Precision Determination of the Neutron Spin Structure Function {ital g}{sup {ital n}}{sub {ital 1}}

We report on a precision measurement of the neutron spin structure function g{sup n}{sub 1} using deep inelastic scattering of polarized electrons by polarized {sup 3}He . For the kinematic range 0.014{lt}x{lt}0.7 and 1{lt}Q{sup 2}{lt}17(GeV /c){sup 2} , we obtain {integral}{sub 0.014}{sup 0.7}g{sup n}{sub 1}(x)dx={minus}0.036{plus_minus}0.004(stat){plus_minus}0.005(syst) at an average Q{sup 2}=5(GeV/c){sup 2}. We find relatively large negative values for g{sup n}{sub 1} at low x . The results call into question the usual Regge theory method for extrapolating to x=0 to find the full neutron integral {integral}{sub 0}{sup 1}g{sup n}{sub 1}(x)dx, needed for testing the quark-parton model and QCD sum rules. {copyright} {ital 1997} {ital The American Physical Society}