Distribution of the Angular Momenta, Level Spacings, and Neutron Widths ofAl28

Abstract

The neutron total cross section from about 1 kev to 450 kev shows the presence of sixty-six peaks, seven of which are of the $s$-wave variety. Thirteen resonances are attributable to $J=0\mathrm{}$, twenty-one to $J=1\mathrm{}$, eighteen to $J=2\mathrm{}$, ten to $J=3\mathrm{}$, and three to $J=4\mathrm{}$. This distribution is in agreement with the theoretical distribution for a value of $2c\tau \equiv 2{\sigma }^2=6\mathrm{}$. The density of all levels for this energy interval is 146 ${\mathrm{Mev}}^{-1\mathrm{}}$ and the average level spacing of the nucleons is 0.48 Mev. The neutron widths vary from 1 to 7 kev and the distribution of the reduced widths appears to agree with an exponential distribution and is also in fair agreement with the Porter-Thomas distribution. The level spacings also agree with an exponential distribution. As obtained from the reduced widths averaged over both values of $J$, the value of the strength function for $l=0\mathrm{}$ is 0.05, averaged over all values of $J$ for $l=1\mathrm{}$ it is 0.49, and for $l=2\mathrm{}$ it is too large in comparison with the $p$-wave strength function. The particularly low value of the cross section below 30 kev and the shape of the wings of the 35-kev resonance can be explained by a multiple-level computation of the interference of the $s$-wave levels. On the basis of the results of the present analyses, the levels are about equally divided between the odd and even values of $l$.