  We study the continuum version of the two-gap BCS model in (3+1)D within the
large-N approximation. We calculate the effective potential of the model which
depends on two independent energy gaps $\sigma$ and $\Delta$, where $\sigma$
describes the Cooper pair made of electrons that belong to the same internal
symmetry whereas $\Delta$ describes the Cooper pair of electrons that have a
different internal symmetry. The effective potential is calculated by
considering that the Debye frequency is an ultraviolet cutoff $\Lambda$, which
is meant to describe the physical lattice of 3D superconductors. Our main
result shows that the extra gap provides a possible inter-band phase transition
that may be either a stable or metastable phase, depending on the competion
between the coupling constants of the model. We also derive the critical
temperature below which the phases may be observed.
