Calculation of the coefficient of symmetry energy term on nuclear binding energy

Using by Fermi gas model, for different nucleon-nucleon potantials, the coefficient of symmetry energy term of stable nucleus was calculated. To calculate the symmetry energy, the Hamiltonian of nucleus which is a quantum system of many particles is written in second quantization formalism. Because of the system has many particles, it is difficult to solve the Hamiltonian based on the wave function of particles. Important point is that number of particles on each quantum state. For this reason, the first quantization is not an useful method. As potantial energy term of hamiltonian, Wigner-Majorana type potantial was selected. Equations of symmetry energy and symmetry energy term coefficient were formed using energy eigenvalues which are defined from expectation values of hamiltonian for symmetrical and anti-symmetrical nucleus. The symmetry energy term coefficient for Yukawa, the square-well and gaussian potantials were calculated in Mathematica® code. The variation of coefficient calculated from each potantial with mass number of nucleus was figured. Also, for every stable nucleus, symmerty energy term coefficients were listed in a table. Keywords: Fermi gas model, Symmetry energy, Wigner-Majorana, stable nucleus, second quantization, nucleon-nucleon potantial.