| Abstract
| - In this paper, I use the extension of the excursion set model of Sheth & Tormen and the barrier shape obtained in Del Popolo & Gambera to calculate the unconditional halo mass function, and the conditional mass function in several cosmological models. I show that the barrier obtained in Del Popolo & Gambera, which takes account of tidal interaction between protohaloes, is a better description of the mass functions than the spherical collapse and is in good agreement with numerical simulations. The results are also in good agreement with those obtained by Sheth & Tormen — only slight differences are observed especially at the low-mass end. Moreover I calculate, and compare with simulations, the temperature function obtained by means of the mass functions calculated previously and also using an improved version of the M-T relation, which accounts for the fact that massive clusters accrete matter quasi-continuously, and finally taking account of the tidal interaction with neighbouring clusters. Even in this case the discrepancy between the Press—Schechter predictions and simulations is considerably reduced.
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