Instability of α boson vacuum in highly compressed baryonic matter

Within the relativistic mean-field (RMF) method we investigate the behavior of boson complex scalar fields associated with super(4)He ( alpha ) nuclei and super(4)He ( alpha ) antinuclei and the conditions that make possible the generation of ( alpha , alpha ) pairs due to the vacuum instability in highly compressed baryonic systems consisting of nucleons (with baryon number B = 1) and/or alpha particles (B = 4). The first part of the paper discusses infinite systems under the assumption that the Lagrangian describing the relativistic field of alpha and alpha particles also comprises a quartic self-interaction term. A wide set of RMF parametrizations is used and we establish in each case the conditions for the onset of vacuum instability. We consider both compressed standard baryonic matter with small admixtures of alpha particles and, vice versa, systems comprising alpha nuclei that are gradually doped with symmetric nuclear matter, and calculate the energy of the Kappa = 0 mode as a function of baryon density [rho][nu] and alpha particle density [rho] alpha for both particle and antiparticle sectors. In the second part of the paper we focus on finite-sized baryonic systems. We illustrate this case with a schematic model consisting of a short-range potential where the strengths of the meson fields are prescribed by the infinite matter values and derive the spectrum of bound states for both particles and antiparticles.