Confinement resonances in photoelectron angular distributions from endohedral atoms

Both dipole and nondipole angular distribution parameters for photoelectrons emitted from the endohedral $\mathrm{Ne}@{\mathrm{C}}_{60}$ atom are investigated within both the framework of the Dirac bubble potential model and spherical, short range potential well of finite thickness $\Delta T$. It is demonstrated, for $1s$, $2s$, and $2p$ photoelectrons of $\mathrm{Ne}$, that because the fullerene shell acts as a resonator in this process, the energy dependence of the photoelectron angular distribution parameters differ considerably from that of the free $\mathrm{Ne}$ atom. For confined $\mathrm{Ne}$, in contrast to the isolated $\mathrm{Ne}$ atom, these parameters as a function of photon energy acquire a significant resonance structure, owing to oscillations in the photoionization matrix elements induced by the fullerene shell.

Figure 1

Nondipole asymmetry parameter ${\gamma }_{1s}\left(\epsilon \right)$ as a function of the photoelectron energy $\epsilon =k^2∕2$ for $1s$ photoionization of $\mathrm{Ne}@{\mathrm{C}}_{60}$ calculated within two different approximations. (1) the $\delta$-potential model (the present theory). (2),(3),(4) the model of a spherical, short range potential well of inner radius $R_{in}$, finite thickness $\Delta T$, and depth $U_0$ (Ref. 8), as follows: (2) $R_{in}=5.75\mathrm{a}.\mathrm{u}.$, $U_0=-0.3027\mathrm{a}.\mathrm{u}.$, $\Delta T=1.89\mathrm{a}.\mathrm{u}.$; (3) $R_{in}=6.139\mathrm{a}.\mathrm{u}.$, $U_0=-0.5099\mathrm{a}.\mathrm{u}.$, $\Delta T=1.0$; (4) $R_{in}=6.389\mathrm{a}.\mathrm{u}.$, $U_0=-0.9515\mathrm{a}.\mathrm{u}.$, $\Delta T=0.5\mathrm{a}.\mathrm{u}.$

Figure 2

Nondipole asymmetry parameter ${\gamma }_{2s}\left(\epsilon \right)$ for $2s$ photoionization of $\mathrm{Ne}@{\mathrm{C}}_{60}$ calculated within the $\delta$-potential theory (line 1) and the SW model (lines 2, 3, and 4) with the same choice of $R_{in}$, $\Delta T$, and $U_0$ as in Fig. 1.

Figure 3

Dipole asymmetry parameter ${\beta }_{2p}\left(\epsilon \right)$ for $2p$ photoionization of $\mathrm{Ne}@{\mathrm{C}}_{60}$ calculated within the $\delta$-potential theory (line 1) and the SW model (lines 2, 3, and 4) with the same choice of $R_{in}$, $\Delta T$, and $U_0$ as in Figs. 1, 2.