Title: A high precision semi-analytic mass function,
Abstract: In this paper, extending past works of Del Popolo, we show how a high
precision mass function (MF) can be obtained using the excursion set approach
and an improved barrier taking implicitly into account a non-zero cosmological
constant, the angular momentum acquired by tidal interaction of
proto-structures and dynamical friction. In the case of the $\Lambda$CDM
paradigm, we find that our MF is in agreement at the 3\% level to Klypin's
Bolshoi simulation, in the mass range $M_{\rm vir} = 5 \times 10^9 h^{-1}
M_{\odot} -- 5 \times 10^{14} h^{-1} M_{\odot}$ and redshift range $0 \lesssim
z \lesssim 10$. For $z=0$ we also compared our MF to several fitting formulae,
and found in particular agreement with Bhattacharya's within 3\% in the mass
range $10^{12}-10^{16} h^{-1} M_{\odot}$. Moreover, we discuss our MF validity
for different cosmologies.