Skyrme crystals with massive pions

Abstract

The crystalline structure of nuclear matter is investigated in the standard Skyrme model with massive pions. A semi-analytic method is developed to determine local minima of the static energy functional with respect to variations of both the field and the period lattice of the crystal. Four distinct Skyrme crystals are found. Two of these were already known–the cubic lattice of half-skyrmions and the α-particle crystal–but two are new. These new solutions have lower energy per baryon number and less symmetry, being periodic with respect to trigonal but not cubic period lattices. Minimal energy crystals are also constructed under the constraint of constant baryon density, and it is shown that the two new non-cubic crystals tend to chain and multi-wall solutions at low densities.