Fig. 4: Energy and temperature dependence of the inelastic scattering branch.

Left panels: Inelastic scattering from confined ⁴He at various incident wave vectors covering different Q − E ranges with different resolutions. The plots correspond to incident wavevectors of: a 4.00 Å⁻¹, b 2.50 Å⁻¹, and c 1.71 Å⁻¹. The Q scales are the same for all three values, but the energy ranges are different. d The peak excitation energies obtained by fitting a Gaussian in energy to the inelastic scattering in a–c with the Q and E uncertainties determined in the fit shown as standard error bars. The solid line is the best fit to the threshold energy of a purely 1D quantum liquid of hard spheres. The fit was obtained by fixing k_F = 0.8 Å⁻¹, as extracted from the S(Q, 0) measurement, and yielded \(K=1.1{8}_{-0.20}^{+0.38}\). Right Panels: Inelastic scattering from confined helium at various temperatures above and below the bulk superfluid transition. The measurements have fixed Q_in = 4.00 Å⁻¹ and temperatures of: e 1.6 K, f 2.5 K, and g 4.2 K. The scattering intensity decreases slightly with increasing temperature but remains large even at the highest temperature studied.