of protons or neutrons, there exists an unpaired nucleon, which needs less energy to be excited. This phenomenon is closely analogous to that of Type 1 superconductivity in solid state physics. The first theoretical description of nuclear pairing was proposed at the end of the 1950s by Aage Bohr, Ben Mottelson, and David Pines (which contributed to the reception of the Nobel Prize in Physics in 1975 by Bohr and Mottelson). It was close to the BCS theory of Bardeen, Cooper and Schrieffer, which accounts for metal superconductivity. Theoretically, the pairing phenomenon as described by the BCS theory combines with the mean field theory: nucleons are both subject to the mean field potential and to the pairing interaction. The Hartree–Fock–Bogolyubov (HFB) method is a more sophisticated approach, enabling one to consider the pairing and mean field interactions consistently on equal footing. HFB is now the de facto standard in the mean field treatment of nuclear systems. Symmetry restoration Peculiarity of mean field methods is the calculation of nuclear property by explicit symmetry breaking. The calculation of the mean field with self-consistent methods (e.g. Hartree-Fock), breaks rotational symmetry, and the calculation of pairing property breaks particle-number. Several techniques for symmetry restoration by projecting on good quantum numbers have been developed. Particle vibration coupling Mean field methods (eventually considering symmetry restoration) are a good approximation for the ground state of the system, even postulating a system of independent particles. Higher-order corrections consider the fact that the particles interact together by the means of correlation. These correlations can be introduced taking into account the coupling of independent particle degrees of freedom, low-energy collective excitation of systems with even number of protons and neutrons. In this way, excited states can be reproduced by the means of random phase approximation (RPA), also eventually consistently calculating corrections to the ground state (e.g. by the means of nuclear field theory). See also Nuclear magnetic moment CHARISSA, a nuclear structure research collaboration Further reading General audience James M. Cork ; Radioactivité & physique nucléaire, Dunod (1949). Introductory texts Luc Valentin ; Le monde subatomique - Des quarks aux centrales nucléaires, Hermann (1986). Luc Valentin ; Noyaux et particules - Modèles et symétries, Hermann (1997). David Halliday ; Introductory Nuclear Physics, Wiley & Sons (1957). Kenneth Krane ; Introductory Nuclear Physics, Wiley & Sons (1987). Carlos Bertulani ; Nuclear Physics in a Nutshell, Princeton University Press (2007). Fundamental texts