Nuclear Bardeen-Cooper-Schrieffer

One of the most amazing phenomena in quantum many-particle systems is the formation of quantum condensates. Of particular interest are strongly coupled fermion systems where bound states arise. In the low-density limit, where even-number fermionic bound states can be considered as bosons, Bose-Einstein condensation is expected to occur at low temperatures. The solution of Eq. (6) with = 2/j, gives the onset of pairing, the solution of Eq. (7) with EinP = 4/i the onset of quartetting in (symmetric) nuclear matter. At present, condensates are investigated in systems where the cross-over from Bardeen-Cooper-Schrieffer (BCS) pairing to Bose-Einstein condensation (BEC) can be observed, see [11,12], In these papers, a two-particle state is treated in an uncorrelated medium. Some attempts have been made to include the interaction between correlated states, see [7,13]. 

If there are many valence protons and neutrons present in the nucleus, traditional shell model calculations lead to insurmountable difficulties. Fortunately, the Bardeen-Cooper-Schrieffer (BCS) theory provides a good approximation method to the seniority-zero shell model, and allows to describe very complex nuclei, too. In the BCS quasiparticle calculations long chains of nuclei can be treated in a relatively simple way. The method was first applied in the theory of superconductivity by Bardeen et al. (1957), then used for nuclear physics by Bohr et al. (1958), Soloviev (1958), and Belyaev (1959). The quasiparticle concept was introduced into nuclear physics by Valatin (1958) and Bogoliubov (1958). The theory is explained in detail in several textbooks (Lawson 1980 Ring and Schuck 1980 Soloviev 1981 Heyde 1990 Nilsson and Ragnarsson 1995 Fenyes 2002). 

BCS Bardeen-Cooper-Schrieffer NQR Nuclear quadrupolar resonance... 

Kamerlingh Onnes, at the University of Leiden, discovered superconductivity in 1911. He found that the resistance of some metallic wires became zero at very low temperature it did not just approach zero, there was no dissipation of heat. At that time his laboratory was the only one equipped for studies at the temperature of liquid He (bp 4.1 K). Theoretical explanations of the phenomenon did not appear until the work of John Bardeen, Leon Cooper, and Robert Schrieffer in 1957. They received the Nobel Prize in Physics in 1972. The expense and difficulty of applying superconductivity to practical problems limits the applications. Nevertheless, superconductor magnets of very high field are now widely used in NMR in chemistry and the medical diagnostic applications of NMR called MRI (magnetic resonance imaging—they wanted to avoid the word "nuclear ). 

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