TSUNAMI 3D: positive and negative signs in % delta-k/k?

[Kaspar Hewitt Klenø]

What's the significance of the sign in the "Uncertainty Information" table (the last table in the .out)?

I see absorption reactions having positive values and fission reactions having negative, so it doesn't seem very straightforward.

Also, how is a line such as this to be interpreted?

u-235 fission                       u-238 n,gamma                -7.4731E-03 +/- 3.7513E-08

[Jordan McDonnell]

Hello, Kaspar.  

What you show there looks like a line printed in the nuclide/reaction contributions to the nuclear data-induced uncertainty in k_eff.  

Specifically, you are seeing a contribution from a cross term, arising from the correlation between u-235 fission and u238 n,gamma.  For that pair of nuclides/reactions, the "sandwich formula" that calculates the contribution to uncertainty in k_eff works out to a negative number, due to the combination of the covariance between these two nuclides/reactions, and their respective sensitivity profile.  

More about the calculation of the uncertainty in k_eff may be seen in the SCALE manual at https://scale-manual.ornl.gov/sams.html#uncertainty-analysis .  

Thank you,

  Jordan McDonnell

[Kaspar Hewitt Klenø]

Thank you. I think I might have understood it now.

[Willem van Rooijen]

Perhaps I can add some more clarification.

The uncertainty in k-eff is due to the covariance of the nuclear data. I will try to explain a bit about covariance.

Suppose one measures the cross section of U-235 on some kind of experimental facility. Then the errors of the various reaction cross sections are not independent. For example, for both the capture and the fission reaction, the neutron must enter into the nucleus to create the so-called compound nucleus, and the compound nucleus then has several possible nuclear reactions (the so-called "output channels" or "decay channels"). Due to the underlying physical phenomenon of compound nucleus formation, the errors in the fission and capture reactions are not independent, that is to say, if there is X% error on the capture cross section then there will be Y% error on the fission cross section. Thus, the errors for the various nuclear reactions of one isotope are not independent because all reactions involve the same nucleus.

Another source of error is the experimental facility itself. For example, if a displayed value is off by X%, that error will apply to all measurements, for all cross sections, leading again to covariances.

Furthermore, the errors of related isotopes are not independent. For example, U-235 and U-238 are both isotopes of uranium, thus if there is an error for one cross section of one isotope (say, fission in U-235), there will necessarily be a non-independent error in the cross sections for the other isotope (say, capture in U-238).

In older nuclear data sets, the covariances were often reduced to variances, that is to say, the errors for the various nuclear reactions and isotopes were deemed to be independent. Nowadays, more and more measurements become available, and nuclear models are being improved, and as a result, the evaluators nowadays are sufficiently confident to add more and more covariances, between the various nuclear reactions of a given isotope, as well as covariances between the various nuclear reactions of different isotopes.

I hope this helps.

Shinichi.

 

2026年5月6日水曜日 22:06:15 UTC+9 Kaspar Hewitt Klenø: