P-wave neutron strength-function measurements and the low-energy optical potential

Using the National Bureau of Standards electron linac and underground time-of-flight facility, precise average neutron-transmission measurements have been made in the energy range $1 \mathrm{keV}\le E\le 600 \mathrm{keV}$ on the elements As, Br, Nb, Rh, Ag, In, Sb, I, La, Ho, Au, and Th. The samples were "thick" in that the $s$-wave self-protection had to be accounted for at low energies. However, the samples were still sufficiently thin that any errors introduced by neglecting $p$-wave self-protection were negligible. The average $R$-matrix theory was employed in the analysis and the $l=0\mathrm{}$ scattering length $R^{\prime }$ and the $p$-wave strength function $S_1$ were extracted from the data. The behavior of $S_1$ vs mass number $A$ in the region of the $3P$ maximum was found to vary smoothly with no evidence of any splitting of the resonance. Using Moldauer's optical potential, which fits the $l=0\mathrm{}$ data well, the behavior of $S_1$ vs $A$ was calculated. The predicted behavior was found to differ significantly from experiment. In particular, experiment indicates $S_1$ peaks at a lower mass number and that the maximum is stronger than indicated by the calculations. When the constants of the potential were changed in order to reproduce the observed behavior of $S_1$, a significant discrepancy with the $l=0\mathrm{}$ data resulted. The results presented here imply an orbital angular momentum dependence of the low-energy optical potential.