Discuss the system of interacting Fermions. Find the expression for superconducting energy gap above the superconducting ground state as $$\Delta = \left[ \frac{2 \hbar^2 k_0 \omega}{m} \right] \frac{\exp (-D / \bar v)}{\exp (-D / (\bar v -1 ))}, \quad D = \frac{2 \pi^2 \hbar^2}{m k_0} \, . $$

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