Soliton matter in the two-dimensional linear sigma model

We consider a one-dimensional model of nuclear matter where the quark clusters are described by solutions of the sigma model on a linear lattice in the self-consistent mean field approximation. Exact expressions are given for the baglike solutions confined to a finite interval, corresponding in the infinite interval limit to the free solitons previously found by Campbell and Liao. Periodic, self-consistent solutions which satisfy Bloch’s theorem are constructed. Their energies and associated quark sigma field distributions are calculated numerically as functions of the baryon spacing, and compared with those of the uniform quark plasma. The predicted configuration of the ground state depends critically on the assumed manner of filling the lowest band of quark single-particle levels, and on the density. In the absence of additional repulsive forces in the model, we find that the high density massless quark plasma is energetically favored and that there is a smooth transition from the baglike state to a uniform plasma with nonvanishing sigma field at comparatively large lattice constants 2d≊10$m_q^{\mathrm{-}1}$ ($m_q$ is the quark mass). If dilute filling of the entire band is employed, the clustered state is stable and a first order phase transition can occur for a range of much smaller lattice spacings 2d≊4$m_q^{\mathrm{-}1}$. .AE