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 Er to 4200 eV (n =109 levels), give the first excellent agreement with the Dyson-Mehta (DM) 6 statistic which applies for the statistical orthogonal ensemble (O.E.)of Wigner and Dyson. The observed Er 6 levels seem to be a nearly pure and complete s population, fitting Wigner's nearest-neighbor spacing law and the Porter-Thomas (PT) singlechannel I'"distribution. The weakest Er and Er 7 levels include some p levels (excess of weak I "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 Er' levels give a nonzero correlation coefficient between adjacent I'"values of p(I'", , I'"~" () =-0.21 -0. 08, and with less fluctuation in QI'0 over adjacent intervals than expected for an uncorre-1ated PT series of I'"values. Assuming a true p level density 3 times that for s levels, S& values are calculated on the basis of the observed excess of weak levels and our known level detection threshold. We obtain 10 So --1.70+0.23, 1.89+0.20, 1.50+0.21, and 1.54+0.22 for 166, 167, 168, 170; and 104S&=~0.75, 0.70+0.20, and 0.80+0.25 for 166, 168, 170. We find 6=0.455 (n =109) for Er, 0.287 (n = 5p) for Er, and p.359 (n =31) for Er 0 vs DM's predicted 4 =0.47 + 0.11, 0.39 +0.11, and 0.34+ 0.11. For a large n, 4 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, p(S;, S;,&) = p =-0. 22, -0.29, -0.09 for 166, 168, 170 vs p =-0.27 (+0.09, 0.13, 0.17 for 166, 168, 170) (O.E.). The probability is O.ppp4 for [4+p]~the Er (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 [+0.9/n fractional uncertainty (O.E.)] for n =109, 30, 50, and 31 for 166, 167, 168, 170.
