September 15, 2014 to October 10, 2014
Nordita, Stockholm
Europe/Stockholm timezone

Pairing Theory of the Wigner energy

Sep 26, 2014, 2:30 PM
132:028 (Nordita, Stockholm)


Nordita, Stockholm


Kai Neergaard


In 1936, Bethe and Bacher suggested that when the Coulomb energy is neglected, the masses of nuclei with given mass number A=N+Z, where N and Z are the numbers of neutrons and protons, rise from N=Z approximately quadratically in N-Z. Myers and Swiatecki found in 1966 a marked deviation from this rule; for small |N-Z| the mass rises more rapidly. They called the resulting apparent extra binding energy in the vicinity of N=Z the Wigner energy. It will be shown that this nonanalytic behaviour of the mass as a function of N-Z arises naturally when the pairing force is taken into account beyond a mean field approximation. In the limit of an equidistant single nucleon spectrum, the symmetry energy, that is, the increment of the mass from N=Z in the absence of the Coulomb energy, is proportional to T(T+1), where T is the isospin, in the ground state of a doubly even nucleus equal to |N-Z|/2. This expression is similar to the one which describes the spectrum of a quantal, axially symmetric rotor, and Frauendorf and Scheikh identified in 1999 the deformation which gives rise to an analogous rotation in isospace as the superfluid pair gap. Large shell corrections modify this bulk behaviour. In recent work by Bentley and Frauendorf, partly in collaboration with the speaker, various approaches to the treatment of these shell corrections are considered. In one approach the pairing force is diagonalised exactly in a small valence space. More recently, the usual pairing correction of the Nilsson-Strutinsky theory is supplemented with a term derived from the Random Phase Approximation. The resulting theory reproduces quite well the empirical masses in the vicinity of N=Z for A not less than 24. A very recent generalisation of the method, which allows its application throughout the chart of nuclides and also on top of a formalism of the Hartree-Fock type, will be discussed.

Presentation materials