Photoionization of Ce$^{3+}$@C$_{82 }$

Photoionization cross section for the Ce$^{3+ }$@C$_{82}$ endohedral fullerene in the energy region 100-150 eV has been studied using our open-shell random phase approximation with exchange method and the C$_{82}$ model potential. Electron affinity (EA) of the C$_{82}$ has been calculated using the density functional theory. The C$_{82}$ fullerene was described by an attractive short range spherical well with potential V(r), given by V(r) =- V$_{0}$ for r$_{i}<$ r$<$ r$_{0}$, otherwise V(r) =0, V$_{0}$ was obtained by solving the resultant transcendental equation using the calculated EA value. The wave functions of the Ce$^{3+}$ confined inside the C$_{82}$ have been calculated by solving the Schr\"{o}dinger equation with both regular and irregular solutions and the continuous boundary conditions of the wave functions and their logarithmic derivatives at r$_{i}$ and r$_{0. }$Our calculation included 32 ionization channels from 5s, 5p and 4f subshells and 14 channels from the 4d$^{10}$ 4f +h$\nu \to $ 4d$^{9}$4f$^{2}$ photoexcitation.$_{ }$Finally the RPAE equation was solved to obtain the partial cross sections with a total of 16 $^{2}$D states, 16 $^{2}$G states and 14 $^{2}$F states. The photoionization of Ce$^{3+}$@C$_{82}$ shows both the resonance and suppression effect and demonstrates a more stronger resonance peak at 106 eV.