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 cross section of the two-electron ionization differential in one-electron energy $d\sigma ^{++}(\omega )/d\epsilon$. We found that at high photon energy prominent oscillations appear in it due to reflection of the second, slow electron wave on the $$ shell, which "dies out" at relatively high $\epsilon$ values, of about 2$\div$3 two-electron ionization potentials. The results were presented for ratios $R_{C_{60}}(\omega ,\epsilon)\equiv d\sigma ^{++}(\omega ,\epsilon)/d\sigma ^{a++}(\omega,\epsilon)$, where $d\sigma ^{a++}(\omega,\epsilon)/d\epsilon$ is the two-electron differential photoionization cross section. We have calculated the ratio $R_{i,ful}= \sigma_{i} ^{++}(\omega)/\sigma_{i}^{a++}(\omega)$, that accounts for 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.