Show that, for a sufficiently large momentum \(\hbar k\) (in fact, such that the slope \(d \varepsilon / d k\) of the energy spectrum is greater than the initial slope \(\hbar c\) ), a state of double excitation in liquid \(\mathrm{He}^{4}\) is energetically more favorable than a state of single excitation, that is, there exist wavevectors \(\boldsymbol{k}_{1}\) and \(\boldsymbol{k}_{2}\) such that, while \(\boldsymbol{k}_{1}+\boldsymbol{k}_{2}=\boldsymbol{k}, \varepsilon\left(k_{1}ight)+\varepsilon\left(k_{2}ight)<\varepsilon(k)\).