Quantum Skyrmion crystals and the symmetry energy of dense matter

Abstract

The canonical quantization method for collective coordinates in crystalline configurations of the generalized Skyrme model is applied in order to find the quantum ground state of Skyrmion crystals and study the quantum corrections to the binding energy resulting from the isospin degrees of freedom. This leads to a consistent description of asymmetric nuclear matter within the Skyrme framework and allows us to compute the symmetry energy of the Skyrmionic crystal as a function of the baryon density, and to compare with recent observational constraints. CONTENTS I. Introduction 1 II. Generalized Skyrme model and classical crystals 2 A. The model 2 B. The classical crystal of Skyrmions 3 C. The Skyrme crystal EoS for symmetric nuclear matter 3 III. Quantization of the Skyrme crystal 4 A. The internal symmetry of Skyrme crystals and the isospin group 4 B. Quantum isospin states and Hilbert space 5 C. Isospin correction to the energy per baryon 7 IV. Quantum skyrmion crystals and the symmetry energy of npe(µ) matter 9 A. The electric charge density of pure Skyrmion matter 9 B. The symmetry energy 10 C. Particle fractions of npeµ matter in β-equilibrium 11 V. Conclusions 12 Acknowledgments 13 A. Calculation of matrix elements 13 B. Isospin inertia tensor of Skyrme crystals 14 References 15

Report on scipost_202312_00005v1

“…In this paper, we propose using the homogeneous Ansatz in the WSS, but quantizing the isospin symmetry -a technique known from the Skyrme model [46,47,48], which is the leading-order low-energy effective theory of the WSS model [18]. The homogeneous Ansatz represents an approximation to describe densely packed nucleons that form nuclear matter above saturation density.…”

Report on scipost_202312_00005v1

“…In this paper, we propose using the homogeneous Ansatz in the WSS, but quantizing the isospin symmetry -a technique known from the Skyrme model [46,47,48], which is the leading-order low-energy effective theory of the WSS model [18]. The homogeneous Ansatz represents an approximation to describe densely packed nucleons that form nuclear matter above saturation density.…”