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 to 4200 eV ( levels), give the first excellent agreement with the Dyson-Mehta (DM) statistic which applies for the statistical orthogonal ensemble (O.E.) of Wigner and Dyson. The observed levels seem to be a nearly pure and complete population, fitting Wigner's nearest-neighbor spacing law and the Porter-Thomas (PT) single-channel distribution. The weakest and levels include some levels (excess of weak values) which are separated by a Bayes-theorem method yielding resulting populations which also give good fits to all statistical O.E. tests. Unexpectedly, the levels give a nonzero correlation coefficient between adjacent values of , and with less fluctuation in over adjacent intervals than expected for an uncorrelated PT series of values. Assuming a true level density 3 times that for levels, values are calculated on the basis of the observed excess of weak levels and our known level detection threshold. We obtain for 166, 167, 168, 170; and for 166, 168, 170. We find () for , 0.287 () for , and 0.359 () for vs DM's predicted . For a large , is much larger for an uncorrelated Wigner (U.W.) spacing sequence or for an incomplete or impure level O.E. set. The correlation coefficient for adjacent spacings, for 166, 168, 170 vs (±0.09, 0.13, 0.17 for 166, 168, 170) (O.E.). The probability is 0.0004 for value for a U.W. set. The values for levels, if our level count is correct, are 38.4, 4.06, 95.3, and 155 eV [ fractional uncertainty (O.E.)] for for 166, 167, 168, 170.
- Received 6 July 1971
DOI:https://doi.org/10.1103/PhysRevC.5.974
©1972 American Physical Society