Standard Solar Models in the Light of New Helioseismic Constraints: I The Solar Core

In this paper, we examine a new updated solar model taking advantage of recent reexamination of the nuclear reactions rates and of the microscopic diffusion of helium and heavy elements. Our best model fits the helioseismic data reasonably well: the base of the convective zone is at r=0.715 Ro, the photospheric helium in mass fraction is 0.243 and the sound speed square difference between the Sun and the model is < 1%. This model leads to a reestimate of the neutrinos fluxes : 7.18 SNU for the chlorine experiment, 127.2 SNU for the gallium detector and 4.82 10^6/cm2/s for the B8 neutrino flux. Acoustic and gravity mode predictions are also estimated. We present 3 models which respect the helioseismic constraints and fit the seismic observations better by taking advantage of the known physical uncertainties: nuclear reaction rates, CNO abundances and microscopic diffusion. We conclude that the standard model in side its inherent uncertainties, is robust in the light of the present acoustic mode detection and that the neutrino fluxes prediction is not well constrained.