Roton-roton interactions and excitations in superfluid helium at large wavevectors

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Abstract
Neutron inelastic scattering measurements have been made of the superfluid 4He 'one-phonon' dispersion relation at wavevector transfers between 2.7 AA-1 and 3.5 AA-1. These measurements were performed at a temperature of 1.1K and at pressures of 24.3 atm, 15.0 atm, and 1.4 atm. At the two higher pressures it was found that the energy of the 'phonon' was greater than 2 Delta , the value predicted by Pitaevskii, Delta being the excitation energy at the roton minimum. It is suggested that this discrepancy arises from the neglect of repulsive roton-roton interactions in the model. The magnitude of these interactions is estimated from the measurements and compared with that obtained using the Jackson-Feenberg theory of liquid helium.