Partial cross sections of doubly excited helium below the ionization threshold $I_7$

Partial photoionization cross sections (PCSs), ${\sigma }_n$, leading to final ionic states of helium, ${\text{He}}^{+}\left(n\right)$, were measured at BESSY II in the region of doubly excited helium up to the ionization threshold $I_7$ of ${\text{He}}^{+}$. The experiments were performed with a time-of-flight (TOF) electron spectrometer and high photon resolution, $\Delta E\cong 6\text{meV}$. The results of these measurements are a most critical assessment of the decay dynamics of double-excitation resonances and agree well with those of recent eigenchannel $R$-matrix calculations. They also confirm the propensity rules set up for the autoionization of doubly excitated states. The mirroring behavior in the PCSs predicted recently by Liu and Starace is only partially observed. By discussing the formulas given by these authors in a more general context, the specific behavior of the PCSs of helium with respect to mirroring can be understood. The mirroring compensation properties between the “fractional partial cross sections” ${\gamma }_P={\sigma }_P∕{\sigma }_T$ and ${\gamma }_Q={\sigma }_Q∕{\sigma }_T$, with ${\sigma }_T={\sigma }_P+{\sigma }_Q$, are introduced and discussed.

Figure 1

The bar diagram along the binding energy axis represents an experimental photoemission spectrum measured with $h\nu =76.2\text{eV}$, with the satellites $n=2$ to 4 representing the ionic final states of ${\text{He}}^{+}\left(n\right)$. The solid curve through the data points represents the PCS ${\sigma }_3$ that can be derived from a large number of such photoemission spectra (not shown here) recorded at different photon energies. For details see text.

Figure 2

Experimental partial cross sections ${\sigma }_n^5$ leading to the final states ${\text{He}}^{+}\left(n\right)$, with $n=2$, 3, and 4, along with the results of the eigenchannel $R$-matrix calculations. The data were taken in the photon-energy region between $75.68\text{eV}$ and $76.77\text{eV}$. The two vertical-bar diagrams in the upper part of the figure give the assignments of the double-excitation resonances by specifying $n^{\prime }$; with the widths of bars being proportional to the linewidths of the corresponding resonances [5]. The vertical arrow in the upper right corner marks the calculated energy of the perturber $6,4_6$. The filled data points are the present experimental results, with the solid curves through the data points representing the fit results. The dashed curves represent the data by Menzel et al. [9] and the dashed-dotted curves the results of the $R$-matrix calculations convoluted with a Gaussian of $6\text{meV}$ width (FWHM) to simulate finite experimental resolution.

Figure 3

Experimental partial cross sections ${\sigma }_n^6$ leading to the final states ${\text{He}}^{+}\left(n\right)$, with $n=2,3,4$, and 5, respectively, in the energy region from $76.85\text{eV}$ to $77.56\text{eV}$, along with the results of the eigenchannel $R$-matrix calculations; for details, see the caption of Fig. 2.

Figure 4

Experimental partial cross sections ${\sigma }_n^7$ leading to the final states ${\text{He}}^{+}\left(n\right)$, with $n=2,3,4$, and 5, respectively, in the energy region from $77.56\text{eV}$ to $77.92\text{eV}$, along with the results of the eigenchannel $R$-matrix calculations. Note that the plotted theoretical results were shifted by $12\text{meV}$ to lower energies; for details, see the caption of Fig. 2.

Figure 5

Partial photoionization cross sections ${\sigma }_n^N$ as a function of scaled photon energy. The vertical arrows mark the energies of the perturbers.

Figure 6

Cross sections below the ionization threshold $I_6$ obtained from eigenchannel $R$ matrix calculations and convoluted with a Gaussian resolution function of $6\text{meV}$ width (FWHM). (a) Total cross section ${\sigma }_T$. In (b) and (c) the PCS ${\sigma }_P$ and ${\sigma }_Q$ were established in different ways: (b1) ${\sigma }_P={\sigma }_1$ and (b2) ${\sigma }_Q={\sigma }_2+{\sigma }_3+{\sigma }_4+{\sigma }_5$; (c1) ${\sigma }_P={\sigma }_1+{\sigma }_3+{\sigma }_4+{\sigma }_5$ and (c2) ${\sigma }_Q={\sigma }_2$.

Figure 7

Fractional partial cross sections ${\gamma }_P={\sigma }_P∕{\sigma }_T$ and ${\gamma }_Q={\sigma }_Q∕{\sigma }_T$ below the ionization threshold $I_6$ obtained from eigenchannel $R$-matrix calculations and convoluted with a Gaussian resolution of $6\text{meV}$ width (FWHM).