0 O ct 1 99 7 The Systematical Uncertainties in Measurements of the Spin - Dependent Structure Function g n 1 with 3 He Target due to Radiative Correction Procedure

The sources of the systematical uncertainties due to radiative correction procedure in measurements of the structure function g n 1 with 3 He target are considered. Their numerical estimations are presented. The relative systematical uncertainty does not exceed 5%. The measurements of the spin-dependent structure functions performed in the last years (SMC, E154/155) have the tendency to decrease essentially the statistical uncertainties comparing with previous ones (EMC, E142/143). Thus the one of main problem is to decrease the magnitude of the systematical uncertainties or define more correct way of their calculation. In general systematical uncertainties come from measured quantities , namely: values of the beam and target polarizations, efficiencies of the coordinate detectors etc. There are also some contributions in total systematic uncertainty due to unmeasured quantities such as radiative corrections (RC) to be applied to extract the one-photon exchange cross section from the measured one. So called radiative events, which originate from loop diagrams and from processes with the emission of additional real photons, cannot completely be removed by experimental methods and so they have to be calculated theoretically and subtracted from measured cross sections. The calculation of the radiative corrections requires knowledge of spin-independent and spin-dependent sturcture functions both in region measured in the considered experiment and beyond it. The choice of different parameterizations of the sturcture functions, elastic and quasielastic formfactors, neglecting of electroweak and higher oreder effects and simplifications in RC procedure leads to uncertainties in calculations of RC. The approach of calculation of these systematical uncertainties is presented in this report. We consider the case of the 3 He target and kinematical region close to HERMES [1] and SLAC [2] experiments. To get the numerical estimations of the system-atical uncertainties due to radiative correction procedure we use the special program [3] and radiative correction calculation code POLRAD 2.0 [4, 5]. The extraction of the spin asymmetry A 1 (x, Q 2) in the experiments measuring spin-dependent structure functions is based on the following formula