5^{th} International Symposium on Nuclear Symmetry Energy NuSYM15, June 29 - July 2, 2015 Kraków, POLAND

### Symmetry and congruence energies in different macroscopic models

**Krzysztof Pomorski**

Maria Curie Sklodowska University Lublin, POLAND

**Abstract**

The nuclear symmetry as well as the congruence (Wigner) energies are essential parts of every macroscopic model which is able to reproduce the binding energies of nuclei [1,2]. It was shown in Ref. [1] that the both energies origins from the term in the liquid drop binding energy proportional to the square of the isospin, i.e. $T(T+1)$, where $T=|N-Z|/2$. A simple isospin dependent liquid drop model model containing the volume and surface terms and the Coulomb direct and exchange energies with the microscopic pairing and shell corrections reproduces well both the experimental masses and the fission barrier heights. In spite of the fact that this model contains 5 adjustable parameters only, the rms-deviation is 0.8 MeV for the 2270 isotopes with $Z,N \ge 8$. Taking in addition the adjustable curvature term and the nucleon number independent average pairing energy [3] improves significantly the binding energy reproduction (rms-dev=0.6 MeV) but unfortunately leads to to low fission barrier heights.

[1] L.G. Moretto, P.T. Lake, L. Phair, and J.B. Elliot, Phys. Rev. C **86**
021303 (2012).

[2] K. Pomorski, Phys. Scripta, T**154**, 014023 (2013).

[3] K. Pomorski, F. Ivanyuk, Int. Journ. Mod. Phys. E**18** , 900 (2009).

[2] K. Pomorski, Phys. Scripta, T

[3] K. Pomorski, F. Ivanyuk, Int. Journ. Mod. Phys. E