Theoretical Studies of ground state and photoionization dynamics of Na$_{\mathrm{\mathbf{x}}}$ inside C$_{\mathrm{\mathbf{n}}}$ (x=20 and n=240)

A number of studies has already been reported on the photoresponse of Na [1] clusters and fullerenes [2]. The hollow space inside fullerene cages can accommodate small metal clusters [3, 4] to form exotic cluster endofullerene molecules. In this work, the ground state of such an endohedral systemis modelled in a jellium-based density functional method with a gradient corrected exchange-correlation functional (LB94) [5] before calculating the system's photoionization in a linear response framework called time-dependent local density approximation (TDLDA) [2]. Plasmon and confinement resonances are found to be the key features of the photoionization cross-sections of the system. Comparisons with free systems, Na$_{\mathrm{x}}$and C$_{\mathrm{n}}$, facilitate detailed understandings of the results. \textbf{References} [1] Chunlei Xia, Chunrong Yin, and Vitaly V. Kresin, Phys. Rev. Lett. 102, 156802 (2009). [2] J. Choi et al., Phys. Rev. A 95, 023404 (2017). [3] Cabrera-Trujillo et al., Phys. Rev. B 53, 16059 (1996). [4] Cabrera-Trujillo et al., Current Problems in Condensed Matter(1998), pp 133-141, Springer, Boston, MA [5] R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994).