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Nucleon Properties in the Quantized Linear Sigma Model at Finite Temperature and Chemical Potential

The linear sigma model at finite temperature and chemical potential is systematically studied using the coherent-pair approximation, in which fully taking quantum of fields are included. The expectation value of the chiral Hamiltonian density is minimized and the resulting equations for the nucleon are solved. The qualitative features of the quantized sigma and pion fields are strong sensitive to the change of temperature and baryonic chemical potential and are in agreement with the mean-field approximation calculations. It is noticed that the nucleon mass increases with increasing coherence parameter. In addition, the nucleon mass increases with increasing temperature and the baryonic chemical potential and then it decreases at higher values of the temperature and baryonic chemical potential. The obtained results show that the mean-square radius of the proton and the neutron increase with increasing temperature or the baryonic chemical potential and that the pion-nucleon coupling constant decreases with the temperature or chemical potential. We conclude that the coherent-pair approximation successfully give better description of the nucleon properties at finite temperature and baryonic chemical potential