Distribution of the Angular Momenta, Level Spacings, and Neutron Widths of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mn>28</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

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 $J=0$, twenty-one to $J=1$, eighteen to $J=2$, ten to $J=3$, and three to $J=4$. This distribution is in agreement with the theoretical distribution for a value of $2c\ensuremath{\tau}\ensuremath{\equiv}2{\ensuremath{\sigma}}^{2}=6$. The density of all levels for this energy interval is 146 ${\mathrm{Mev}}^{\ensuremath{-}1}$ 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 $l=0$ is 0.05, averaged over all values of $J$ for $l=1$ it is 0.49, and for $l=2$ 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 $l$.