The ratio 2 Delta/T-c in Eliashberg theory

We study in general terms the ratio 2 Delta/T-c within Eliashberg theory of superconductivity. We point out that, in the calculation of 2 Delta/T-c, it is possible to replace in a systematic and explicit way any boson spectrum by a two Einstein peak spectrum, without changing the result by more than a few percent. This allo,vs to reduce the general problem to a 4 parameters problem and makes it possible to extract from 2 Delta/T-c the maximum information on the boson spectrum. We make use of this two peak representation to obtain a complete description of all the possible outcome for the value of 2 Delta/T-c. We find specific correlations between some characteristic averages of the boson spectrum and the value of 2 Delta/T-c, which are far from perfect but are good enough for practical use. As an example we apply our results to the specific cases of the cuprates and the fullerenes superconductors in order to show how the knowledge of 2 Delta/T-c can help to narrow the possible origins of the pairing mechanism. Finally we give interpolation formulae which allow to bypass the numerical calculation of 2 Delta/T-c from Eliashberg equations and still provide the answer with a precision which is quite enough for practical purposes.