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

Precise measurements of the spin structure functions of the proton g(1)(p)(x,Q(2)) and deuteron g(1)(d)(x,Q(2)) are presented over the kinematic range 0.0041 <= x <= 0.9 and 0.18 GeV2 <= Q(2)<= 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 g(1)(n) is extracted by combining proton and deuteron data. The integrals of g(1)(p,d) at Q(2)=5 GeV2 are evaluated over the measured x range. Neglecting any possible contribution to the g(1)(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 a(0) in a leading-twist next-to-next-to-leading-order analysis.