The morphology of clusters of galaxies may be described with a set of parameters which contain information concerning the formation and evolutionary history of these systems. In this paper we present a preliminary study of the morphological parameters of a sample of 28 compact Abell clusters extracted from Digitized Palomar Sky Survey data, measured with a procedure based on the use of the CIAO-SHERPA software, developed at the Centre for Astrophysics for X-ray data analysis. The morphology of galaxy clusters is parametrized by their apparent ellipticity, position angle of the major axis, centre coordinates, core radius and beta-model power-law index. Our procedure provides estimates of these parameters ( and of the related uncertainties) by simultaneously fitting them all, overcoming some of the difficulties induced by sparse data and low-number statistics typical of this kind of analysis. The cluster parameters were fitted in a 6 x 6 Mpc(2) region, measuring the background in a 4 < R < 5 Mpc annulus. We also explore the correlations between shape and profile parameters and other cluster properties. Our results can be summarized as follows: one-third of this compact cluster sample has core radii smaller than 100 kpc, i.e. near the limit that our data allow us to resolve, possibly consistent with cusped models. The remaining clusters span a broad range of core radii up to similar to 1500 kpc, including some apparently regular clusters with well-resolved core radii. More than 80 per cent of this sample has ellipticity higher than 0.2. The alignment between the cluster and the major axis of the dominant galaxy is confirmed at a high significance level, while no correlation is observed with other bright cluster members. No significant correlation is found between cluster richness and ellipticity. Instead, cluster richness is found to correlate, albeit with large scatter, with the cluster core radius. Finally, in contrast to claims in previous works, a flat universe seems to be favoured, and in any case is not excluded, by the power-law index of our number density profiles.
