On the critical temperature for the phonon-induced superconductivity

We have considered phonon-induced superconductivity and decoupled normal and anomalous propagators on the second stage of the equations of motion. This procedure leads to the energy dependent order parameter and the resulting equation for the superconducting transition temperature T-c partially reproduces the structure of Eliashberg equations. Making use of the Lorentzian density of states we have observed an analytical equation for T-c. We have evaluated T-c as a function of the electron-phonon coupling constant lambda and found that our simple approach works well in the strong-coupling limit. The possible extension to the case of correlated electrons has also been briefly discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.