Probing confinement resonances by photoionizing Xe inside a C${}_{60}^{+}$ molecular cage

Double photoionization accompanied by loss of $n$ C atoms ($n=0$, 2, 4, 6) was investigated by merging beams of Xe@C${}_{60}^{+}$ ions and synchrotron radiation and measuring the yields of product ions. The giant $4d$ dipole resonance of the caged Xe atom has a prominent signature in the cross section for these product channels, which together account for 6.2 $\pm$ 1.4 of the total Xe $4d$ oscillator strength of 10. Compared to that for a free Xe atom, the oscillator strength is redistributed in photon energy due to multipath interference of outgoing Xe $4d$ photoelectron waves that may be transmitted or reflected by the spherical C${}_{60}^{+}$ molecular cage, yielding so-called confinement resonances. The data are compared with an earlier measurement and with theoretical predictions for this single-molecule photoelectron interferometer system. Relativistic $R$-matrix calculations for the Xe atom in a spherical potential shell representing the fullerene cage show the sensitivity of the interference pattern to the molecular geometry.

Figure 1

Theoretical calculations of the cross sections for photoionization of endohedral Xe@C${}_{60}$, showing the predictions in different approximations for redistribution of Xe $4d$ oscillator strength due to confinement resonances. Time-dependent density functional theory (TDDFT) (solid black curve) [8], random phase approximation with exchange (RPAE1) (dashed green curve) [10], RPAE2 (dashed blue curve) [12], time-dependent local density approximation (TDLDA1) (solid green curve) [13], TDLDA2 (solid magenta curve) [14], $R$-matrix1 (dotted cyan curve) [15] and $R$-matrix2 (dotted orange curve) [16]. The experimental results [18] for Xe@C${}_{60}^{+}$ are shown as circles with error bars. The data have been scaled in cross section to give an integral oscillator strength of 10 in this energy region, corresponding to a filled Xe $4d$ subshell. For comparison, the photoionization cross section for the free Xe atom is shown as a thick solid red curve, as recommended by West and Morton [19].

Figure 2

Ion beam mass spectra measured at high mass resolution (left panels), and low mass resolution (right panels). Upper panels are for samples prepared with a natural mixture of Xe isotopes, and lower panels for samples prepared with highly enriched ${}^{136}$Xe. The three peaks in the lower left spectrum correspond to ${}^{136}$Xe@C${}_{60}^{+}$ containing zero, one and two ${}^{13}$C atoms. The top right panel corresponds to the conditions for the merged-beams experiment of Kilcoyne et al. [18] and the lower right for the current measurements.

Figure 3

Comparison of present DARC $R$-matrix calculation with recommended experimental data for photoionization of a free Xe atom [19].

Figure 4

Two-dimensional doubly charged product ion scans for a primary ion beam of C${}_{60}^{+}$ measured at a fixed photon energy of 65 eV. The demerging magnet and spherical electrostatic plates deflect the product ions across the detector in orthogonal directions [23], permitting scans of the photo-product space.

Figure 5

Measured cross sections for double photoionization of ${}^{136}$Xe@C${}_{60}^{+}$ accompanied by the loss of 0, 2, 4, and 6 C atoms (solid circles) along with their corresponding empty-cage cross sections (open circles). Blue circles with error bars denote absolute measurements from Table . Strong enhancement due to Xe $4d$ photoionization is evident.

Figure 6

Net Xe $4d$ contributions to double photoionization of ${}^{136}$Xe@C${}_{60}^{+}$ accompanied by the loss of $n$ $=$ 0, 2, 4 and 6 C atoms, along with their sum. The individual oscillator strengths found in the different channels are $1.71\pm 0.38$ ($n$ $=$ 0), $1.51\pm 0.33$ ($n$ $=$ 2), $2.10\pm 0.46$ ($n$ $=$ 4), and $0.85\pm 0.19$ ($n$ $=$ 6).

Figure 7

Comparison of the present measurements for the sum of Xe $4d$ contributions from Fig. 6 with the present $R$-matrix results for photoionization of Xe@C${}_{60}^{+}$. Two sets of parameters for the shell potential were applied: $r_0=0.31$ nm, $r_1=0.40$ nm, $U_0=8.8$ V (Rmat1, green short-dashed curve) and $r_0=0.33$ nm, $r_1=0.39$ nm, $U_0=8.2$ V (Rmat2, red solid curve). The experimental results have been scaled to give an integral oscillator strength of 10 in this energy range. Also shown are the experimental data [19] (blue open circles) and the present $R$-matrix results (blue long-dashed curve) for photoionization of the free Xe atom.

Figure 8

Comparison of the present measurements for the sum of Xe $4d$ contributions from Fig. 6 with nonrelativistic $R$-matrix calculation [15] (dashed blue curve) and relativistic $R$-matrix calculations (Ref. [16], dotted green curve and current DARC Rmat2 calculation, solid red curve) for photoionization of Xe@C${}_{60}^{+}$.

Figure 9

Oscillatory structure of the encapsulated-Xe photoionization cross section made visible by displaying the ratio $\Delta$(Xe)/$\sigma$(Xe) $=$ $[\sigma$(Xe@C${}_{60}^{+}$)-$\sigma$(Xe)$]$/$\sigma$(Xe) as a function of the photoelectron energy and the photoelectron de Broglie wavelength, respectively. The experimental and theoretical data result from the cross sections provided in Fig. 7. For determining the experimental data points the $\sigma$(Xe) data of West and Morton [19] were combined with the present results for the sum of all Xe $4d$ contributions to $\sigma$(Xe@C${}_{60}^{+}$). At a $4d$ photoelectron energy of 21 eV, about five de Broglie half waves fit inside the inner diameter of the C${}_{60}$ cage.