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In this article we calculate the probabilty of having
$\Delta(1232)$ resonance in frozen and hot neutron, nuclear and
?-stable matter. We use the temperature dependence correlation
functions that are generated through a lowest order constrained
variational calculation with the $\Delta-Reid$ potential. The $NN
\rightarrow N\Delta$ transition is built in through a two-pion
exchange interaction. The electrons and muons are treated
relativistically in the total Hamiltonian at given temperature and
density, in order to make the fluid electrically neutral and
stable with respect to $\beta-decay$. We ignore the weak
interaction. It is seen that the $\Delta$ probability in neutron
matter is much larger than in nuclear and $\beta-stable$ matter at
a given temperature and density. As we increase the temperature,
the $\Delta$ probability decreases in nuclear and neutron matter.
However, this decrease is not significant in case of
$\beta-stable$ nuclear matter. There is overall agreement between
our $\Delta$ probability calculation and the recent experiments
performed on $^{3}He$ up to $^{208}Pb$ nuclei. It is concluded
that the isobar degrees of freedom could make the equation of
state of neutron star matter harder at finite temperature and
suppress the numbers of protons and leptons in the proto-neutron
stars.
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