Polarization and Differential Cross Section for Neutron Scattering from Silicon

The polarization of neutrons scattered from Si and the unpolarized differential cross section for the process are measured at 5 angles and at neutron energies from 0.2 to 0.7 Mev. The differential cross sections in the present work, together with previously measured cross sections, are analyzed in terms of the properties of the resonance levels seen in ${\mathrm{Si}}^{29}$ (${\mathrm{Si}}^{28}$+$n$) by means of the $R$-function formalism of Lane and Thomas. The levels in ${\mathrm{Si}}^{29}$ at neutron energies of 0.536 Mev and 0.571 Mev are assigned to be $D_{\frac{5}{2}}$ and $P_{\frac{3}{2}}$, respectively. The phase shifts obtained from this analysis are used to predict the polarization in the scattering from ${\mathrm{Si}}^{28}$. The predicted values agree well with the measured polarization in scattering from natural Si. However, the rapid variation of the polarization with energy limits the usefulness of Si as an analyzer near the resonance energies. At neutron energies below 0.4 Mev and above 0.65 Mev the polarization is practically zero. The agreement between calculated and measured polarizations gives added confirmation of previous measurements of the polarization of the neutrons in the ${\mathrm{Li}}^7(p, n){\mathrm{Be}}^7$ reaction, which has been used as the neutron source in the present study.