Neutron total cross section of sulfur: Single level to multilevel to optical model

This paper is a further analysis of the high resolution total cross section of sulfur for 25-1100 keV neutrons that previously were measured by Halperin, Johnson, Winters, and Macklin and evaluated by single-level analysis. The usual procedure in reporting the results of high resolution neutron cross sections has been to present the data and resonance parameters with corresponding neutron strength functions resulting from some type of $R$-matrix analysis. Often the important nonresonant phase shifts are not reported. In this paper, making use of both strength functions and phase shifts, we extend the analysis to include an average nuclear potential (a spherical optical model). An optical model analysis not only facilitates comparison with a broad spectrum of other nucleon-nucleus experiments, but also may provide an incentive for microstructure calculations. Six average empirical functions, two each for $s_{\frac{1}{2}}$, $p_{\frac{1}{2}}$, and $p_{\frac{3}{2}}$ partial waves, are derived from the $R$-matrix analysis. From these we deduce optical model parameters, the real and imaginary well depths for $s$- and $p$-wave neutrons, and the spin-orbit well depth for $p$ waves. The resulting real well is deeper for $p$ waves than for $s$ waves and for averages over partial waves at higher energies. The depth of the imaginary wells are about half those deduced at higher energies. An interesting feature of the analysis is that the multilevel curve including interference effects is produced from single-level parameters including the phase shifts.