Calculating the Thermodynamic Potential of a Deuteron in Hot Nuclear Matter*

In this work, we study the properties and thermodynamic potential of a deuteron at finite temperatures typical for the hadronic phase in heavy-ion collisions at RHIC and the LHC, T = 100-160 MeV. Employing previously calculated in-medium nucleon self-energies in the pertinent single-particle propagators, we use Python to compute the imaginary and real parts of the two-particle propagator of the proton-neutron (pn) system. In connection with a schematic (separable) interaction for the pn interaction which reproduces the vacuum binding energy of the deuteron, we use the two-particle propagator to quantify the modifications of the deuteron properties in a hot medium through the computation of the pn scattering amplitude. We find a strong broadening of the deuteron scattering amplitude as temperature increases, driven by the collisional widths of the nucleons. Further, we use Matsubara formalism to obtain an expression of the thermodynamic distribution of deuterons at finite temperature in terms of thermal Bose factors. Using this and the scattering amplitude, we can compute the fully resummed thermodynamic potential of the deuteron. This calculation indicates an increasing suppression of the deuteron's contribution to the thermodynamic potential in a hadron resonance gas at finite temperatures, T = 100-160 MeV, suggesting the dissolution of the deuteron bound state under these conditions.