Photo-double-ionization of He-like and Be-like systems in excited states within an intermediate-energy $R$-matrix framework

In this article we apply the intermediate-energy $R$-matrix method to photo-double-ionization of the metastable $1s2s{}^{1,3}{S}^e$ and $1s2p{}^{1,3}{P}^o$ states of He, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$, along with the $1s^{2}2s2p{}^{1,3}{P}^o$ and $1s^{2}2s3s{}^{1,3}{S}^e$ states of Be, ${\mathrm{O}}^{4+}$, and ${\mathrm{Ne}}^{6+}$. We compare our results with other theoretical data where possible and achieve excellent agreement. We examine trends between the various excited states and ground states of the systems.

Figure 1

Photo-double-ionization cross section for the $1s2s{}^{1,3}{S}^e$ states of He. Black solid line: Present calculation; blue diamonds: CCC data Kheifets $et$ $al$. [15]; green squares: TDCC data of Colgan and Pindzola [10]; brown dashed line: shape function of Pattard [16] [Eq. (3)] fit to the current data.

Figure 2

Photo-double-ionization cross section for the $1s2s{}^3{S}^e$ state of ${\mathrm{Li}}^{+}$. Black solid line: Present calculation; red circles: RMPS data of McLaughlin [3]; green squares: TDCC data of Kleiman [9]; brown dashed line: shape function of Pattard [16] [Eq. (3)] fit to the current data.

Figure 3

Photo-double-ionization cross section for the ground and excited $S$ and $P$ states of He, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$.

Figure 4

Photo-double-ionization cross section from the ground, and $S$ and $P$ excited states of He, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$ multiplied by $Z^4$ and plotted against the excess energy above the double ionization threshold divided by $Z^2$.

Figure 5

Ratio of double to single photoionization from the ground and $S$ and $P$ excited states of He, ${\mathrm{O}}^{6+}$, and ${\mathrm{Ne}}^{8+}$ multiplied by $Z^2$ and plotted against the excess energy above the double ionization threshold divided by $Z^2$.

Figure 6

Photo-double-ionization cross section for the $1s^{2}2s2p{}^{3}P$ state of Be. Black solid line: Present calculation; red circles: RMPS data of Griffin $et$ $al$ [11]; blue squares: data from a hybrid atomic orbital with numerical grid method based on the finite-element discrete-variable representation and exterior complex scaling by Yip $et$ $al$. [12]; brown dashed line: shape function of Pattard [16] [Eq. (3)] fit to the current data.

Figure 7

Photo-double-ionization cross section from the ground and $S$ and $P$ excited states of Be, ${\mathrm{O}}^{4+}$, and ${\mathrm{Ne}}^{6+}$.

Figure 8

Photo-double-ionization cross section from the ground and $S$ and $P$ excited states of Be, ${\mathrm{O}}^{4+}$, and ${\mathrm{Ne}}^{6+}$ multiplied by ${\epsilon }_{\mathrm{diff}}^2$ and plotted against the excess energy above the double ionization threshold divided by ${\epsilon }_{\mathrm{diff}}$.