An Interpretation of the Resonance Scattering of Neutrons by Cobalt in Terms of the Breit-Wigner Equation

Abstract

The neutron transmission of a Co foil (8.67 mg/${\mathrm{cm}}^{2}$) was measured for epi-thermal pile neutrons which were filtered through various thicknesses of ${\mathrm{B}}^{10}$. The detector consisted of an annular B${\mathrm{F}}_{3}$ counter. As used for the transmission measurements this counter was set up to count only neutrons scattered by a second Co foil (9.55 mg/${\mathrm{cm}}^{2}$). The counter sensitivity as a function of neutron energy was studied. Effective total cross sections of 3100 b and over were calculated from observed transmissions. By means of ${\mathrm{B}}^{10}$ absorption, a resonance was located at 108\ifmmode\pm\else\textpm\fi{}10 ev and this was associated with resonance scattering of the neutrons. The total resonance cross section ${\ensuremath{\sigma}}_{0}$ was estimated to be 12,500\ifmmode\pm\else\textpm\fi{}1250 b and the magnitude of the resonance scattering, expressed by $\ensuremath{\gamma}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{\sigma}}_{s}({E}_{r})$, was estimated to be \ensuremath{\sim}45,000 ev-b, here $\ensuremath{\gamma}$ denotes the total level width and ${\ensuremath{\sigma}}_{s}({E}_{r})$ denotes the elastic scattering cross section at resonance. The neutron transmission was calculated from the single-level Breit-Wigner equation for the case where scattering is the predominant process. This equation was written in a conventional form involving, besides energy dependence, the parameters $\ensuremath{\Gamma}$, $R$, and $j$; where the neutron width is $\ensuremath{\Gamma}{(\frac{E}{{E}_{r}})}^{\frac{1}{2}}$; where $4\ensuremath{\pi}{R}^{2}$ represents the scattering from the surface of the initial nucleus, and where $j$ is the spin quantum number of the compound nucleus. Calculated transmissions agreed with experimental transmissions in two instances: (1) $\ensuremath{\Gamma}=2.0\ifmmode\pm\else\textpm\fi{}0.1$ ev, $R=+0.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ cm, $j=4$, and (2) $\ensuremath{\Gamma}=5.0+0.5$ ev, $R=+0.97\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ cm, $j=3$. However, the value ${\ensuremath{\sigma}}_{0}=12500\ifmmode\pm\else\textpm\fi{}1250$ b is consistent only with $j=4$. A negative $R$ will mean that the minimum of the dispersion curve ${\ensuremath{\sigma}}_{s}(\mathrm{E})$ vs. $E$ occurs above the resonance energy ${E}_{r}$ and such was found to be inconsistent with the data. Finally, mention is made of the similar scattering resonance which takes place in manganese, ${E}_{r}\ensuremath{\approx}300$ ev; here ${\ensuremath{\sigma}}_{0}$ lies between 4000 and 5000 b and $\ensuremath{\Gamma}\ensuremath{\sim}10$ ev.