Electron-ion collision spectroscopy: Lithium-like xenon ions

The resonant process of dielectronic recombination (DR) has been applied as a spectroscopic tool to investigate intra-$L$-shell excitations $2s-2p_j$ in Li-like ${}^{136}{\text{Xe}}^{51}+$. The experiments were carried out at the electron cooler of the Experimental Storage Ring of the GSI-Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. The observed center-of-mass energy range (0–505 eV) covers all resonances associated with the $2s+e^{-}\to {\left(2p_{1/2}n{l}_j\right)}_J$ and ${\left(2p_{3/2}n{l}_j\right)}_J$ DR processes. Energies and strengths of isolated $2p_{1/2}n$ and $2p_{3/2}n$ DR-resonance groups were obtained for principal quantum numbers $n$ up to 43 and 36, respectively. The $2s-2p_{1/2}$ and $2s-2p_{3/2}$ excitation energies were deduced to be 119.816(42) eV and 492.174(52) eV. The excitation energies are compared with previous measurements of other groups and with recent QED calculations. In addition, the experimental spectra and extracted resonance strengths are compared with multiconfiguration Dirac-Fock calculations. Measurements and theory are found to be in good agreement with each other.

Figure 1

Distribution of collision angles in the electron and ion beam overlap section of the electron cooler (left), and potential distribution of the drift tube used to accelerate or decelerate the electrons (right). The drift tubes are schematically shown as well. For details, see the text.

Figure 2

Simulated Monte Carlo response function $f(E^{\prime },E_s)$ for a set energy value in the center-of-mass frame of $E_s=10\text{eV}$ (black line) for a cathode potential $U_{\mathrm{cath}}=32.088\text{kV}$ and a corresponding drift tube voltage $U_{\mathrm{dt}}^{\left(M\right)}=1161.21\text{V}$. The temperatures $k_B{T}_{\perp }=120$ meV and $k_B{T}_{\parallel }=200$ meV were used. Please note the axis break and the according different scales used to emphasize details of the response function.

Figure 3

Rate coefficients of a synthetic DR resonance at $E_{\mathrm{DR}}=10$ eV (vertical line). Displayed are the rate coefficient as obtained from a convolution with the anisotropic Maxwellian velocity distribution [Eq. (9)] with $k_B{T}_{\parallel }=200\mu \text{eV}$ and $k_B{T}_{\perp }=120\text{meV}$ (black line) and the rate coefficient from a full Monte Carlo simulation (gray area). Please note the axis break and the according different scales.

Figure 4

Measured ${}^{136}{\text{Xe}}^{51+}$ DR spectrum (black line) after substraction of residual gas and RR background. Resonance energies, using the excitation energies $E_{\mathrm{ex}}(2s\to 2p_{1/2})=119.820$ eV from Ref. [9] and $E_{\mathrm{ex}}(2s\to 2p_{1/2})=492.4$ eV from Ref. [10] and hydrogen-like Dirac binding energies [Eq. (13)], are indicated by two sets of vertical bars. The shaded areas are the results of our MCDF calculations for ${\mathrm{Xe}}^{51+}\left(2s\right)+e^{-}\to {\mathrm{Xe}}^{50+}{\left(2p_{1/2}n{l}_j\right)}_J$ (light gray) and ${\mathrm{Xe}}^{50+}{\left(2p_{3/2}n{l}_j\right)}_J$ (dark gray) and cover DR Rydberg resonances for $n$ up to 28. The MCDF energies are shifted by the same values $-0.47$ and $-0.345$ eV for each of the $2p_{1/2}n{l}_j$ and $2p_{3/2}n{l}_j$ resonances, respectively. The calculated cross sections have been convoluted with the experimental response functions (see Sec. 3c3).

Figure 5

Measured ${}^{136}{\text{Xe}}^{51+}$ DR spectrum in the energy range of the $2s+e^{-}\to {\left(2p_{3/2}9l_j\right)}_J$ resonance group (black line) in comparison with our MCDF calculation for the ${\left(2p_{3/2}9{\mathrm{l}}_j\right)}_J$ resonance group (dark shaded areas) and for the $n=22$ and $n=23$ groups of the $2p_{1/2}n{l}_j$ Rydberg resonance series (light shaded areas) shifted by $-0.345$ eV and $-0.47$ eV, respectively. The theoretical cross sections have been convoluted with the Monte Carlo response function (see Sec. 3c3). Corresponding resonance strengths and (shifted) energies from our MCDF calculations are given by black and white vertical lines for ${\left(2p_{3/2}9{\mathrm{l}}_j\right)}_J$ and ${\left(2p_{1/2}n{l}_j\right)}_J$ resonances, respectively. The vertical bars indicate resonance positions from the energy-shifted MCDF theory (black) and from the hydrogenlike (Dirac) approximation (gray). The later are calculated according to Eqs. (12) and (13) with measured $2s\to 2p_j$ excitation energies from Refs. [9, 10].

Figure 6

${}^{136}{\text{Xe}}^{51+}$ DR spectrum in the energy range of the $2s+e^{-}\to {\left(2p_{1/2}18l_j\right)}_J$ resonance group. The experimental results (black line) are compared with the result of the MCDF calculation (light shaded area). The theoretical energy scale is shifted by $-0.47$ eV and the theoretical cross section has been convoluted with the experimental response function (see Sec. 3c3). Theoretical resonance strengths and (shifted) energies are given by black vertical lines. Black and gray vertical bars indicate resonance positions from the energy-shifted MCDF theory and from $2s\to 2p_{1/2}$ excitation energy [9] combined with hydrogen-like approximated binding energies, respectively.

Figure 7

$•$ Residua $E_{\mathrm{res}}$ (see text) versus calibrated energy $E_{\mathrm{c}}.\mathrm{m}.$. The extracted energy-dependent $1\sigma$ energy uncertainty [Eq. (15)] is indicated as a gray area. The calibration was carried out with the combined data of the present experiment with Li-like ${\mathrm{Xe}}^{51+}$ and a second experiment with Be-like ${\mathrm{Xe}}^{50+}$ [44] that used identical settings.

Figure 8

Measured DR spectrum (solid line), fitted synthetic DR spectrum (gray area), and corresponding artificial resonance energies $E_{\mathrm{DR}},\mathit{i}$ and resonance strengths $S_i$ (dashed bars). Full bars represent the average energies ${\overline{E}}_{\mathrm{DR}}$ (see text and Table 1) and strengths $S={\sum }_i{S}_i$. (a) $2s+e^{-}\to {\left(2p_{1/2}18l_j\right)}_J$ resonance group. (b) $2s+e^{-}\to {\left(2p_{3/2}9l_j\right)}_J$ resonance group. The hatched areas belong to the $2p_{1/2}n$ resonance series.

Figure 9

$\Delta n=0$ transition energies in ${}^A{\text{Xe}}^{51+}$. This work ($⊠$), previous experimental results ($\square$) [6, 9, 10, 11], and theory ($•$) [13, 14, 45, 46, 47, 48, 49, 50]. Panel (a) shows data for the $2s-2p_{1/2}$ transition, and panel (b) that for the $2s-2p_{3/2}$ transition. The data are the same as in Table 2.

Figure 10

Measured and theoretical scaled DR resonance strengths for $\Delta n=0$ DR in ${}^{136}{\text{Xe}}^{51+}$. Experimental data for $2s+e^{-}\to 2p_{1/2}n$ ($•$) and $2s+e^{-}\to 2p_{3/2}n$ ($\blacksquare$). Open symbols ($\circ$ and $\square$) show the corresponding results of the present MCDF calculations. Shaded and hatched areas show the resonance strengths as derived from the experiment for unresolved very high principal quantum numbers $n$.