1 Introduction

Cosmological simulations based on CDM models predict that the forest of H I Lyman-$\alpha$ absorption lines, observed in QSO spectra, originates in the fluctuations of the underdense and moderately overdense regions of the intergalactic medium (e.g. Cen et al. 1994; Petitjean et al. 1995; Zhang et al. 1995; Hernquist et al. 1996; Miralda-Escudé et al. 1996; Theuns et al. 1998). The high H I column density systems (Lyman limit and damped Lyman-$\alpha$ systems), on the other hand, arise from radiatively cooled gas in galaxy-sized halos (e.g. Katz et al. 1996).

In the past few years, the association of high column density absorption systems ( $N(\mbox{H {\sc i}}) \raisebox{-5pt}{$\;\stackrel{\textstyle >}{\sim}\;$ } 10^{16}$ cm^-2) with galactic objects has been widely verified at redshifts up to $z \sim 1$, by direct imaging of QSO fields and follow-up spectroscopy. The observed impact parameters for galaxies giving rise to Mg II absorption systems suggest the presence of extended gaseous halos of spherical geometry and radii $R \sim 50\ h^{-1}$ kpc (where h is the Hubble constant in units of 75 km s^-1 Mpc^-1, and q₀=0) (Bergeron & Boissé 1991; Bergeron et al. 1992; Steidel et al. 1994; Guillemin & Bergeron 1997). While damped Lyman-$\alpha$ systems (DLASs) are likely due to smaller structures (Wolfe et al. 1992; Le Brun et al. 1997).

The correlation properties of absorbers along the line of sight (LOS) were studied recently. A trend of increasing correlation signal with increasing H I column density at $z \sim 2$ is detected for QSO absorption lines up to N(H I $) \sim 10^{17}$ cm^-2 (Cristiani et al. 1997). At the same redshift, higher column density systems are expected to be more correlated according to the hierarchical clustering scenario, as they are believed to be associated with galactic or proto-galactic structures. The classic approach to compute the correlation function is complicated by their rareness. In the hypothesis that DLASs are indeed galaxies, Wolfe (1993) handles this problem by comparing the density of Lyman-$\alpha$ emitters in the field and at the redshift of observed DLASs ( $<z>\; = 2.6$), with that of randomly chosen fields at similar redshift. A Poissonian distribution of galaxies in the fields centred on DLASs is ruled out with more than 99.5% confidence, but little else can be said on the correlation function.

Close pairs or groups of QSO LOSs represent an alternative, efficient tool to investigate the correlation properties of absorbers. Francis & Hewett (1993) find two candidate DLASs in the spectrum of Q2138-4427 at $z_{\rm a} \simeq 2.38$ and 2.85 matching in redshift two weaker Lyman-$\alpha$ absorptions in the spectrum of the companion quasar Q2139-4434, at a separation of 8 arcmin on the plane of the sky. Later deep imaging of the field of Q2139-4434 has indeed confirmed the presence of a group of red, radio quiet galaxies at $z\simeq 2.38$. This galaxy cluster, with mass $\gg$ $3 \times 10^{11}\ M_{\odot}$, could have collapsed before redshift 5 (Francis et al. 1996, 1997, 2001a).

In this paper, we use two QSO pairs and a triplet to analyse the correlation behaviour of high matter density peaks. We assume that high matter density peaks are traced by optically thick absorbers (i.e. with column density N(H I $) \raisebox{-5pt}{$\;\stackrel{\textstyle >}{\sim}\;$ }2\times 10^{17}$ cm^-2) and by strong metal systems (characterised by C IV rest equivalent width $W_{\rm r}(\lambda1548) \ge 0.5$ Å).

The structure of the paper is the following: Sect. 2 describes the observations and data reduction of 6 new UVES spectra of three QSO pairs (Q2344+1228 and Q2343+1232, UM680 and UM681, Q2139-4433 and Q2139-4434); in Sect. 3, we describe in more detail one sub-damped and two damped Lyman-$\alpha$ systems detected in the spectra, with a particular attention to chemical abundances. Section 4 is dedicated to the description of the observed coincidences. The discussion is reported in Sect. 5 and the summary of results in Sect. 6.

All through the paper, we adopt a cosmology with q₀ = 0.5 and h = H₀ / 75 km s^-1 Mpc^-1. Spatial separations are always comoving.