Evolution and nucleosynthesis of zero-metal intermediate-mass stars

New stellar models with masses ranging between 4 and 8 M-circle dot, Z = 0, and Y = 0.23 are presented. The models have been evolved from the pre-main sequence up to the asymptotic giant branch (AGB). At variance with previous claims, we find that these updated stellar models do experience thermal pulses in the AGB phase. In particular, we show the following : 1. In models with a mass larger than 6 M-circle dot, the second dredge-up is able to raise the CNO abundance in the envelope enough to allow a normal AGB evolution, in the sense that the thermal pulses and the third dredge-up take place. 2. In models of lower mass, the efficiency of the CNO cycle in the H-burning shell is controlled by the carbon produced locally via the 3 alpha reactions. Nevertheless, the He-burning shell becomes thermally unstable after the early AGB. The expansion of the overlying layers induced by these weak He-shell flashes is not sufficient by itself to allow a deep penetration of the convective envelope. However, soon after the development of the maximum luminosity of the He flash is attained, a convective shell systematically forms at the base of the H-rich envelope. The innermost part of this convective shell probably overlaps the underlying C-rich region left by the intershell convection during the thermal pulse so that fresh carbon is dredged up in a hot H-rich environment and an H flash occurs. This flash favors the expansion of the outermost layers already started by the weak thermal pulse, and a deeper penetration of the convective envelope takes place. Then the carbon abundance in the envelope rises to a level high enough that the further evolution of these models closely resembles that of more metal-rich AGB stars. These stars provide an important source of primary carbon and nitrogen, so a major revision of the chemical evolution in the early Galaxy is required. We suggest that the chemical imprint of these Population III stars could be found in the old and metal-poor components of the Milky Way.