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Nonlinear optical properties in the fullerene C$_{60}$ and the extractedhigher fullerenes -- C$_{70}$, C$_{76}$, C$_{78}$, and C$_{84}$ -- aretheoretically investigated by using the exciton formalism and thesum-over-states method. We find that off-resonant third order susceptibilitiesof higher fullerenes are a few times larger than those of C$_{60}$. Themagnitude of nonlinearity increases as the optical gap decreases in higherfullerenes. The nonlinearity is nearly proportional to the fourth power of thecarbon number when the onsite Coulomb repulsion is $2t$ or $4t$, $t$ being thenearest neighbor hopping integral. This result, indicating important roles ofCoulomb interactions, agrees with quantum chemical calculations of higherfullerenes.Comment: 8 pages; 3 figures; Figures should be requested to the author  (E-mail: harigaya@etl.go.jp

Effects of Coulomb interaction on the nonlinear optical response in , and higher fullerenes