Nuclear Effects in Deep Inelastic Scattering of Polarized Electrons off Polarized He and the Neutron Spin Structure Functions

It is shown that the nuclear effects playing a relevant role in Deep Inelastic Scattering of polarized electrons by polarized 3He are mainly those arising from the effective proton and neutron polarizations generated by the S′ and D waves in 3He. A simple and reliable equation relating the neutron, g 1 , and 3He, g3 1 , spin structure functions is proposed. It is shown that the measurement of the first moment of the 3He structure function can provide a significant check of the Bjorken Sum Rule. 13.60.Hb,14.20.Dh,13.88.+e,25.30.Fj Typeset using REVTEX 1 The spin structure functions (SSF) of the nucleon g 1 and g N 2 provide information on the spin distribution among the nucleon partons and can allow important tests of various models of hadron’s structure [1]. Our experimental knowledge is limited at present to the proton SSF g 1 [2,3] and it is for this reason that new experiments [4–6] are under way aimed at improving the knowledge of g 1, as well as at measuring, for the first time, the proton SSF g 2 and the neutron SSF g n 1 and g n 2 . The latter quantities are expected to be obtained from the spin asymmetry measured in Deep Inelastic Scattering (DIS) of longitudinally polarized electrons off polarized nuclear targets, viz ~ 2H and ~ 3He. As is well known, the use of ~ 3He targets, which will be considered in this paper, is motivated by the observation that, in the simplest picture of He (all nucleons in S wave), protons have opposite spins so that their contribution to the asymmetry largely cancels out. However, such a cancellation does not occur if other components of the three body wave function are considered; moreover, the fact that electrons scatter off nucleons having a certain momentum and energy distribution may, in principle, limit the possibility to obtain information on nucleon SSF from scattering experiments on nuclear targets. The aim of this Rapid Communication is to quantitatively illustrate whether and to which extent the extraction of g 1 from the asymmetry of the process ~ 3He(~e, e)X could be hindered by nuclear effects arising from small wave function components of He, as well as from Fermi motion and binding correction effects on DIS. To this end, we use the spin dependent spectral function of He [7], which allows one to take into account at the same time Fermi motion and binding corrections, unlike previous calculations [8] where only Fermi motion effects were considered. It should be pointed out that our paper is also based on a recent, improved description of inclusive scattering of polarized electrons by polarized nuclei [9,10], which leads in the quasi elastic kinematics to appreciable differences with respect to previous calculations [7,11]; therefore we will also check whether these differences persist in the DIS region. In the Bjorken limit the longitudinal asymmetry for inclusive scattering of longitudinally polarized electrons off a polarized J = 1 2 target with atomic weight A, reads as follows: