Analysis of the Distribution of the Spacings Between Nuclear Energy Levels. II

The statistic $\Lambda \mathrm{}\left(n\right)\mathrm{}$, previously defined for the purpose of comparing empirical distributions of energy-level spacings with theoretical distributions, is applied to the recently published series of neutron-capture levels observed in the even-$A$ erbium isotopes. When the empirical values of $\Lambda \mathrm{}\left(n\right)\mathrm{}$ in the energy range of the highest experimental resolution were averaged over all possible sets of $n$ successive spacings, the resulting value ${\Lambda }^{*}\mathrm{}\left(n\right)\mathrm{}$ is found to decrease sharply with increasing values of $n$. This decrease is consistent with that of the expectation value $〈\Lambda \mathrm{}\left(n\right)\mathrm{}〉$ calculated for Wigner's Gaussian orthogonal ensemble of real symmetric matrices.