Off center effect on the photoabsorption spectrum of the Xe@C$_{60}$ endohedral fullerene

The absolute differential oscillator strengths (DOS's) for the photoabsorption of the Xe atom encapsulated at different locations of the C$_{60}$ have been evaluated using the time-dependent-density-functional-theory. The calculations are performed in the energy region of the Xe 4$d$ giant resonance with the locations of the Xe atom at the center and 0.2 {\AA}, 0.3 {\AA}, 0.4 {\AA}, 0.5 {\AA}, 0.8 {\AA}, 1.5 {\AA}, 2.0 {\AA} away from the center. The results demonstrate that the main confinement resonances result only when the Xe atom is located in a very small region of the C$_{60}$. This region is about 0.3 {\AA} around the center of the C$_{60}$ (3.5 {\AA} is the C$_{60}$ radius). These results explain the absence of the confinement resonances in the photoionization of the encapsulated lanthanide atoms such as Ce@C$_{82}$ [1], Pr@C$_{82}$ [2] as these atoms (Ce, Pr) are usually located 1.8-2.0 {\AA} off the center of the C$_{82}$. \\[4pt] [1] K Mitsuke et al, J. Chem. Phys. {\bf 122} 064304 (2005)\\[0pt] [2] H Katayanag et al, J. Quant. Spectrosc. Radiat. Transfer, {\bf 109} 1590 (2008)