Partial Photoionization Cross Sections and Angular Distributions for Double Excitation of Helium up to the $N=13$ Threshold

Partial photoionization cross sections ${\sigma }_N(E_{\gamma })$ and photoelectron angular distributions ${\beta }_N(E_{\gamma })$ were measured for the final ionic states ${\mathrm{He}}^{+}(N>4)$ in the region between the $N=8$ and $N=13$ thresholds ($E_{\gamma }>78.155\mathrm{eV}$) using the cold target recoil ion momentum spectroscopy technique (COLTRIMS). Comparison of the experimental data with two independent sets of theoretical predictions reveals disagreement for the branching ratios to the various ${\mathrm{He}}_N^{+}$ states. The angular distributions just below the double ionization threshold suggest an excitation process for highly excited $N$ states similar to the Wannier mechanism for double ionization.

Figure 1

(a) The kinetic energies of the emitted photoelectrons displayed as function of the photon energy. The lines can be assigned to different hydrogenlike finals states of the residual ${\mathrm{He}}^{+}(N)$ ion with $N$ denoting the principal quantum number. (b) The relative partial cross sections ${\sigma }_N(E_{\gamma })$. The steplike structure in ${\sigma }_{N=5}$ is a technical artifact. [The curve should be shifted up for $E>78.5\mathrm{eV}$]. The data was normalized by dividing the count rate of the various channels by the total number of detected ${\mathrm{He}}^{+}$ ions. This method ensures that fluctuations in the absolute count rate, possibly caused by a varying target density or photon flux, do not affect the results.

Figure 2

Comparison between experiment (black) and theory. The blue (dark gray) and the red (light gray) curves are results from $R$-matrix [7] and CCC calculations (both in the velocity gauge). The statistical errors in each black curve are very small (about twice the line width). However, there might be a systematic error (less than 10%) that could reduce the measured cross sections as a whole. The theoretical data were convoluted with a Gaussian distribution of 3.9 meV FWHM. The energy scale is shown relative to the respective experimental or theoretical double ionization thresholds (Experiment: 79.0052 eV, $R$ matrix: 79.006 eV, CCC: 79.0089 eV). The overall mismatch between the curves is 4.5 meV (CCC-experiment) and 7.0 meV ($R$ matrix-experiment). A general shift between the curves is indicated by a tilted dashed line.

Figure 3

(a) The angular distributions ($\beta$ parameter) of photoelectrons from different channels as a function of the photon energy. The partial cross sections ${\sigma }_N$, displayed in arbitrary units, demonstrate the correlation between both curves. This correlation is a known feature which was also observed at lower energies [12]. Because of space limitations other measured $\beta$ parameters for $N=5$, 6, 8, 10 are not shown. The larger error bars are assigned to the middle part of the scan where less statistics was acquired ($78.48\mathrm{eV}<E_{\gamma }<78.792\mathrm{eV}$). (b) Comparison with two calculations at the corresponding threshold for each final state $N$. The experimental error bars are of the same size as the circles. (c) The ionization and excitation into high $N$ states depends on the orientation of the $\mathrm{e}\mathrm{\text{−}}\alpha \mathrm{\text{−}}\mathrm{e}$ system relative to the polarization vector. Highly excited final states are populated preferably in conjunction with $\beta \approx -1$.