Elastic Scattering Angular Distributions of Fast Neutrons on Light Nuclei

Abstract

New measurements of the total cross section of ${\mathrm{Be}}^{9}$ (resolution 4 kev) give maxima of 7.75\ifmmode\pm\else\textpm\fi{}0.20 barns ($\ensuremath{\Gamma}=25$ kev) and 5.25\ifmmode\pm\else\textpm\fi{}0.20 barns ($\ensuremath{\Gamma}=8$ kev) for the 0.62 Mev and 0.81 Mev resonances, consistent with $J=3$ and $J=2$ for the respective compound state spin values. Elastic scattering angular distributions indicate that the 0.62-Mev resonance may be formed by $p$-wave neutrons with the $s$-wave potential scattering (${\ensuremath{\delta}}_{0}=\ensuremath{-}54.2\ifmmode^\circ\else\textdegree\fi{}$) spin-dependent and all channel spin 1, or possibly by $d$-wave neutrons with the resonance scattering all channel spin 2. Potential scattering phase shifts for ${\mathrm{B}}^{10}$ are ${\ensuremath{\delta}}_{0}=\ensuremath{-}53.5\ifmmode^\circ\else\textdegree\fi{}$ at 0.55 Mev; ${\ensuremath{\delta}}_{0}=\ensuremath{-}60.7\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\delta}}_{1}=\ensuremath{-}4.0\ifmmode^\circ\else\textdegree\fi{}$ at 1.00 Mev; and ${\ensuremath{\delta}}_{0}=\ensuremath{-}66.9\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\delta}}_{1}=\ensuremath{-}10.3\ifmmode^\circ\else\textdegree\fi{}$, and ${\ensuremath{\delta}}_{2}=\ensuremath{-}2.9\ifmmode^\circ\else\textdegree\fi{}$ at 1.50 Mev. The 0.43-Mev resonance in ${\mathrm{B}}^{11}$, agrees with a $J=2$, $l=1$ assignment, while the 1.28-Mev resonance is best fitted by $J=3$, $l=2$; with a mixing ratio of channel spin 2 equal to 10 times channel spin 1. Potential scattering is nearly all $s$-wave up to 1.50 Mev where ${\ensuremath{\delta}}_{0}=\ensuremath{-}90\ifmmode^\circ\else\textdegree\fi{}$. ${\mathrm{C}}^{12}$ has pure $s$-wave scattering at 0.55 Mev (${\ensuremath{\delta}}_{0}=\ensuremath{-}50.1\ifmmode^\circ\else\textdegree\fi{}$) and 1.00 Mev (${\ensuremath{\delta}}_{0}=\ensuremath{-}68.9\ifmmode^\circ\else\textdegree\fi{}$), and at 1.50 Mev a small amount of $p$-wave appears, (${\ensuremath{\delta}}_{0}=\ensuremath{-}79.4\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\delta}}_{1}=\ensuremath{-}5.7\ifmmode^\circ\else\textdegree\fi{}$). In general the observed $s$-wave phase shifts are larger than those calculated from a hard sphere model, whereas the $p$- and $d$-wave phase shifts are smaller.