Extant chemical evolution models underestimate the Galactic production of Sr, Y and Zr as well as the Solar System abundances of s-only isotopes with 90<A<130. To solve this problem, an additional (unknown) process has been invoked, the so-called LEPP (Light Element Primary Process). In this paper we investigate possible alternative solutions. Basing on Full Network Stellar evolutionary calculations, we investigate the effects on the Solar System s-only distribution induced by the inclusion of some commonly ignored physical processes (e.g. rotation) or by the variation of the treatment of convective overshoot, mass-loss and the efficiency of nuclear processes. Our main findings are: 1) at the epoch of the formation of the Solar System, our reference model produces super-solar abundances for the whole s-only distribution, even in the range 90<A<130; 2) within errors, the s-only distribution relative to 150Sm is flat; 3) the s-process contribution of the less massive AGB stars (M<1.5 M_SUN) as well as of the more massive ones (M>4.0 M_SUN) are negligible; 4) the inclusion of rotation implies a downward shift of the whole distribution with an higher efficiency for the heavy s-only isotopes, leading to a flatter s-only distribution; 5) different prescriptions on convection or mass-loss produce nearly rigid shifts of the whole distribution. In summary, a variation of the standard paradigm of AGB nucleosynthesis would allow to reconcile models predictions with Solar System s-only abundances. Nonetheless, the LEPP cannot be definitely ruled out, because of the uncertainties still affecting stellar and Galactic chemical evolution models.
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