18-22 September 2023
GSI Darmstadt, Germany
Europe/Berlin timezone

Self-energy of pion and its impact on equation of state

20 Sep 2023, 12:10
Theory Seminar Room (GSI)

Theory Seminar Room


SB3 3.170a
Oral Microscopic calculations of neutron-rich, dense nuclear matter Microscopic calculations of neutron-rich, dense nuclear matter


Dr Ninoy Rahman (GSI)


We study the pionic self-energy and its impact on the energy-momentum dispersion relation of
pion in neutron-rich conditions such as interior of a neutron star. In such neutron-rich state, the
negatively charged pions can be produced copiously. Furthermore, these negatively charged pions
can form a Bose-Einstein condensate with zero momentum above nuclear saturation densities. In
this paper, we evaluate the self-energy of the negatively charged pion using the phase shift data
from the pion-nucleon scattering as well the pion-pion scattering experiments. The self-energy is
determined at material conditions present in a neutron star during binary merger. We notice that
the pion-nucleon scattering can lead to both positive (attractive) and negative (repulsive) pionic
self-energy. This pion-nucleon interaction can lead to a few percent change in the pion energy from
its free value at supranuclear densities. On the other hand, the repulsive pion-pion interaction
results in purely positive self-energy. While evaluating the self-energy related to the purely pionic
interaction, we consider both the condensed pions with zero momentum, and the thermal pions
with finite momenta. At zero temperature, the self-energy due to the pion-pion interaction is
dominated by the condensate part. Whereas, the thermal part can prevail over the condensate
part at finite temperatures. Similar to the pion-nucleon case, the self-energy due to the pion-pion
interaction also results in a few percent change in the pion energy compared to that of the free pion.
Overall, we see that the pionic self-energy is dominated by the pion-pion interaction at lower pion
momenta and by the pion-nucleon interaction at greater momenta. Moreover, the pion momentum,
where the pion-nucleon interaction becomes dominant over the pion-pion interaction, depends on the
matter condition. Furthermore, we studied the impact of the interacting pions on the high-density
nuclear equation of state, and on the neutron star structure under the β-equilibrium condition. For
this study, we modified the non-pionic SFHo equation of state is modified to include pions. The
introduction of pions softens the equation of state and reduces the maximum neutron star mass
compared to that of the equation of state without pions. Moreover, the pion production leads to
the shrinking of the NS radius for a given central baryonic number density. Furthermore, we notice
rather similar mass-radius, and mass-density relations of the neutron star between the EOS with
interacting pions and the EOS with free/non-interacting pions.

Primary author


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