  We present the proton and neutron vector form factors in a convenient
parametric form that is optimized for momentum transfers $\lesssim$ few
GeV$^2$. The form factors are determined from a global fit to electron
scattering data and precise charge radius measurements. A new treatment of
radiative corrections is applied. This parametric representation of the form
factors, uncertainties and correlations provides an efficient means to evaluate
many derived observables. We consider two classes of illustrative examples:
neutrino-nucleon scattering cross sections at GeV energies for neutrino
oscillation experiments and nucleon structure corrections for atomic
spectroscopy. The neutrino-nucleon charged current quasielastic (CCQE) cross
section differs by 3-5% compared to commonly used form factor models when the
vector form factors are constrained by recent high-statistics electron-proton
scattering data from the A1 Collaboration. Nucleon structure parameter
determinations include: the magnetic and Zemach radii of the proton and
neutron, $[r_M^p, r_M^n] = [ 0.739(41)(23), 0.776(53)(28)]$ fm and $[r_Z^p,
r_Z^n] = [ 1.0227(94)(51), -0.0445(14)(3)]$ fm; the Friar radius of nucleons,
$[(r^p_F)^3, (r^n_F)^3] = [2.246(58)(2), 0.0093(6)(1)]$ fm$^3$; the electric
curvatures, $[\langle r^4 \rangle^p_E, \langle r^4 \rangle^n_E ] =
[1.08(28)(5), -0.33(24)(3)]$ fm$^4$; and bounds on the magnetic curvatures, $[
\langle r^4 \rangle^p_M, \langle r^4 \rangle^n_M ] = [ -2.0(1.7)(0.8),
-2.3(2.1)(1.1)]$ fm$^4$. The first and dominant uncertainty is propagated from
the experimental data and radiative corrections, and the second error is due to
the fitting procedure.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;Nuclear Theory;Atomic Physics