We present the first science results from our Hubble Space Telescope Survey for Lyman limit absorption systems (LLS) using the low dispersion spectroscopic modes of the Advanced Camera for Surveys and the Wide Field Camera 3. Through an analysis of 71 quasars, we determine the incidence frequency of LLS per unit redshift and per unit path length, l(z) and l(x) respectively, over the redshift range 1 < z< 2.6, and find a weighted mean of l(x)=0.29 +/-0.05 for 2.0 < z < 2.5 through a joint analysis of our sample and that of Ribaudo et al. (2011). Through stacked spectrum analysis, we determine a median (mean) value of the mean free path to ionizing radiation at z=2.4 of lambda_mfp = 243(252)h^(-1) Mpc, with an error on the mean value of +/- 43h^(-1) Mpc. We also re-evaluate the estimates of lambda_mfp from Prochaska et al. (2009) and place constraints on the evolution of lambda_mfp with redshift, including an estimate of the breakthrough redshift of z = 1.6. Consistent with results at higher z, we find that a significant fraction of the opacity for absorption of ionizing photons comes from systems with N_HI <= 10^{17.5} cm^(-2) with a value for the total Lyman opacity of tau_lyman = 0.40 +/- 0.15. Finally, we determine that at minimum, a 5-parameter (4 power-law) model is needed to describe the column density distribution function f(N_HI, X) at z sim 2.4, find that f(N_HI,X) undergoes no significant change in shape between z sim 2.4 and z sim 3.7, and provide our best fit model for f(N_HI,X).
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