Page 187 - Carbon Nanotubes

Metal-coated fullerenes 179

i
500nm

0
rl 0 1
-ti rl 520nm
v) ii
N

0
0 200 400 600
No. of Cs-atoms on C60

Fig. 13. Mass spectra of C&s, clusters ionized at different photon energies near the ionization thresh-
old; the values of x corresponding to the closing of electronic shells are indicated.

The electronic shell closings obtained from this model The energy E of the levels is more conveniently rep-
are listed in Table I. Note that the agreement with the resented on a momentum scale. The sequence of Iev-
shells found experimentally in pure metal clusters is els at the left vertical axis corresponds to the infinitely
quite good. We should mention, at this point, that an deep well without the central barrier. The presence of
intensity anomaly is not observed in the mass spectrum the barrier primarily affects energy levels with low an-
each time a new energy level (subshell) is filled. For gular momentum because only these have a high prob-
large clusters only a ‘bunching’ of the subshells on the ability density near the center of the well. Also drawn
energy scale leads to a pronounced shell structure (it in Fig. 14 is the zigzagging ‘path’ of the highest occu-
is plausible that, for example, the filling of a two-fold pied level of a C60 Cs, cluster taking on various val-
degenerate s-state will have little effect on a system ues of Rc,/R,,, as it grows from x = 1 to x = 500.
containing hundreds of electrons). To determine this path, we used RC6,, = 4 A and the
Consider now the solutions of the spherical poten- Cs-density bulk value of 0.009 atoms per A3. The
tial well with a barrier at the center. Figure 14 shows (sub-)shells resulting from this path are listed in Table 1.
how the energies of the subshells vary as a function Obviously, the agreement with the experimentally ob-
of the ratio between the radius of the C60 barrier RC60 served shell closings has not been improved by includ-
and the outer radius of the metal layer R,,,. The sub- ing C60 as an impenetrable barrier at the center of the
shells are labeled with n and 1, where n is the princi- metal cluster. Varying RCW and the Cs-density within
pal quantum number used in nuclear physics denoting reasonable bounds does not significantly improve the
the number of extrema in the radial wave function, situation. On the other hand, this simple model shows
and I is the angular momentum quantum number. that the shell structure of a metal sphere does not