Collisions Fermi theory

In the Einstein-Bose statistics, there is no such clear physical way to find the revised law of collisions as in the Fermi-Dirac statistics. The law can be derived from the quantum theory but not in a simple enough way to describe here. In contrast to the Fermi-Dirac statistics, in which the presence of one molecule in a cell prevents another from entering the same cell, the situation with the Einstein-Bose statistics is that the presence of a molecule in a cell increases the probability that another one should enter the same cell. In fact, the number of molecules going into the fcth cell per second turns out to have a factor (1 + Nk), increasing linearly with the mean number Nk of molecules in that cell. Thus, the law of collisions for the Einstein-Bose statistics is just like Eq. (4.1), only with + signs replacing the — signs. In fact, we may write the law of collisions for both forms of statistics in the form... 

One conceptual element of the BCS theory is the formation of - Cooper pairs, namely pairing of -> electrons close to the Fermi level due to a slight attraction resulting from phonon interaction with the crystal lattice. These pairs of electrons act like bosons which can condense into the same energy level. An energy band gap is to be left above these electrons on the order of 10-3 eV, thus inhibiting collision interactions responsible for the ordinary - resistance. As a result, zero electrical resistivity is observed at low temperatures when the thermal energy is lower than the band gap. The founders of the BCS theory, J. Bardeen, L. Cooper, and R. Schrieffer, were awarded by the Nobel Prize in 1972. 

In Eq. 3.4, a relates to the electron structure and scattering in the metal. From the free electron theory of metal, Fermi velocity is defined as the fi ee electron movement velocity at the highest energy (E ), and the relaxation time r is the time between the first and second collisions of the electron. So the electron mean free path Ip nearby the Fermi surface can be expressed as Ip = v t. In addition, o can be also expressed as below " ... 

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