Photoionization of Xe$^{+ }$ion confined in C$_{60}$ fullerene*

Photoionization cross section for the Xe$^{+ }$@C$_{60 }$ endohedral fullerene has been studied using our open-shell random phase approximation with exchange method and a C$_{60}$ model potential. The C$_{60}$ 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$_{0}$=0.3028 a.u. The wave functions of the Xe$^{+}$ confined inside the C$_{60}$ have been evaluated 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 all the intershell coupling among the 4d-$\varepsilon $f, 5s-$\varepsilon $p, and 5p-$\varepsilon $s,$\varepsilon $d transitions. $_{ }$The RPAE equation was solved to obtain the partial cross sections with a total of 12 $^{2}$D states, 9 $^{2}$P states and 6 $^{2}$S states. The photoionization of Xe$^{+}$@C$_{60}$ shows stronger correlated confinement resonances.