Two-electron photoionization of endohedral atoms

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