A precise determination of the neutron skin thickness of a heavy nucleus sets
a basic constraint on the nuclear symmetry energy (the neutron skin thickness
is the difference of the neutron and proton rms radii of the nucleus). The
parity radius experiment (PREX) may achieve it by electroweak parity-violating
electron scattering (PVES) on 208Pb. We investigate PVES in nuclear mean field
approach to allow the accurate extraction of the neutron skin thickness of
208Pb from the parity-violating asymmetry probed in the experiment. We
demonstrate a high linear correlation between the parity-violating asymmetry
and the neutron skin thickness in successful mean field forces as the best
means to constrain the neutron skin of 208Pb from PREX, without assumptions on
the neutron density shape. Continuation of the experiment with higher precision
in the parity-violating asymmetry is motivated since the present method can
support it to constrain the density slope of the nuclear symmetry energy to new
accuracy.Comment: 4 pages, 3 figures, some changes in text and references, version to
appear in Phys. Rev. Let
