Multiple scattering effects in Glauber model descriptions of single-nucleon removal reactions

he Glauber/eikonal model is a widely used tool for study of intermediate- and high-energy nuclear reactions. When calculating the Glauber/eikonal model phase-shift functions, the optical limit approximation (OLA) is often used. The OLA neglects the multiple scattering of the constituent nucleons in the projectile and the target nuclei. On the other hand, the nucleon-target version of the Glauber model (the NTG model) proposed by B. Abu-Ibrahim and Y. Suzuki includes multiple scattering effects between the projectile nucleons and the target nuclei. The NTG model has been found to improve the description of the elastic scattering angular distributions and the total reaction cross sections of some light heavy-ion systems with respect to the OLA. In this work, we study the single-nucleon removal reactions (SNRR) induced by carbon isotopes on \nuc{12}{C} and \nuc{9}{Be} targets using both the NTG model and the OLA. Reduction factors (RFs) of the single nucleon spectroscopic factors are obtained by comparing the experimental and theoretical SNRR cross sections. It is found that, on average, the RFs obtained with the NTG model is smaller than those using the OLA by 7.8\%, in which, the averaged differences in one-neutron removal is 10.6\% and those in one-proton removal is 4.2\%. But the RFs still have a strong dependence on the neutron-proton asymmetry $\Delta S$ of the projectile nuclei even when the NTG model is used.