Precise determination of the spin structure function g₁ of the proton, deuteron, and neutron

Precise measurements of the spin structure functions of the proton g₁^px,Q² and deuteron g₁^dx,Q² are presented over the kinematic range 0.0041 <= x <= 0.9 and 0.18 GeV² <= Q² <= 20 GeV². The data were collected at the HERMES experiment at DESY, in deep-inelastic scattering of 27.6 GeV longitudinally polarized positrons off longitudinally polarized hydrogen and deuterium gas targets internal to the HERA storage ring. The neutron spin structure function g₁ⁿ is extracted by combining proton and deuteron data. The integrals of g₁^p,d at Q² = 5 GeV² are evaluated over the measured x range. Neglecting any possible contribution to the g₁^d integral from the region x <= 0.021, a value of 0.330 ± 0.011(theo) ± 0.025(exp) ± 0.028(evol) is obtained for the flavor-singlet axial charge a₀ in a leading-twist next-to-next-to-leading-order analysis