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Nuclear Data for Reactor Fluxes

A.A. Sonzogni, E.A. McCutchan, T.D. Johnson

National Nuclear Data Center

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Outline

  • Summation method to calculate antineutrino spectra.

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  • How did we get involved in this???? (decay heat and delayed nu-bar work, libraries)

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  • Some recent work on the data involved in summation calculations.

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How to calculate antineutrino spectra

  1. Conversion Method: Use the precisely measured electron spectra following the thermal neutron fission of 235,238U and 239,241Pu.

Fit the electron spectrum with a set of hypothetical decay branches.

Uses nuclear data to obtain effective Z as function of end point energy.

P. Huber, Phys. Rev. C 84, 024617 (2011).

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(2) Summation Method: Combine fission yields with decay data.

P. Vogel et al. Phys. Rev. C 24, 1543 (1981).

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Summation Method

where CFYi is the cumulative fission yield defined recursively as:

with bki the decay probability from level k to level i. In matrix notation:

The antineutrino spectrum for an equilibrated fissioning system is calculated as:

where IFY are the independent fission yields, and the matrix A has the decay probability data.

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is the spectrum generated by the decay of a single level:

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is the antineutrino spectrum generated in the decay to the level Elk with intensity Iβlki in the daughter, normalized to 1.

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Summation Method

Some issues in this method:

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  • Cumulative Fission Yields have embedded decay probabilities, which should be compatible with the decay probabilities used in the spectra calculation.

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  • Decay data is only complete and of high quality for nuclides close to the valley of stability.

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  • For nuclides with a large Q-values, decay schemes obtained using Germanium detectors lead to large beta intensities for low-lying levels. One should use data from Total Absorption Gamma Spectroscopy (TAGS) experiments.

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A.A. Sonzogni, T.D. Johnson, E.A. McCutchan, PRC91, 011301(R) (2015)

Summation Method

Update ENDF/B decay data with Iβ from TAGS and Rudstam data.

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Surprisingly, fewer contributors at high energy.

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Calculations using JEFF yields (compatibility).

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It includes calculated spectra for very neutron rich nuclides (Moller-Kawano)

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Systematics of all fissioning systems

Integral of the signal is needed to study the anomaly

Link to delayed neutron yield commonly parameterized by

3Z-A

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235U thermal fission yields

235U thermal Yi/<σI>

Yi/<σI>: fractional contribution to antineutrino multiplicity above threshold

Yi=CFYi∫σ(e)Iνi(e)

<σI>=ΣYi

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Data Libraries

ENSDF, www.nndc.bnl.gov/ensdf

Contains nuclear structure and decay data.

ENDF/B, www.nndc.bnl.gov/endf

American. Main effort is for neutron-induced cross sections and spectra. It also contains fission and decay data in a numerical format.

JEFF, www.oecd-nea.org/dbdata/jeff/

European. Similar to ENDF/B.

JENDL, wwwndc.jaea.go.jp/jendl/jendl.html

Japanese. Similar to ENDF/B.

Managed by the NNDC

Additionally the NNDC is responsible for the decay data in ENDF/B that is needed for the calculations.

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A. Algora et al, PRL 105, 202501 (2010).

Large <Eγ>

Small <Eβ>

Small <Eν>

Neutrons

Longer T1/2

High excitation energy β- feeding

Small <Eγ>

Large <Eβ>

Large <Eν>

No neutrons

Shorter T1/2

Low excitation energy β- feeding

Earlier Work on Decay Heat

239Pu gamma decay heat

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235U Thermal

Relation to decay heat

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235U Thermal

92Rb, 100Nb, 96Y, 101Nb,102Nb

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Fission Yield Effects

ENDF/B fission yields were released in 1992. We studied the effect of corrections due to a) better decay data, b) improved isomeric ratios, c) anomalous yields.

IT 100%

3

0

β- 100%

96Y

ENDF/B-VII.1 Fission Yields (1992)

8+

0-

96Y

β- 100%

ENSDF (Current)

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Thermal 235U spectrum

Corrected yields:

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  • No electron excess.

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  • Better agreement with JEFF.

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Spectrum for fast reactors

  • HEU reactors.
  • 235U contributes most of the fission.
  • Needed for future experiments pursuing the anomaly.
  • Currently, it can only be obtained by summation.

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  • Use corrected ENDF/B yields.
  • Incorporate TAGS results.
  • Significant differences in the shape with 1981 values.
  • TAGS data make a big difference.

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Spectrum for fast reactors II

  • For fast neutrons, the increase in excitation energy makes the fission yield distribution broader.

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  • The delayed nu-bar per 100 fissions increases from 1.585 to 1.67.
  • When using corrected fission yields, the antineutrino spectrum for fast neutrons is harder than the spectrum for thermal neutrons.

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  • In agreement with JEFF yields and as expected.

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96Y – one nuclide with a large effect

95.5 % of the decay is ground state to ground state

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96Y – one nuclide with a large effect

For the isomer, on the other hand, due to angular momentum, the feeding is concentrated at high excitation energies

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96Y – Two Different Isomers

Both spectra are normalized to 1

The ground state produces about 7 times more antineutrinos above the threshold than the isomer

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96Y – Isomeric Ratio Effect

96Y Isomeric Ratio:

At about 5.2 MeV, changing IR from 0 to 100% changes the calculated to experimental ratio by 7%.

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CFY ~ 0.05

There is no journal publication of IR.

Estimates of IR vary from 18% to 70%

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Conclusions

Updated the ENDF/B decay data to incorporate new TAGS and other decay data that are relevant to antineutrinos or decay heat.

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Decomposed total spectrum into individual contributions, derived systematics of the energy integrated cross section weighted antineutrino spectrum.

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Studied the effect of correcting thermal 235U ENDF/B fission yields. Without these corrections results will not be reliable, leading to a fast spectrum softer than the thermal.

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Calculated the fast 235U antineutrino spectrum, good agreement with JEFF yields, TAGS data make a big impact.

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Identified pieces of data, such as the 96Y Isomeric Ratio, that have big impact and could merit a precise measurement.

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TAGS (Total Absorption Gamma Spectroscopy) experiments

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NaI crystals

Radioactive source

Plastic detector for beta-gamma coincidences

TAGS measure the gamma spectrum after beta decay with low resolution but high efficiency.

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232Th

238U

235U

241Pu

238Np

233U

239Pu

252Cf

Systematics of Delayed nu-bars

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