1. NPA5, Eilat, 7. 4. 2011 Anomalous Properties of Neutron Resonances in Pt Isotopes P.E. Koehler, J.A. Harvey, K.H. Guber Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA Frantisek Becvar, Milan Krticka Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic

2. NPA5, Eilat, 7. 4. 2011 Outline  Expected properties - Random Matrix Theory (Gaussian Orthogonal Ensemble)  Experimental data on neutron resonances in Pt isotopes from ORELA  Results  Distribution of neutron and total gamma widths in Pt isotopes  Distribution of spacing between resonances

3. NPA5, Eilat, 7. 4. 2011 Random Matrix Theory  RMT (GOE) - a “statistical” theory of spectra  It is assumed to describe the features of spectra in the region of high density of states (neutron resonances in heavy nuclei)  Only the joint probability distributions of the eigenvalues and eigenfunctions (and not the individual spectra) are predicted  The spectral distribution functions are calculated as averages over the ensemble  If the observed spectral properties agree with RMT predictions one concludes that the system is generic (chaotic) - no additional information cannot be deduced from the spectrum  Disagreement of data with RMT predictions indicates that available spectral information may be used to deduce further properties of the system (additional quantum numbers).

4. NPA5, Eilat, 7. 4. 2011 Properties of Random Matrices (RMT) Predictions of distribution of  the nearest-neighborhood spacing of levels  correlations between the nearest spacings  correlations between the next-nearest spacings  …  the long-range correlations among energies of levels  the distribution of the overlaps with a random vector (e.g. the overlap of the resonance wave function with the configuration projectile + target) Levels must have the same J  (conserved quantum numbers)

5. NPA5, Eilat, 7. 4. 2011 Properties of neutron resonances Consensus view from last ~50 Years:  Reduced Neutron Widths Follow the Porter-Thomas distrib. Reduced neutron width  n ~ E n 1/2  n (0) … for s- wave  n ~ E n 3/2  n (1) … for p- wave …  n = f(E n,l)  n (l) Porter-Thomas =  2 distrib. with =1

6. NPA5, Eilat, 7. 4. 2011 Properties of neutron resonances Consensus view from last ~50 Years:  Reduced Neutron Widths Follow the Porter-Thomas distrib.  Spacing of Resonances Follows the Wigner distribution  The most comprehensive test is assumed to come from so-called nuclear data ensemble (NDE) - a set of resonance energies consisting of 30 sequences in 27 different nuclides Haq, Pandey, Bohigas, Phys. Rev. Lett. 48 (1982) 1086  Fluctuation properties of resonance energies in the NDE were found to be in remarkably close agreement with GOE predictions. Hence, the NDE often is cited as providing striking confirmation of RMT predictions for the GOE

7. NPA5, Eilat, 7. 4. 2011 ORELA The facility consists of a  180-MeV electron accelerator  neutron producing targets  buried and evacuated flight tubes up to 200 m long leading to underground detector locations  Neutrons are produced by bremsstrahlung from a Ta radiator  Moderated or unmoderated neutrons are available (further tailoring of the spectral shape is done with movable filters).  Pulse widths from 4 - 30 ns are available at a repetition rates 12 - 1000 Hz. The Oak Ridge Electron Linear Accelerator

8. NPA5, Eilat, 7. 4. 2011 ORELA Measurements Electron Beam Neutron Production Target Collimator Neutrons Deuterated Benzene (C 6 D 6 ) Detectors Sample Capture Setup Collimator Sample 6 Li-glass Detector T.O.F. 40 m 80 m Transmission Setup Measured 192,194,195,196,nat Pt targets in both set ups, 525 Hz, 8ns pulse width

9. NPA5, Eilat, 7. 4. 2011 ORELA Measurements  Resonance parameters deduced using the SAMMY fitting (R-matrix) code

10. NPA5, Eilat, 7. 4. 2011 Testing the PTD Using 192,194 Pt+n ORELA Data 192,194,196 Pt+n ORELA data are excellent - better in many ways: More resonances  Better sensitivity (~10x)  Better separation of s and p waves ( ≈ 10 )  Better J  assignments Improved Maximum-Likelihood analysis:  Analysis threshold T 0 much higher than experimental one  Used energy-dependent threshold  Maximizes statistical significance while eliminating p-wave contamination

11. NPA5, Eilat, 7. 4. 2011 Koehler et al., Phys. Rev. Lett. 105, 072502 (2010)  Maximum-Likelihood (ML) analysis: 192 Pt: = 0.57±0.16 194 Pt: = 0.47±0.19 196 Pt: = 0.60±0.28  Confidence levels (CL) from ML analysis are sometimes problematic Testing the PTD Using 192,194 Pt+n ORELA Data

12. NPA5, Eilat, 7. 4. 2011 Testing the PTD Using 192,194 Pt+n ORELA Data  Confidence levels (CL) from ML analysis are sometimes problematic  Additional simulations assuming = 1 performed and the probability that the low value of (e.g. = 0.47 for 194 Pt) obtained from ML analysis checked as a function of

13. NPA5, Eilat, 7. 4. 2011 Phys. Rev. Lett. 105, 072502 (2010)  Maximum-Likelihood (ML) analysis: 192 Pt: = 0.57±0.16 194 Pt: = 0.47±0.19 196 Pt: = 0.60±0.28  CL is very high but depends on due to the experimental threshold applied - was “fixed” in simulations Testing the PTD Using 192,194 Pt+n ORELA Data  Two additional statistics applied to limit the range of (similar to von Mises, Kolmogorov-Smirnov, Anderson-Darling statistics)  = 1 assumed in all cases  Combining all the restrictions for two nuclei – PTD rejected at 99.997% CL

14. NPA5, Eilat, 7. 4. 2011  Auxiliary ML analysis verified that p-wave contamination is negligibly small  The probability 0.069% for 192 Pt and 0.0047% for 194 Pt obtained  At most one p-wave resonance can occur above the threshold Testing the PTD Using 192,194 Pt+n ORELA Data s-wave p-wave

15. NPA5, Eilat, 7. 4. 2011 Total Gamma Widths  No correlation between neutron and gamma widths observed  Distribution of widths significantly different ( 192 Pt vs 194 Pt, 195 Pt) … sum over partial gamma widths to all levels which the resonance decays to  distribution of   is relatively narrow Experiment

16. NPA5, Eilat, 7. 4. 2011 Total Gamma Widths  Simulations of the distribution performed (DICEBOX code - F. Becvar, NIMA 417, (1998) 434)  Especially “wide” distribution for 194 Pt target cannot be obtained with “standard” models of level density (BSFG, CT) and radiative strength functions (SLO, KMF, EGLO,…) if PTD ( = 1) governs fluctuations of partial gamma widths LD: CT E1: SLO

17. NPA5, Eilat, 7. 4. 2011 Total Gamma Widths  Simulations of the distribution performed (DICEBOX code - F. Becvar, NIMA 417, (1998) 434)  Especially “wide” distribution for 194 Pt target cannot be obtained with “standard” models of level density (BSFG, CT) and radiative strength functions (SLO, KMF, EGLO,…) if PTD ( = 1) governs fluctuations of partial gamma widths Possible Solutions:  much smaller than 1 ( = 0.2 - 0.5)  Radiative SF is strongly suppressed at low E   Some of the partial gamma widths do not behave statistically … all these explanations seem to work

18. NPA5, Eilat, 7. 4. 2011 Missing levels Estimate of the fraction of observed resonances

19. NPA5, Eilat, 7. 4. 2011 Test of Wigner distribution of spacings  Simulated values of a statistics (testing function) S 2 under the assumption about Wigner (GOE) and Poisson distribution  Poisson distribution can be ruled out, Wigner on the border of acceptability  Based on validity of a  2 distribution with degrees of freedom = 0.44

20. NPA5, Eilat, 7. 4. 2011 Conclusions  Neutron resonance parameters in Pt were measured with unprecedented sensitivity to weak resonances  Validity of Porter-Thomas distribution (PTD) for fluctuations of reduced neutron widths can be rejected at very high confidence level (99.997%)  Distribution of total gamma widths indicates additional problems in Pt region (PTD violation or very strange RSF shape)  Wigner distribution of spacings can still be valid  Violation of PTD might have important consequences – e.g. significantly higher density of levels (resonances) at neutron separation energy, …  Is PTD (in reduced neutron widths) violated only in Pt nuclei? Very high quality data needed to answer this question.

21. NPA5, Eilat, 7. 4. 2011 Thank you very much for your attention!