  We derive an equation of state (EOS) for strange matter, starting from an
interquark potential which (i) has asymptotic freedom built into it, (ii) shows
confinement at zero baryon density and deconfinement at high density and (iii)
gives a stable configuration for chargeless, beta--stable quark matter. This
EOS is then used to calculate the structure of Strange Stars, and in particular
their mass-radius relation. Our present results confirm and reinforce the
recent claim by Li et al (Astron. and Astrophys. 303 (1995) L1) and Bombaci
(Phys.Rev. C55 (1997) 1587) that the compact objects associated with the x-ray
pulsar Her X-1, and with the x-ray burster 4U 1820-30 are strange stars.
