  We study the physical properties of the Lyman-alpha forest by applying the
inversion method described by Pichon et al. (2001) to the high resolution and
high S/N ratio spectrum of the z_em=2.40 quasar HE 1122-1628 obtained during
Science Verification of UVES at the VLT. We compare the column densities
obtained with the new fitting procedure with those derived using standard Voigt
profile methods. The agreement is good and gives confidence in the new
description of the Lyman-alpha forest as a continuous field as derived from our
method. We show that the observed number density of lines with logN>13 and 14
is, respectively, 50 and 250 per unit redshift at z~2. We study the physical
state of the gas, neglecting peculiar velocities, assuming a relation between
the overdensity and the temperature. T=Tbar * rho^(2beta). There is an
intrinsic degeneracy between the parameters beta and Tbar. We demonstrate that,
at a fixed beta, the temperature at mean density, Tbar, can be uniquely
extracted however. While applying the method to HE 1122-1628, we conclude that
for 0.2<beta<0.3, 6000<Tbar<15000 K at z~2. We investigate the small scale
structure of strong absorption lines using the information derived from the
Lyman-beta, Lyman-gamma and Civ profiles. Introducing the Lyman-beta line in
the fit allows us to reconstruct the density field up to rho~10 instead of 5
for the Lyman-alpha line only. There may be small velocity shifts ~10km.s^{-1}
between the peaks in the Civ and Hi density profiles. Although the statistics
is small, it seems that Civ/Hi and n_HI are anti-correlated. This could be a
consequence of the high sensitivity of the Civ/Hi ratio to temperature. The
presence of associated Ovi absorption, with similar profile, confirms that the
gas is photo-ionized and at a temperature of T~10^5 K.
