  We generate new standard solar models using newly analyzed nuclear fusion
cross sections and present results for helioseismic quantities and solar
neutrino fluxes. We discuss the status of the solar abundance problem and
investigate whether nonstandard solar models with accretion from the
protoplanetary disk might alleviate the problem. We examine a broad range of
possibilities, analyzing both metal-enriched and metal-depleted accretion
models and exploring three scenarios for the timing of the accretion. Only
partial solutions are found: one can bring either the depth of the convective
zone or the surface helium abundance into agreement with helioseismic results,
but not both simultaneously. In addition, detailed results for solar neutrino
fluxes show that neutrinos are a competitive source of information about the
solar core and can help constrain possible accretion histories of the Sun.
Finally, we briefly discuss how measurements of solar neutrinos from the
CN-cycle could shed light on the interaction between the early Sun and its
protoplanetary disk.
