Phonon-roton modes of liquid 4He beyond the roton in MCM-41

We present neutron scattering measurements of the phonon-roton (P-R) mode of superfluid 4He confined in 47 \AA MCM-41 at T = 0.5 K at wave vectors, Q, beyond the roton wave vector (Q_R =1.92 \AA$^{-1}$). Measurements beyond the roton require access to high wave vectors (up to Q = 4 \AA$^{-1}$) with excellent energy resolution and high statistical precision. The present results show for the first time that at T = 0.5 K the P-R mode in MCM-41 extends out to wave-vector Q$\simeq$3.6 \AA$^-1$ with the same energy and zero width (within precision) as observed in bulk superfluid 4He. Layer modes in the roton region are also observed. Specifically, the P-R mode energy, $\omega_Q$, increases with Q for Q > QR and reaches a plateau at a maximum energy Q = 2{\Delta} where {\Delta} is the roton energy, {\Delta} = 0.74 $\pm$ 0.01 meV in MCM-41. This upper limit means the P-R mode decays to two rotons when its energy exceeds 2{\Delta}. It also means that the P-R mode does not decay to two layers modes. If the P-R could decay to two layer modes, $\omega_Q$ would plateau at a lower energy, $\omega_Q$ = 2{\Delta}L where {\Delta}L = 0.60 meV is the energy of the roton like minimum of the layer mode. The observation of the P-R mode with energy up to 2{\Delta} shows that the P-R mode and the layer modes are independent modes with apparently little interaction between them.