We derive H I column density and Doppler width distributions for a sample of Lyα clouds with 3.4 < z < 4.0, using a high resolution spectrum of the quasar Q 0000−26 (zem = 4.127) obtained with the Keck telescope. Simulated Lyα forest spectra with matching characteristics are analyzed similarly in order to gauge the effects of line blending/blanketing and noise in the data. The H I column density distribution, after corrections for incompleteness resulting from line blanketing, is well described by a single power law function with index β = −1.55±0.05 over the column density range of 12.6 < logN < 16.0. A steepening in the column density distribution at log N(H I)> 14.5 may be present. The Doppler width distribution of the clouds is consistent with a Gaussian function with a mean of 23 km s −1 and a dispersion of 8 km s −1, but with a cutoff at 15 km s −1, ie, no clouds with b < 15 km s −1 are required to describe the data. While the H I column density distribution found here is consistent with that derived from similar quality data at lower redshifts, both the mean Doppler width and the cutoff value are smaller than those found at lower redshift. There is a hint for clustering in the clouds ’ line of sight distribution in the velocity interval 100 < ∆v < 160 km s −1, but the evidence is only marginal. Analyses of the proximity effect indicate a value of J LL ν ∼ 2 ×10 −22 erg s −1 cm −2 Hz −1 sr −1 for the mean intensity of the metagalactic UV ionizing background at z ∼ 4.1, which is consistent with that expected from high-redshift quasars
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