beta delayed neutron covariances tim johnson, libby mccutchan, alejandro sonzogni national nuclear...

Beta Delayed Neutron Covariances

Tim Johnson, Libby McCutchan, Alejandro Sonzogni

National Nuclear Data Center

Beta Delayed Neutron CRP #2 - Alejandro Sonzogni

Many bn 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 Qbn>0


Link between basic and more macroscopic quantities used in applied nuclear physics

nd: Delayed nu-bar, number of neutrons for single fission event. It can be calculated as:

nd =S CFYi Pni , about 0.015/fission for 235U

CFY: cumulative fission yield.

Pn: beta-delayed neutron probability.

Pn and T1/2 values of beta-delayed neutron emitters are relevant in nuclear power and astrophysics.


Following Loaiza et al. & Than Dat et al., the recommended delayed nubars (MF=1, MT455) are plotted for a number of systems.


Same plot as before, for summation calculations using JEFF-3.1 yields and ENDF/B-VII.1 decay data

232Th 238U 235U 241Pu238Np

233U 239Pu

252Cf


232Th 238U

As before, but plotting lighter and heavier fission fragments contributions


As before, but with ENDF/B yields

237Np


Disagreements in fission yields for 237Np

ENDDF/B yields are larger than JEFF’s for neutron rich nuclide


Disagreements in fission yields for 237Np


Disagreements in fission yields for 252Cf


Delayed neutron activity Covariances

Ad(t): Delayed neutron activity following the decay of an equilibrated system

To obtain Ad(t), we solve the Bateman’s equations:dNi(t)/dt=-liNi +S lki Nk , with boundary conditions:dNi(0)/dt=0, that is, Ni(0)~CFYi/li , then:

Ad(t)= S li Pni Ni(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.


Delayed neutron activity Covariances

For N histories, we obtain Adi(tk), so the average value would be:

<Ad(tk)>= N-1 S Adi(tk)

The uncertainty as:

D2Ad(tk)= <Ad(tk) Ad(tk)> - <Ad(tk)><Ad(tk)>

And the covariance matrix:

s(Ad(tk), Ad(tj) )=skj=<Ad(tk) Ad(tj)> - <Ad(tk)><Ad(tj)>

Covariances are obtained by a Monte Carlo method


Delayed neutron activity for 235U


Delayed neutron activity uncertainty for 235U


Delayed neutron activity divided by Keepin’s values


Delayed neutron activity correlations for 235U


Six group parameters fit

In the ENDF-6 libraries, the delayed neutron activity is given as a sum of 6 or 8 exponential terms:

Ad(t)= S ai exp(-li t)

In order to properly propagate uncertainties, we not only need the uncertainties in ai and li, but also the correlations:

< ai ak >, < ai lk >, < li lk>

For each history, we fit Ad(t) with a Keepin-like function, using Keepin’s parameter as a starting point.


Six-group fit


Six-group fit

The ak have uncertainties in the 10-17%, while the lk in 2-10%, due to a more uncertain fission yield data


Chi-square distribution of the fits


6-group Parameters Correlation Matrix

a2 & a4 anticorrelation

l4 & l5 correlation


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 (T1/2 < 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.


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beta delayed neutron covariances tim johnson, libby mccutchan, alejandro sonzogni national nuclear...

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