1s) line

lower energies the TES and PES data diverge strongly. At the lowest energy of the TES measurements, 0.5 keV/amu, the difference is already a factor of 8, see figure 3.

Considering the absolute calibration of the cross sectional data it is of note that our PES data were calibrated to previous data from our group at 5 keV/amu [22, 23]. By this procedure we obtain an absolute systematic uncertainty of 20% associated to the PES data. The TES results are put on an absolute scale by normalizing the sum of all reaction channels to the total one-electron capture cross sections determined by Nuttet al. [27]. It is to be realized that the work by Nuttet al.is also the main source in the 0.5–2 keV/amu energy range on which the recommended cross sections for one-electron capture are based [16]. The theoretical and experimental one-electron capture cross sections by respectively Shimakura et al.[21] and Okuno et al.[17] exceed the data of Nuttet al. [27] by a factor of 2 to 3. Assuming the unlikely scenario that the data by Nutt et al. would be off by a factor of 2 to 3, there remains a difference of approximately a factor of 3 between the PES and TES data. Together with the Queen’s University of Belfast group (McCullough et al.) we will attempt to resolve these inconsistencies between different experimental and theoretical data sets.

The difference between the cross sections for HeII(np→1s) line emission and those for total charge transfer increases for lower impact energies. The total one-electron capture cross section σtot is equal to the sum of all Lyman transitions, the metastable He⁺(2s) production cross section σp(2s), and the cross section for direct capture into the He⁺(1s) ground state,σc(1s) (see e.g. [23]), i.e.,

σtot =

nσ(np →1s) +σp(2s) +σc(1s) (1)

As mentioned before, at low impact energiesσp(2s) is small compared to

nσ(np→ 1s) [23, 26] and there is no significant contribution from np states with n ≥3 to Lyman emission. Thus the HeII(2p → 1s) emission cross section might be compared directly to the total cross sections (see figure 3). The increasing difference between the respective cross sections towards lower impact energies indicates that one-electron capture goes fully into the He⁺(1s) ground state when decreasing the projectile energy. This is in line with our previous conclusions [23] based on measurements above 1 keV/amu and existing TES [28] and fragmentation work [27], that the dominant charge transfer channel swaps around a few keV/amu from non-dissociative capture into 2p

He²⁺+H2 →He¹⁺(2p) +H2⁺ (2)

to capture into the ground state associated with target-ion dissociation and excitation He²⁺+H2 →He¹⁺(1s) +H⁺+H(n≥2). (3) The fact that the dissociative channel produces mainly excited atomic hydrogen was inferred from our H Lyman-α measurements. The H Lyman-α cross sections were of similar magnitude as the He⁺(1s) cross sections [23]. This indirect evidence was later

FIG. 4. Comparison of n= 3→n = 2line emission cross sections following one-electron capture in collisions of six-fold charged C, N, O, and Ne ions colliding on He (partly from our previous work [30–33]. The theoretical curves are constructed from AO calculations for C⁶⁺ [34] and MO calculations for O⁶⁺ [35].

reaction channel mandates that theoretical calculations of one-electron transfer at low energies need to include an appropriate description of both electrons and the molecular nature of the target.

3.2. T wo−electron capture

Results for two-electron capture are depicted in the right panel of figure 3. In the overlapping energy range of 0.5–1 keV/amu, the results of Okuno et al. [17] exceed the recommended data [16] by a factor of 2–3, just as for one-electron capture. The MO calculations by Shimakura et al.[21] predict a two-electron capture cross section approx-imately half of the ones measured by Okuno et al. [17]. Our measured HeI(1s2p→ 1s²) line emission cross sections (cf. figure 3) follow the same energy dependence as the total two-electron capture cross sections by Okuno et al. [17] and Shimakura et al. [21], but are smaller by a factor of 10 and 5, respectively. This seems to imply that capture into He(1s2p) is a weak two-electron capture channel. It is of note that capture into the He(1s3s) and He(1s3d) states is included in the HeI(1s2p → 1s²) line emission because they decay to the He(1s2p) state. Therefore, capture processes into He(1s3s) and He(1s3d) states are also minor reaction channels. In our spectra we do not observe any appreciable emission from HeI(1snp→1s²) lines with n ≥3 [4].

From this it is concluded that two-electron capture proceeds mainly into either the

FIG. 5. Comparison of our total one-electron capture cross sections for N⁴⁺– H2 and N⁵⁺– H2. The total cross sections are determined from the relevant line emission cross sections.

seems the most likely, since the total amount of energy needed to remove the electrons from H2 molecules is 50.8 eV (assuming Franck-Condon type transitions). This should be compared with the binding energies of the He(1s²) and He(1s2s¹S) states which are 79 and 58.4 eV, respectively. From the potential-energy curves of the He²⁺ - H2 system it is seen that the He(1s²) state can only be populated at small impact parameters [21] and therefore a large cross section is unlikely. We conclude that the difference between our partial cross section results and the total two-electron capture cross sections of Okunoet al. must be due to capture into the He(1s2s¹S) metastable state.

The MO calculations [21] did predict that at energies below 100 eV/amu where two-electron capture dominates over one-electron capture, singly excited He(1s3l) states are populated. The predicted strong population of these He(1s3l) states has been used to explain the aforementioned anomalously intense HeI(1s3l → 1s2l) emission observed when helium plasmas are brought in contact with cold hydrogen molecules. There are two possible explanations for the apparent discrepancy. 1) Ion temperatures in the helium plasmas, i.e., the corresponding ion energies are much lower than the energies in both our

to higher levels, which is a trend well-known from Landau-Zener type of calculations.

2) The energy gap between the He(1s2s¹S) state and the He(1s3l) states is so small that the He(1s3l) states can very efficiently be populated from He(1s2s¹S) by low-energy plasma electrons. At low temperatures electron impact excitation of HeI(1s2s¹S→1s3l) transitions is associated with large collision strengths [29].