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We calculate the column density distribution of damped Lyman alpha systems,modeled as spherical isothermal gaseous halos ionized by the external cosmicbackground. The effects of self-shielding introduce a hump in thisdistribution, at a column density N_{HI} \sim 1.6x10^{17} X^{-1} cm^{-2}, whereX is the neutral fraction at the radius where self-shielding starts beingimportant. The most recent compilation of the column density distribution byStorrie-Lombardi & Wolfe shows marginal evidence for the detection of thisfeature due to self-shielding, suggesting a value X \sim 10^{-3}. Assuming aphotoionization rate \Gamma \sim 10^{-12} s^{-1} from the external ionizingbackground, the radius where self-shielding occurs is inferred to be about3.8kpc. If damped Lyman alpha systems consist of a clumpy medium, this shouldbe interpreted as the typical size of the gas clumps in the region where theybecome self-shielding. Clumps of this size with typical column densities N_H\sim 3x10^{20} cm^{-2} would be in hydrostatic equilibrium at thecharacteristic photoionization temperature \sim 10^4 K if they do not containdark matter. Since this size is similar to the overall radius of damped \lyasystems in Cold Dark Matter models, where all halos are assumed to containsimilar gas clouds producing damped absorbers, this suggests that the gas indamped absorbers is in fact not highly clumped.Comment: 9 pages, 3 eps figures, references added, Fig.2 modified, the  inferred size of the clouds increases a little, accepted for publication in  ApJ Letter

Self-shielding Effects on the Column Density Distribution of Damped L[CLC]y[/CLC]α Systems