  We propose an extension of the second-order Barker-Henderson perturbation
theory for polydisperse hard-sphere multi-Morse mixture. To verify the accuracy
of the theory, we compare its predictions for the limiting case of monodisperse
system, with predictions of the very accurate reference hypernetted chain
approximation. The theory is used to describe the liquid-gas phase behavior of
the mixture with different type and different degree of polydispersity. In
addition to the regular liquid-gas critical point, we observe the appearance of
the second critical point induced by polydispersity. With polydispersity
increase, the two critical points merge and finally disappear. The
corresponding cloud and shadow curves are represented by the closed curves with
'liquid' and 'gas' branches of the cloud curve almost coinciding for higher
values of polydispersity. With a further increase of polydispersity, the cloud
and shadow curves shrink and finally disappear. Our results are in agreement
with the results of the previous studies carried out on the qualitative van der
Waals level of description.
