Inelastic neutron scattering of a quantum translator-rotator encapsulated in a closed fullerene cage: Isotope effects and translation-rotation coupling in ${\text{H}}_2@{\text{C}}_{60}$ and $\text{HD}@{\text{C}}_{60}$

We report an inelastic neutron-scattering (INS) investigation of coupled quantum translation and rotation of hydrogen molecules trapped inside the closed isotropic cages of ${\text{C}}_{60}$. The low-lying states that characterize the translation-rotation manifold of the hydrogen molecules are accurately determined in our study of the INS peak energies. A comparison between the spectra of ${\text{H}}_2$ and HD isotopomers provides quantitative insight into the coupling between rotational and translational angular momentum with HD exhibiting the strongest effects due to mixing of the rotational eigenstates.

Figure 1

The energy levels of the quantum rotator translators, ${\text{H}}_2@{\text{C}}_{60}$ and $\text{HD}@{\text{C}}_{60}$. The quantum numbers $n$, $l$, $J$, $I$, and $\lambda$ are defined in the text.

Figure 2

The INS spectrum of ${\text{H}}_2@{\text{C}}_{60}:\text{HD}@{\text{C}}_{60}$ recorded at 1.8 K on the IN4C time-of-flight spectrometer. The ${\lambda }_n=1.8\text{Å}$ spectrum is offset.

Figure 3

The temperature dependence of the INS spectrum. NE gain ${\lambda }_n=3\text{Å}$: $T=1.8$, 20, 80, 120 200 K ascending (all $\times 5$). NE loss ${\lambda }_n=1.65$ and $1.5\text{Å}$: $T=1.8\text{K}$ (closed symbols) and 100 K (open symbols). Spectra offset for clarity.

Figure 4

The temperature dependence of the $J=0\leftrightarrow 1$ INS peaks in NE gain and loss for $\text{HD}@{\text{C}}_{60}$: the amplitudes are plotted relative to the amplitude at 1.8 K with Debye-Waller correction factors applied, determined from the temperature dependence of the $+14.6\text{meV}$ peak. Solid lines: INS amplitude assuming Boltzmann populations within the manifold of translation-rotation lines of HD.