Vacancy decay in endohedral atoms

It is demonstrated that the fullerene shell dramatically affects the radiative and Auger vacancy decay of an endohedral atom $A@{\mathrm{C}}_{60}$. The collectivized electrons of the ${\mathrm{C}}_{60}$ shell add new possibilities for radiative and nonradiative decays similar to that in ordinary atoms where the vacancies in the initial and final state almost always belong to different subshells. It is shown that the smallness of the atomic shell radii as compared to that of the fullerene shell provides an opportunity to derive the simple formulas for the probabilities of the electron transitions. It is shown that the radiative and Auger (or Koster-Kronig) widths of the vacancy decay due to electron transition in the atom $A$ in $A@{\mathrm{C}}_{60}$ acquire an additional factor that can be expressed via the polarizability of the ${\mathrm{C}}_{60}$ at transition energy. It is demonstrated that due to an opening of the nonradiative decay channel for vacancies in subvalent subshells the decay probability increases by five to six orders of magnitude.

Figure 1

Real and imaginary parts of the dynamical dipole polarizability of ${\mathrm{C}}_{60}$.

Figure 2

The ratio ${\eta }_{RR}\left(\omega \right)$ of the radiative widths for the same transition in endohedral and free atom as a function of photon energy. $\mathrm{\Delta }{E}_1=26.85\mathrm{eV}$ corresponds to the $2s$-$2p$ transition in Ne; $\mathrm{\Delta }{E}_2=13.50\mathrm{eV}$ is the $3s$-$3p$ transition in Ar or $4s$-$4p$ in Kr; $\mathrm{\Delta }{E}_3=11.20\mathrm{eV}$ and $\mathrm{\Delta }{E}_4=9.90\mathrm{eV}$ are the $5s$-$5p_{3∕2}$ and $5s$-$5p_{1∕2}$ transitions in Xe, respectively. All transition energies are given in Ref. 18.

Figure 3

The ratio of Auger and radiative widths ${\eta }_{AR}\left(\omega \right)$ as a function of transition energy. Arrows have the same meaning as in Fig. 2.

Figure 4

The fluorescence yield $J_R\left(\omega \right)$ as a function of transition energy.