Neutron polarization in polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ targets

Simple formulas for the neutron and proton polarizations in polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ targets are derived assuming (1) quasielastic final states; (2) no final-state interactions; (3) no meson-exchange currents; (4) large momentum transfers; (5) factorizability of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ SU(4) response-function components. Numerical results from a wide variety of bound-state solutions of the Faddeev equations are presented. It is found that this simple model predicts the polarization of neutrons in a fully polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ target to be 87%, while protons should have a slight residual polarization of -2.7%. Numerical studies show that this model works very well for quasielastic electron scattering.