Roton-Rotation Coupling of Acetylene in ${}^4\mathrm{H}\mathrm{e}$

Rotational absorption spectra of acetylene in superfluid ${}^4\mathrm{H}\mathrm{e}$ calculated using a path-integral correlation function approach are seen to result in an anomalously large distortion constant in addition to a reduced rotational constant, with values in excellent agreement with recent experiments. Semianalytic treatment of the dynamics with a combined correlated basis function-diffusion Monte Carlo method reveals that this anomalous behavior is due to strong coupling of the higher rotational states of the molecule with the roton and maxon excitations of ${}^4\mathrm{H}\mathrm{e}$, and the associated divergence of the ${}^4\mathrm{H}\mathrm{e}$ density of states in this region.

Figure 1

PICF rotational excitations for HCCH in a cluster of 64 ${}^4\mathrm{H}\mathrm{e}$ (broad solid lines, height proportional to the spectral weight). Thin solid lines: corresponding CBF-DMC absorption spectra $S_J(\omega )$, $J=1,2,3$, for HCCH in bulk ${}^4\mathrm{H}\mathrm{e}$, lines broadened by 10 mK. Bottom panel: density of states ${\epsilon }^{\prime }(p)+{\hslash }^{2}p/M$. Dotted lines: edges of the roton-maxon bands coupling the $J=2,3$ states to $\ell =0,1$ states, respectively.

Figure 2

Absorption spectrum $S_J(\omega )$ for the $J=0\to 2$ transition of HCCH in ${}^4\mathrm{H}\mathrm{e}$, where the gas phase rotational constant value is varied between $0.5\times B$ (bottom curve) and $1.5\times B$ (top curve), in steps of $0.1\times B$. Asterisks mark the locations of the gas phase transition energies, $6B$.