description of the normal state above $ T_{c} $ in the strong-coupling limit [@Nozieres-SchmittRink-85] and, as we shall see, to capture the essential physics of exotic pairing via a central potential, respectively. The later can be understood, in essence, by noting that the angular momentum quantum numbers $ l,m $ describe the internal rotational degrees of freedom of the Cooper pairs, and so they are a key ingredient to describe their dynamics in the case of a central attraction. The additional index $ \kappa  $ has been introduced to ensure the generality of (\[central V amplitude in terms of its eigenfunctions\]), and it refers to the relative motion of the electrons in a pair in the radial direction. Evidently for interaction potentials of the type we are interested in such radial motion is “locked” so that the distance between the two electrons remains constant, and equal to $ r_{0} $. We will therefore disregard these vibrational modes, assuming that there is a single kernel factor $ R_{l}\left( \left| \mathbf{k}\right| \right)  $ for each value of $ l $. Obviously in that case there is a single coupling constant $ V_{l} $ for each value of the angular momentum quantum number. 