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Bounded potentials are good models to represent the effective two-bodyinteraction in some colloidal systems, such as dilute solutions of polymerchains in good solvents. The simplest bounded potential is that of penetrablespheres, which takes a positive finite value if the two spheres are overlapped,being 0 otherwise. Even in the one-dimensional case, the penetrable-rod modelis far from trivial, since interactions are not restricted to nearest neighborsand so its exact solution is not known. In this paper we first derive the exactcorrelation functions of penetrable-rod fluids to second order in density atany temperature, as well as in the high-temperature and zero-temperature limitsat any density. Next, two simple analytic theories are constructed: ahigh-temperature approximation based on the exact asymptotic behavior in thelimit $T\to\infty$ and a low-temperature approximation inspired by the exactresult in the opposite limit $T\to 0$. Finally, we perform Monte Carlosimulations for a wide range of temperatures and densities to assess thevalidity of both theories. It is found that they complement each other quitewell, exhibiting a good agreement with the simulation data within theirrespective domains of applicability and becoming practically equivalent on theborderline of those domains. A perspective on the extension of both approachesto the more realistic three-dimensional case is provided.Comment: 19 pages, 11 figures, 4 tables: v2: minor changes; published final  versio

Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories