  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.
