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

The neutron transmission of a Co foil (8.67 mg/cm²) was measured for epi-thermal pile neutrons which were filtered through various thicknesses of B¹⁰. The detector consisted of an annular BF₃ 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/cm²). 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 B¹⁰ absorption, a resonance was located at 108±{}10 ev and this was associated with resonance scattering of the neutrons. The total resonance cross section σ₀ was estimated to be 12,500±{}1250 b and the magnitude of the resonance scattering, expressed by γ·σₛ(Eᵣ), was estimated to be {~}45,000 ev-b, here γ denotes the total level width and σₛ(Eᵣ) 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 Γ, R, and j; where the neutron width is Γ(EEᵣ)1/2; where 4πR² 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) Γ=2.0±0.1 ev, R=+0.93×10^-12 cm, $j=4$, and (2) Γ=5.0+0.5 ev, R=+0.97×10^-12 cm, $j=3$. However, the value σ₀=12500±1250 b is consistent only with $j=4$. A negative R will mean that the minimum of the "dispersion" curve σₛ(E) vs. E occurs above the resonance energy Eᵣ and such was found to be inconsistent with the data. Finally, mention is made of the similar scattering resonance which takes place in manganese, Eᵣ≈300 ev; here σ₀ lies between 4000 and 5000 b and Γ~10 ev.