Neutron-Resonance Spectroscopy. VIII. The Separated Isotopes of Erbium: Evidence for Dyson's Theory Concerning Level Spacings

H. I. Liou, H. S. Camarda, S. Wynchank, M. Slagowitz, G. Hacken, F. Rahn, and J. Rainwater
Phys. Rev. C 5, 974 – Published 1 March 1972
PDFExport Citation

Abstract

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 Γn0 distribution. The weakest Er168 and Er170 levels include some p levels (excess of weak Γn0 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 Γn0 values of ρ(Γnj0,Γnj+10)=0.21±0.08, and with less fluctuation in ΣΓn0 over adjacent intervals than expected for an uncorrelated PT series of Γn0 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 ρ0.27 (±0.09, 0.13, 0.17 for 166, 168, 170) (O.E.). The probability is 0.0004 for [Δ+ρ]the Er166(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.

  • Received 6 July 1971

DOI:https://doi.org/10.1103/PhysRevC.5.974

©1972 American Physical Society

Authors & Affiliations

H. I. Liou, H. S. Camarda*, S. Wynchank, M. Slagowitz, G. Hacken, F. Rahn, and J. Rainwater

  • Columbia University, New York, New York 10027

  • *Present address: National Bureau of Standards, Gaithersburg, Md.
  • Present address: Brooklyn College, N.Y., N.Y.

References (Subscription Required)

Click to Expand
Issue

Vol. 5, Iss. 3 — March 1972

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review C

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×