Random phase approximation with exchange for the photoionization of confined atoms: Xe in C₆₀ fullerene

Photoionization of a Xe atom confined inside C$_{60}$ has been studied using the random phase approximation with exchange (RPAE) method. The C$_{60}$ fullerene has been descr ibed by an attractive short range spherical well with potential $V(r)$, given by $V(r)=-V_ 0$ for $r_i<r<r_0$, otherwise $V(r)=0$ where $r_i$ and $r_0$ are respectively, the inner and outer radii of the spherical shell. The radial parts of the wave funct ion in the three regions $r<r_i$, $r_i<r<r_0$ and $r>r_0$ have been obtained by solving the Schr\"{o}dinger equation using both regular and irregular solutions and the continuous boundary conditions at $r_i$ and $r_0$. The photoionization cross sections for the Xe 4d, $5s$ and $5p$ ele ctrons in the Xe@C$_{60}$ endohedral molecule have been evaluated and compared with those of the photoionization for the free Xe atom and other previo us calculations for the Xe@C$_{60}$ fullerene. Our method surmounted the weaknesses of the previous model potential calculation s and demonstrated significantly stronger correlated confinement resonances for the Xe@C$_{60}$ photoionization.