TRANSITION-TEMPERATURE OF SUPERCONDUCTORS - LOWER AND UPPER-BOUNDS OFTHE DENSITY-OF-STATES N(0) FOR SUPERCONDUCTIVITY

For superconductivity, a large dynamical screening factor F in the Cou lomb interaction is found to be necessary. Using an analytical express ion for F, it is shown that there are lower and upper bounds of the de nsity of states at the Fermi level N(0) [doping x] for superconductivi ty. A critical point in the x - T(c) plane is found in the case of the Coulomb interaction greater than the electron phonon interaction at l arge x. An algebraic expression for the isotope effect applicable to l ow T(c) and high T(c) superconductors is given.