The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus
with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. Originally conceived
for real photons, the GDH integral can be generalised to the case of photons with virtuality Q
2. For spin-1/2 targets such as the nucleon, it then represents the non-perturbative limit of the first moment of the spin structure function
g
1
(
x,
Q
2
) in deep inelastic scattering (DIS). The data collected by HERMES with a deuterium target are presented together with a re-analysis
of previous measurements on the proton. This provides an unprecedented and complete measurement of the generalised GDH integral
for photon-virtuality ranging over 1.2&
lt;
Q
2
&
lt;12.0 GeV
2 and for photon-nucleon invariant mass squared W
2 ranging over 1&
lt;
W
2
&
lt;45 GeV
2, thus covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. These data allow the study
of the Q
2-dependence of the full GDH integral, which is sensitive to both the Q
2-evolution of the resonance form factors and contributions of higher twist. The contribution of the nucleon-resonance region
is seen to decrease rapidly with increasing Q
2. The DIS contribution is sizeable over the full measured range, even down to the lowest measured Q
2. As expected, at higher Q
2 the data are found to be in agreement with previous measurements of the first moment of g
1. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton-neutron difference
evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at
Q
2
= 5 GeV
2.
Received: 20 October 2002 / Published online: 15 January 2003
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