With close pairs of quasars at different redshifts, a background quasar sightline can be used to study a foreground quasars environment in absorption. We search 149 moderate resolution background quasar spectra, from Gemini, Keck, the MMT, and the SDSS to survey Lyman Limit Systems (LLSs) and Damped Ly-alpha systems (DLAs) in the vicinity of 1.8 < z < 4.0 luminous foreground quasars. A sample of 27 new quasar-absorber pairs is uncovered with column densities, 17.2 < log (N_HI/cm^2) < 20.9, and transverse (proper) distances of 22 kpc/h < R < 1.7 Mpc/h, from the foreground quasars. If they emit isotropically, the implied ionizing photon fluxes are a factor of ~ 5-8000 times larger than the ambient extragalactic UV background over this range of distances. The observed probability of intercepting an absorber is very high for small separations: six out of eight projected sightlines with transverse separations R < 150 kpc/h have an absorber coincident with the foreground quasar, of which four have log N_HI > 10^19. The covering factor of log N_HI > 10^19 absorbers is thus ~ 50 % (4/8) on these small scales, whereas < 2% would have been expected at random. There are many cosmological applications of these new sightlines: they provide laboratories for studying fluorescent Ly-alpha recombination radiation from LLSs, constrain the environments, emission geometry, and radiative histories of quasars, and shed light on the physical nature of LLSs and DLAs.
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