Bounds on superconducting properties in Eliashberg theory

The author establishes bounds on some of the properties of an Eliashberg superconductor. It is shown that the normalized specific heat jump at T/sub c/ and the thermodynamic critical field deviation function, are bounded above by a value not much greater than is observed in some known superconductors. Also, a lower limit exists for the dimensionless ratio γ(0) T/sub c/ 2/H/sub c/ 2(0). Here γ(0) is the Sommerfeld constant, T/sub c/ is the critical temperature and H/sub C/(0) the zero temperature thermodynamic critical field. On the other hand, the ratio of twice the gap edge to T/sub c/ can rise to 11.5 and the reduced upper critical magnetic field in the clean limit to 1.5. Finally, some results are presented for the very strong coupling limit by which they mean that T/sub c/ is taken to be comparable in size to a typical phonon energy