Two-electron photoionization of endohedral atoms

Using $\mathrm{He}@{\mathrm{C}}_{60}$ as an example, we demonstrate that the static potential of the fullerene core essentially alters the cross section of the two-electron ionization differential in one-electron energy $d{\sigma }^{++}\left(\omega \right)∕d\epsilon$. We found that at high photon energy prominent oscillations appear in it due to reflection of the second slow electron wave on the ${\mathrm{C}}_{60}$ shell, which “dies out” at relatively high $\epsilon$ values, of about 2–3 two-electron ionization potentials. The results were presented for ratios $R_{{\mathrm{C}}_{60}}(\omega ,\epsilon )\equiv d{\sigma }^{++}(\omega ,\epsilon )∕d{\sigma }^{a++}(\omega ,\epsilon )$, where $d{\sigma }^{a++}(\omega ,\epsilon )∕d\epsilon$ is the two-electron differential photoionization cross section. We have calculated the ratio $R_{i,\mathrm{ful}}={\sigma }_i^{++}\left(\omega \right)∕{\sigma }_i^{a++}\left(\omega \right)$, that accounts for reflection of both photoelectrons by the ${\mathrm{C}}_{60}$ shell. We have also calculated the value of two-electron photoionization cross section ${\sigma }^{++}\left(\omega \right)$ and found that this value is close to that of an isolated He atom. Results similar to $\mathrm{He}@{\mathrm{C}}_{60}$ are presented for $\mathrm{He}@{\mathrm{C}}_{70}$ and $\mathrm{He}@{\mathrm{C}}_{76}$.

Figure 1

The reflection and refraction factors $D_L^2$ $(L=0,1)$ as a function of photoelectron energy $\epsilon$ for $\mathrm{He}@{\mathrm{C}}_{60}$.

Figure 2

The cross sections ratio ${\tilde{R}}_{{\mathrm{C}}_{60}}(\omega ,\epsilon )$ as a function of photoelectron energy $\epsilon$ for different values of photon energy $\omega$.

Figure 3

The cross sections ratios ${\tilde{R}}_{{\mathrm{C}}_{60}}^{\left(h\right)}$, ${\tilde{R}}_{{\mathrm{C}}_{60}}^{\left(l\right)}$, and ${\xi }_{{\mathrm{C}}_{60}}\left(\omega \right)=R_{{\mathrm{C}}_{60}}\left(\omega \right)∕D_1^2(\omega -I^{++})$ as functions of $\omega$ for $\mathrm{He}@{\mathrm{C}}_{60}$.

Figure 4

The reflection and refraction factors $D_1^2$ as a function of photoelectron energy $\epsilon$ for $\mathrm{He}@C_N$ with $N=60,70,76$.

Figure 5

The cross sections ratio ${\tilde{R}}_{i,\mathrm{ful}}$ as a function of photon energy $\omega$ for $\mathrm{He}@{\mathrm{C}}_{60}$, $\mathrm{He}@{\mathrm{C}}_{70}$, and $\mathrm{He}@{\mathrm{C}}_{76}$.

Figure 6

The cross sections ratios ${\tilde{R}}_C^{\left(h\right)}$ as a function of $\omega$ for $\mathrm{He}@{\mathrm{C}}_{60}$, $\mathrm{He}@{\mathrm{C}}_{70}$, and $\mathrm{He}@{\mathrm{C}}_{76}$.