Trends in correlation and confinement impacts on the e-Xe@C$_{60}$ generalized oscillator strengths*

The response of endohedral Xe@C$_{60}$ to fast electron impact ionization is theoretically studied by calculating its 4d, 5s and 5p generalized oscillators strengths (GOS). The calculation methodology combines the plane wave Born approximation, single-electron Hartree-Fock approximation, and multi-electron random phase approximation with exchange, all in the presence of the C$_{60}$ confinement. The confinement is accounted for in the framework of both a spherical $\delta$-potential [1] and square-well-potential [2] models to evaluate the effect of the finite thickness of the C$_{60}$ cage on said GOS's. Impressive confinement brought impact on the latter is revealed. Vitality of accounting for electron correlation in calculations of the Xe@C$_{60}$ 5s and 5p GOS's is demonstrated. Trends in contributions of multipolar transitions beyond dipole transitions in the calculated GOS's are unraveled. We challenge experimentalists to conduct corresponding measurements.\\[4pt] [1] M.Ya. Amusia, A.~S.~Baltenkov, and B. G. Krakov, Phys. Lett. A, \textbf{243}, 99 (1998).\\[0pt] [2] V.~K.~ Dolmatov, Adv. Quant. Chem. \textbf{58}, 13 (2009).