We investigate the phase behavior of a single-component system in 3dimensions with spherically-symmetric, pairwise-additive, soft-coreinteractions with an attractive well at a long distance, a repulsive soft-coreshoulder at an intermediate distance, and a hard-core repulsion at a shortdistance, similar to potentials used to describe liquid systems such ascolloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692(2001)] that, even with no evidences of the density anomaly, the phase diagramhas two first-order fluid-fluid phase transitions, one ending in agas--low-density liquid (LDL) critical point, and the other in agas--high-density liquid (HDL) critical point, with a LDL-HDL phase transitionat low temperatures. Here we use integral equation calculations to explore the3-parameter space of the soft-core potential and we perform molecular dynamicssimulations in the interesting region of parameters. For the equilibrium phasediagram we analyze the structure of the crystal phase and find that, within theconsidered range of densities, the structure is independent of the density.Then, we analyze in detail the fluid metastable phases and, by explicitthermodynamic calculation in the supercooled phase, we show the absence of thedensity anomaly. We suggest that this absence is related to the presence ofonly one stable crystal structure.
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