_{1}

^{*}

We study the asymmetric nuclear matter in a nonperturvative manner at finite temperatures using thermofield dynamics method. The nucleon-meson interaction is taken to examine the binding energy (
*E*
_{B}), pressure (
*P*) for various proton fractions.

The properties of hot dense nuclear matter are very important in the context of neutron stars [

Such phase transitions have been identified in multifragmentation experiments and in the crusts of neutron stars [

A model for infinite nuclear matter consisting of interacting nucleons and pions was considered in [

The article is organised as follows. In Section 2, we review the thermofield dynamics to consider hot and dense nuclear matter and obtain expressions for temperature-dependant pressure P, binding energy B and nuclear density ρ. In Section 3, we evaluate numerically the above applying variational technique, study their characteristics and discuss the results so obtained.

We consider the effective Hamiltonian for pion nucleon interaction at zero temperature [

where

and the effective Hamiltonian

We have taken

where

with

The above reduces to ground state expectation, in zero temperature limit value for the operator

where

where

where

where

For zero chemical potential and for free fields, extremization of the free energy then yields

with Hamiltonian density as

If we substitute this value the free energy density becomes

Similarly for the fermionic sector the thermal vacuum is

where

and

where

with

and

In the above,

In nucleon sector for fermions

with

where

Here the thermodynamic potential [

where

The temperature dependent kinetic energy due to the mesons is given by

where

where

we shall now assume a phenomenological term corresponding to meson repulsion due to composite structure of mesons given as

Finally, the nucleon repulsion term given as

where

where

as before.

The thermodynamic potential density Ω is given by

where the last term corresponds to nucleon number conservation with

and similarly the meson sector contribution

Thus the thermodynamic potential density now is a functional of

which is of the same form as [

where

Once we substitute the optimised dressing as in Equation (30), the above simplifies to

which is different from

with

where J is given in Equation (25). We may note that the change in

The parameters a,

compressibility K of the symmetric nuclear matter i.e.

The fourth parameter

The pion-nucleon coupling constant

In _{B} with different baryon densities at different temperatures. The saturation binding energy increases from −16 MeV at zero temperature to higher values with rise of temperature. This clearly shows that the temperature has a significant effect on symmetric nuclear matter.

In

In _{P}s the Pressuer becomes negative at different lower densities reaching zero Pressure at zero nucleon densities. So the

asymmetric nuclear matter behaves differently at different nucleon densities.

In

temperatures for different proton fractions. It shows that the slope becomes negative as the relative nucleon densities increases to a certain value and then increases at higher values. The trend is same at different higher temperatures but terminates to a certain value of slope at certain lower densities.

In this paper, we study the warm equation of state (EOS) of asymmetric nuclear matter taking pion-nucleon interaction with repulsive effect due to ρ and ω mesons. We observe here that our results are comparable with the Non-Linear Walecka (NLWM) and Quark Meson Coupling (QMC) model [

is continuous above the critical temperature T_{c} at which

Saroj KumarSahu, (2015) Finite Temperature Asymmetric Nuclear Matter Using Pion Dressing. Journal of Applied Mathematics and Physics,03,1308-1315. doi: 10.4236/jamp.2015.310159