Terahertz spectroscopy of the helium endofullerene He@C 60 .

We studied the quantized translational motion of single He atoms encapsulated in molecular cages by terahertz absorption. The temperature dependence of the THz absorption spectra of 3 He@C 60 and 4 He@C 60 crystal powder samples was measured between 5 and 220 K. At 5 K there is an absorption line at 96.8 cm -1 (2.90 THz) in 3 He@C 60 and at 81.4 cm (2.44 THz) in 4 He@C 60 , while additional absorption lines appear at higher temperature. An anharmonic spherical oscillator model with a displacement-induced dipole moment was used to model the absorption spectra. Potential energy terms with powers of two, four and six and induced dipole moment terms with powers one and three in the helium atom displacement from the fullerene cage center were sufficient to describe the experimental results. Excellent agreement is found between potential energy functions derived from measurements on the 3 He and 4 He isotopes. One absorption line corresponds to a three-quantum transition in 4 He@C 60 , allowed by the anharmonicity of the potential function and by the non-linearity of the dipole moment in He atom displacement. The potential energy function of icosahedral symmetry does not explain the fine structure observed in the low temperature spectra.