1. Beta Delayed Neutron Covariances Tim Johnson, Libby McCutchan, Alejandro Sonzogni National Nuclear Data Center

2. Beta Delayed Neutron CRP #2 - Alejandro Sonzogni Many  n emitters have high fission yield values, in particular Br (Z=35), Rb (Z=37), I (Z=53) and Cs (Z=55) Chart colored by 235U fission yields, highlighted by Q  n>0

3. Beta Delayed Neutron CRP #3 - Alejandro Sonzogni Link between basic and more macroscopic quantities used in applied nuclear physics d : Delayed nu-bar, number of neutrons for single fission event. It can be calculated as: d =  CFY i Pn i, about 0.015/fission for 235U CFY: cumulative fission yield. Pn: beta-delayed neutron probability. Pn and T 1/2 values of beta-delayed neutron emitters are relevant in nuclear power and astrophysics.

4. Beta Delayed Neutron CRP #4 - Alejandro Sonzogni Following Loaiza et al. & Than Dat et al., the recommended delayed nubars (MF=1, MT455) are plotted for a number of systems.

5. Beta Delayed Neutron CRP #5 - Alejandro Sonzogni Same plot as before, for summation calculations using JEFF- 3.1 yields and ENDF/B-VII.1 decay data 232Th 238U 235U 241Pu 238Np 233U 239Pu 252Cf

6. Beta Delayed Neutron CRP #6 - Alejandro Sonzogni 232Th 238U As before, but plotting lighter and heavier fission fragments contributions

7. Beta Delayed Neutron CRP #7 - Alejandro Sonzogni As before, but with ENDF/B yields 237Np

8. Beta Delayed Neutron CRP #8 - Alejandro Sonzogni Disagreements in fission yields for 237Np ENDDF/B yields are larger than JEFF’s for neutron rich nuclide

9. Beta Delayed Neutron CRP #9 - Alejandro Sonzogni Disagreements in fission yields for 237Np

10. Beta Delayed Neutron CRP #10 - Alejandro Sonzogni Disagreements in fission yields for 252Cf

11. Beta Delayed Neutron CRP #11 - Alejandro Sonzogni Disagreements in fission yields for 252Cf

12. Beta Delayed Neutron CRP #12 - Alejandro Sonzogni Delayed neutron activity Covariances A d (t): Delayed neutron activity following the decay of an equilibrated system To obtain A d (t), we solve the Bateman’s equations: dN i (t)/dt=- i N i +  ki N k, with boundary conditions: dN i (0)/dt=0, that is, Ni(0)~CFY i / i, then: A d (t)=  i Pn i N i (t) We use a Monte Carlo method, the only correlation in fission yields is that they are normalized to 2, and the branching ratios are normalized to 1.

13. Beta Delayed Neutron CRP #13 - Alejandro Sonzogni Delayed neutron activity Covariances For N histories, we obtain A di (t k ), so the average value would be: = N -1  A di (t k ) The uncertainty as:   A d (t k )= - And the covariance matrix:  (A d (t k ), A d (t j ) )=  kj = - Covariances are obtained by a Monte Carlo method

14. Beta Delayed Neutron CRP #14 - Alejandro Sonzogni Delayed neutron activity for 235U

15. Beta Delayed Neutron CRP #15 - Alejandro Sonzogni Delayed neutron activity uncertainty for 235U

16. Beta Delayed Neutron CRP #16 - Alejandro Sonzogni Delayed neutron activity divided by Keepin’s values

17. Beta Delayed Neutron CRP #17 - Alejandro Sonzogni Delayed neutron activity correlations for 235U

18. Beta Delayed Neutron CRP #18 - Alejandro Sonzogni Six group parameters fit In the ENDF-6 libraries, the delayed neutron activity is given as a sum of 6 or 8 exponential terms: A d (t)=  a i exp(- i t) In order to properly propagate uncertainties, we not only need the uncertainties in a i and i, but also the correlations:,, For each history, we fit A d (t) with a Keepin-like function, using Keepin’s parameter as a starting point.

19. Beta Delayed Neutron CRP #19 - Alejandro Sonzogni Six-group fit

20. Beta Delayed Neutron CRP #20 - Alejandro Sonzogni Six-group fit The a k have uncertainties in the 10-17%, while the k in 2- 10%, due to a more uncertain fission yield data

21. Beta Delayed Neutron CRP #21 - Alejandro Sonzogni Chi-square distribution of the fits

22. Beta Delayed Neutron CRP #22 - Alejandro Sonzogni 6-group Parameters Correlation Matrix a 2 & a 4 anticorrelation 4 & 5 correlation

23. Beta Delayed Neutron CRP #23 - Alejandro Sonzogni Conclusions Delayed nu-bars and neutron activities have been very precisely measured. In summation calculations decay data is of good quality, but there are problems in the fission yields data. Our work test the relatively short-lived (T 1/2 < 100 s) subset of fission yields. We look forward to the next generation experiments and the results of the current WPEC Subgroup. We will generate covariance matrices for all targets of interest.

24. Beta Delayed Neutron CRP #24 - Alejandro Sonzogni Advertisement: Possible next workshop on Modeling of Antineutrino Flux from Nuclear Reactors June 2016 Port Jefferson, NY Perhaps Tuesday 6/14 – Thursday 6/16

25. Beta Delayed Neutron CRP #25 - Alejandro Sonzogni BNL JFK Pt Jefferson

26. Beta Delayed Neutron CRP #26 - Alejandro Sonzogni Location: Pt Jefferson Village Center Hotel, about 100 yards away. About $140/night. Train to Manhattan and JFK, about 1:40 h and $25 round trip. Train station 1 mile from Hotel. Plenty of restaurants nearby