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

Jinesh Kallunkathariyil
Jagiellonian University Kraków, POLAND

### Alpha Cluster Model of Atomic Nuclei and the Nuclear Equation of State

Zbigniew Sosin$^{1}$, Jan Błocki$^{2}$, Jinesh Kallunkathariyil$^{1}$, Jerzy Łukasik$^{3}$, Piotr Pawłowski$^{3}$

$^{1}$M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
$^{2}$NCBJ, Theoretical Physics Division (BP2), Świerk, Poland
$^{3}$IFJ-PAN, Kraków, Poland

Abstract
The nuclear system energy based on the equation of state is presented. In this description besides interactions of the equilibrated spin-isospin matter corrections for the eventual spin-isospin polarization were also taken into account. With such an interaction clusters appear and they can be represented by alpha particles. Taking into account an additional interaction between clusters the binding energy and sizes of the even-even nuclei with $N=Z$ were very accurately described. From the behavior of $^{4}$He, $^{3}$He and $t$ limits of the equation of state parameters are established.