Roton energy gap and spontaneous symmetry breaking

We study elementary excitations in superfluid helium-4 employing an approach based on the spontaneous symmetry breaking. In particular, we calculate the roton energy gap at zero temperature $\mathrm{\Delta }(0)$. The relation that we have derived is $\mathrm{\Delta }(0)\mathrm{/}{k}_B{T}_{\lambda }=4$. The theoretical value of $\Delta (0)/k_B$ is 8.707 K, which is significantly close to the experimental value of 8.712 K. The deviation between the theoretical and experimental values is less than 0.1%.