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