Neutron Scattering Lengths

The schematic treatment of nuclear reactions is applied to the case $E_n\to 0$ as a means of interpreting measurements of the scattering length $a$. It is found that the quantity $\Delta =(a-R)\mathrm{}$ rather than $a$ is significant for determining the resonance properties of the compound nucleus, where $R$ is the phenomenological nuclear radius. In some cases this treatment can resolve ambiguity in the evaluation of $a$ without the necessity of polarization measurements and assign the $J$ value of a low-lying resonance or two, but it can only be used successfully for separated isotopes. For practically pure isotopes it can be used to determine rough values of level spacing $D$ from the measured position of the levels nearest $E_n=0\mathrm{}$, or conversely. Values of $D$ obtained in this way are plotted against $A$ to yield an estimate of a parameter in the statistical formula for level density; this estimate suggests a somewhat more rapid increase in level spacing with decreasing excitation than given by the simplest statistical formula.