Short Contribution Nuclear Superconductivity

I would like, for a moment, to consider the many-body problem in the nucleus in the light of what we now know about an analogous many-body problem, that of electrons in metals. In ordinary metals, it is found experimentally that the low-lying excitations of the system possess an essentially individual particle character. The specific heat depends linearly on the temperature, and the Fermi surface is well-defined, as is evidenced by the de Haas-van Alphen effect. The main problem 'which faces the theoretical physicist is that of reconciling these facts with the rather strong long-range Coulomb interactions between the electrons. This may be done, however, by taking into account properly the polarization effects produced by the Coulomb interactions. When this is done, (by, for instance, introducing the plasma field to describe the polarization waves), one obtains a system of "effective" electrons, which interact through a screened Coulomb interaction with a range of the order of the inter-particle spacing. The "effective" electrons consist of the original electrons plus their associated screening clouds. It is then feasible to show that the elementary excitations of the "effective" electron system possess the desired individual particle character, although a completely satisfactory mathematical proof of this fact does not yet exist. This situation is rather similar to that obtaining with the shell model for the nucleus, and one might hope for a similar happy ending here. I do not, however, believe that we will find it in just this form. To see why, let us consider the "unusual" metals, the superconductors. Recently Bardeen, Cooper and Schrieffer 1) have proposed a theory