Dense matter equation of state and phase transitions from a Generalized Skyrme model

Abstract

Skyrmion crystals are the field configurations which minimize the energy per baryon in the infinitely large topological charge sector of the Skyrme model, at least for sufficiently high density. They are, therefore, an important tool to describe the ground state of cold, symmetric nuclear matter at high density regimes. In this work, we analyze different crystalline phases and the existence of phase transitions between them within the generalized Skyrme model, making special emphasis in describing symmetric nuclear matter in a wide regime of densities. Furthermore, we propose a new energy-minimizing crystalline phase for densities lower than the nuclear saturation point (n0) which also presents a good qualitative behavior in the zero density limit, improving the predictive power of the model by allowing the description of matter with n < n0.

Quantum Skyrmion crystals and the symmetry energy of dense matter

“…This has been first found in the case where the EoS was motivated by certain limits of the Skyrme model [19]. Later on, it has been confirmed in the full Skyrme model computation [20]. Remarkably, some Skyrme model-based EoS lead to observables which pass the current available observational data, concerning e.g., mass-radius curves, tidal deformabilities and quasiuniversal relations between the moment of inertia, Love numbers and the quadrupole moment of slowly rotating stars [21].…”

“…A more detailed description of the construction of the Skyrme crystal and the comparison of different symmetries can be found in [20], and we have kept the same notation for this work. As in that previous work, the unit cell has size 2L and a baryon content of B cell = 4.…”

“…As in that previous work, the unit cell has size 2L and a baryon content of B cell = 4. Then, for each value of L we obtain the minimum of energy as explained in [20]. It turns out that the energy-size curve, E cell (L), is a convex function which has a minimum at a certain L * .…”

“…It has been recently shown [20] that this picture is significantly modified if the sextic term is added. First of all, the FCC to BCC phase transition is moved to much smaller densities, approximately 4-5 saturation densities, which easily can be found in the center of heavy NS.…”

“…The starting point in these computations consists in the numerical derivation of the lowest energy periodic Skyrmion solution representing infinite nuclear matter, at a given density, using a variational approach [20]. Next, one can find the corresponding EoS by studying the dependence of the energy of such solutions on the density.…”