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We study the physical properties of the Lyman-alpha forest by applying theinversion method described by Pichon et al. (2001) to the high resolution andhigh S/N ratio spectrum of the z_em=2.40 quasar HE 1122-1628 obtained duringScience Verification of UVES at the VLT. We compare the column densitiesobtained with the new fitting procedure with those derived using standard Voigtprofile methods. The agreement is good and gives confidence in the newdescription of the Lyman-alpha forest as a continuous field as derived from ourmethod. We show that the observed number density of lines with logN>13 and 14is, respectively, 50 and 250 per unit redshift at z~2. We study the physicalstate of the gas, neglecting peculiar velocities, assuming a relation betweenthe overdensity and the temperature. T=Tbar * rho^(2beta). There is anintrinsic degeneracy between the parameters beta and Tbar. We demonstrate that,at a fixed beta, the temperature at mean density, Tbar, can be uniquelyextracted however. While applying the method to HE 1122-1628, we conclude thatfor 0.2<beta<0.3, 6000<Tbar<15000 K at z~2. We investigate the small scalestructure of strong absorption lines using the information derived from theLyman-beta, Lyman-gamma and Civ profiles. Introducing the Lyman-beta line inthe fit allows us to reconstruct the density field up to rho~10 instead of 5for 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 statisticsis small, it seems that Civ/Hi and n_HI are anti-correlated. This could be aconsequence of the high sensitivity of the Civ/Hi ratio to temperature. Thepresence of associated Ovi absorption, with similar profile, confirms that thegas is photo-ionized and at a temperature of T~10^5 K.Comment: 15 pages, 21 figures, accepted for publication in A&A. Quoted results  from other papers in section 4.2 have been modifie

Physical properties and small-scale structure of the Lyman-αforest: Inversion of the HE 1122-1628 UVES spectrum