NeutronResonance Spectroscopy. VIII. The Separated Isotopes of Erbium: Evidence for Dyson's Theory Concerning Level Spacings
Abstract
Results are given for highresolution neutronresonancespectroscopy studies of the separated erbium isotopes (164, 166, 167, 168, 170) using the Nevis Synchrocyclotron. These results, particularly Er^{166} to 4200 eV (n=109 levels), give the first excellent agreement with the DysonMehta (DM) Δ statistic which applies for the statistical orthogonal ensemble (O.E.) of Wigner and Dyson. The observed Er^{166} levels seem to be a nearly pure and complete s population, fitting Wigner's nearestneighbor spacing law and the PorterThomas (PT) singlechannel Γ^{0}_{n} distribution. The weakest Er^{168} and Er^{170} levels include some p levels (excess of weak Γ^{0}_{n} values) which are separated by a Bayestheorem method yielding resulting s populations which also give good fits to all statistical O.E. tests. Unexpectedly, the Er^{166} levels give a nonzero correlation coefficient between adjacent Γ^{0}_{n} values of ρ(Γ^{0}_{nj},Γ^{0}_{nj+1})=0.21+/0.08, and with less fluctuation in Γ^{0}_{n} over adjacent intervals than expected for an uncorrelated PT series of Γ^{0}_{n} values. Assuming a true p level density 3 times that for s levels, S_{1} values are calculated on the basis of the observed excess of weak levels and our known level detection threshold. We obtain 10^{4}S_{0}=1.70+/0.23, 1.89+/0.20, 1.50+/0.21, and 1.54+/0.22 for 166, 167, 168, 170; and 10^{4}S_{1}=<=0.75, 0.70+/0.20, and 0.80+/0.25 for 166, 168, 170. We find Δ=0.455 (n=109) for Er^{166}, 0.287 (n=50) for Er^{168}, and 0.359 (n=31) for Er^{170} vs DM's predicted Δ=0.47+/0.11, 0.39+/0.11, and 0.34+/0.11. For a large n, Δ is much larger for an uncorrelated Wigner (U.W.) spacing sequence or for an incomplete or impure s level O.E. set. The correlation coefficient for adjacent spacings, ρ(S_{j},S_{j+1})≡ρ=0.22, 0.29, 0.09 for 166, 168, 170 vs ρ~0.27 (+/0.09, 0.13, 0.17 for 166, 168, 170) (O.E.). The probability is 0.0004 for [Δ+ρ]<=the Er^{166}(4.2keV) value for a U.W. set. The <D> values for s levels, if our s level count is correct, are 38.4, 4.06, 95.3, and 155 eV [+/0.9n fractional uncertainty (O.E.)] for n=109, 30, 50, and 31 for 166, 167, 168, 170.
 Publication:

Physical Review C
 Pub Date:
 March 1972
 DOI:
 10.1103/PhysRevC.5.974
 Bibcode:
 1972PhRvC...5..974L