Spatial structure of Cooper pairs in nuclei

We discuss the spatial structure of the Cooper pair in dilute neutron matter and neutron-rich nuclei by means of the BCS theory and the Skyrme-Hartree-Fock-Bogioliubov model, respectively. The neutron pairing in dilute neutron matter is close to the region of the BCS-BEC crossover in a wide density range, giving rise to spatially compact Cooper pair whose size is smaller than the average interaparticle distance. This behavior extends to moderate low density ($\sim 10^{-1}$ of the saturation density) where the Cooper pair size becomes smallerst ($\sim 5$ fm). The Cooper pair in finite nuclei also exhibits the spatial correlation favoring the coupling of neutrons at small relative distances r \lesim 3 fm with large probability. Neutron-rich nuclei having small neutron separation energy may provide us opportunity to probe the spatial correlation since the neutron pairing and the spatial correlation persists also in an area of low-density neutron distribution extending from the surface to far outside the nucleus.Comment: 13 pages, 5 figures, chapter in "Fifty Years of Nuclear BCS", eds. R.A. Broglia and V.Zelevinsk

A challenge for critical point of spin glass in ground state

We show several calculations to identify the critical point in the ground state in random spin systems including spin glasses on the basis of the duality analysis. The duality analysis is a profound method to obtain the precise location of the critical point in finite temperature even for spin glasses. We propose a single equality for identifying the critical point in the ground state from several speculations. The equality can indeed give the exact location of the critical points for the bond-dilution Ising model on several lattices and provides insight on further analysis on the ground state in spin glasses.Comment: 7 pages, 2 figures, to appear in Proceedings of 4th YSM-SPIP (Sendai, 14-16 December 2012