Neutron-Resonance Spectroscopy. VIII. The Separated Isotopes of Erbium: Evidence for Dyson's Theory Concerning Level Spacings
Results are given for high-resolution neutron-resonance-spectroscopy studies of the separated erbium isotopes (164, 166, 167, 168, 170) using the Nevis Synchrocyclotron. These results, particularly Er166 to 4200 eV (n=109 levels), give the first excellent agreement with the Dyson-Mehta (DM) Δ statistic which applies for the statistical orthogonal ensemble (O.E.) of Wigner and Dyson. The observed Er166 levels seem to be a nearly pure and complete s population, fitting Wigner's nearest-neighbor spacing law and the Porter-Thomas (PT) single-channel Γ0n distribution. The weakest Er168 and Er170 levels include some p levels (excess of weak Γ0n values) which are separated by a Bayes-theorem method yielding resulting s populations which also give good fits to all statistical O.E. tests. Unexpectedly, the Er166 levels give a nonzero correlation coefficient between adjacent Γ0n values of ρ(Γ0nj,Γ0nj+1)=-0.21+/-0.08, and with less fluctuation in Γ0n over adjacent intervals than expected for an uncorrelated PT series of Γ0n values. Assuming a true p level density 3 times that for s levels, S1 values are calculated on the basis of the observed excess of weak levels and our known level detection threshold. We obtain 104S0=1.70+/-0.23, 1.89+/-0.20, 1.50+/-0.21, and 1.54+/-0.22 for 166, 167, 168, 170; and 104S1=<=0.75, 0.70+/-0.20, and 0.80+/-0.25 for 166, 168, 170. We find Δ=0.455 (n=109) for Er166, 0.287 (n=50) for Er168, and 0.359 (n=31) for Er170 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(Sj,Sj+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 Er166(4.2-keV) 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.
Physical Review C
- Pub Date:
- March 1972