  Deep optical B band images of the ROSAT HRI error region of RX J0720.4-3125
reveal the presence of two faint stellar-like objects with B = 26.1 +/- 0.25
and B = 26.5 +/- 0.30. Exposures obtained through U, V and I filters are not
sensitive enough to detect the two candidates and provide upper limits of U =
24.9, V = 23.2 and I = 21.9. These new observations virtually establish that RX
J0720.4-3125 is a slowly rotating, probably completely isolated neutron star.
The absence of an optical counterpart brighter than B = 26.1 seems incompatible
with a neutron star atmosphere having a chemical composition dominated by
Hydrogen or Helium. UBI photometry of field stars shows astonishingly little
interstellar reddening in the direction of the X-ray source. Together with the
small column density detected by the ROSAT PSPC, this suggests a mean particle
density in the range of n = 0.1 - 0.4 cm-3. Such average densities would imply
very low velocities relative to interstellar medium (Vrel < 10 km/s) if the
source were powered by accretion. These stringent constraints may be relaxed if
the neutron star is presently crossing a small size structure of higher density
or if the effective temperature of the heated atmosphere is overestimated by
the blackbody approximation. Alternatively, RX J0720.4-3125 could be a young
and highly magnetized cooling neutron star.
