Parametric Equations for the Energy Gap. Extended BCS Case

The generalised form of the gap equation which comprises also some non-BCS approaches is defined and solved. The parametric gap equations have been derived in a few equivalent cases and discussed in$\text{}_{}$dissimilar limits. It is shown that the relations between the critical temperature and zero-temperature energy gap can be extended for all systems under consideration. The main benefits and incontestable advantage of the presented method are demonstrated with regard to the general BCS case.