We present a new survey for damped Ly alpha systems with redshifts z approximate to 1.6-3.0. The survey is based on a sample of 228 QSOs drawn from the Large Bright QSO Survey (LBQS). We find a total of 20 candidate damped Ly alpha lines with rest frame equivalent widths determined from low-resolution spectroscopy of W greater than or equal to 10 Angstrom. Using intermediate-resolution spectroscopy, we and other workers confirm 12 of these candidates and an additional candidate with W < 10 Angstrom as damped Ly alpha systems with H I column densities N(H I) greater than or equal to 2 x 10(20) cm(-2). All the systems were drawn from a redshift path Delta z = 121.0 along which it is possible to detect damped Ly alpha candidates with W greater than or equal to 5 Angstrom at 5 sigma statistical significance. We combine the results of the LBQS damped survey with results of previous surveys for damped systems to form a ''statistical sample'' of 62 damped Ly alpha systems with N(H I) greater than or equal to 2 x 10(20) cm(-2). These systems are drawn from a total redshift path Delta z = 323.8. A list of 18 additional damped Ly alpha systems not found in systematic surveys is also presented. Therefore, we are aware of 80 damped Ly alpha absorption systems at the time of writing (1995 March) with N(H I) greater than or equal to 2 x 10(20) cm(-2). The following is a summary of results based on the ''statistical sample. 1. The LBQS damped survey increases the sensitivity for finding damped Ly alpha systems in the redshift interval z approximate to 1.6-2.5. 2. Using the ''statistical sample,'' we find that the quantity n(z), the number of absorbers per unit redshift interval with N(H I) greater than or equal to 2 x 10(20) cm(-2) shows no evidence for intrinsic evolution. The new n(z) exhibits little scatter around a systematic increase of n(z) with z and is in excellent agreement with our previous determination of n(z). 3. Our determination of Omega(g)(z), the comoving mass density of neutral gas at redshift z, shows a monotonically increasing form of Omega(g)(z) with z for the first time. The new data support and strengthen the earlier conclusion that the comoving density of neutral gas increases with redshift. Comparison of n(z) for systems having N(H I) greater than or equal to 2 x 10(20) cm(-2) with a subset having N(H I) greater than or equal to 10(21) cm(-2) shows the decrease of Omega(g) with time to arise from the decline of the high column density systems. 4. We determine f(hr, z), the frequency distribution of H I column densities. The new f(N, z) shows considerably less scatter than was present in the previous result, especially in the highest redshift bin z = 2.5-3.5, where f(N, z) is now well represented by a single N-1 power law. The new f(N, z) shows the decline of the high column density systems with time explicitly. 5. We interpret the evolution of Omega(g)(z) to result from gas consumption by star formation. The principal arguments are as follows: (a) there is good agreement between Omega(g) in the highest redshift bin and Omega(star), the density of visible matter in nearby galaxies, (b) Omega(g)(z) decreases monotonically with decreasing z and approaches the neutral gas density determined from 21 cm emission by nearby galaxies at z = 0, (c) gas consumption by star formation in nearby spirals increases rapidly with increasing N(H I), which is consistent with our finding that the high column density systems disappear with time, and (d) detailed investigations of individual objects reveal gas that is quiescent, cold, and possibly in a state of rotation; i.e., the type of gas in which stars are known to form. 6. We present a new model for the evolution of f(N, z). The model incorporates star formation in randomly oriented exponential disks. The star formation rates are consistent with the Schmidt-Kennicutt expressions for star formation. The model predictions are in good agreement with the data. 7. Comparison between the neutral gas content of damped Ly alpha systems with the baryonic density predicted by big bang nucleosynthesis shows the damped systems at high z to contain at least 10% of the baryonic content of the universe. All the evidence cited above supports the idea that the damped Ly alpha systems are the progenitors of current galaxies.
