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 $\Delta (0)$. The relation that we have derived is $\Delta (0) / k_B T_\lambda = 4$. 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%.