  According to the BCS model the probability of filling of pair electron states
vk2 as a function of kinetic energy is smeared i.e. is not a step function.
This means that part of energy of connection through virtual phonons is
consumed to increase the kinetic energy in an electron system at the transition
to the superconducting state. In this work a modified mechanism of vk2
formation is proposed which takes into account the dynamics of fluctuations
near the phase transition. The estimations of superconducting gap and isotopic
effect for a matrial with parameters of high-temperature superconductors give
values comparable with these observed

Superconductivity