Prediction of
Reactor Neutrino Spectra
David Lhuillier
CEA Saclay - France
General Considerations
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Origin of Reactor Antineutrinos
• b-decay of the fission products
of U and Pu isotopes
• Ab initio approach: build up the
total spectrum with individual
contribution of ~800 nuclei.
ee-
n
n
• Reference spectra approach:
measure the mean fission b
spectrum of U an Pu isotopes
and weight them by the
predicted fission rates.
All predictions require a reactor simulation with core geometry, initial fuel
composition and power history.
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Energy Spectrum
Exponential decrease of
emitted spectrum
b-inverse detection reaction
n e + p ® e+ + n
Detected Spectrum
Relevant E range [1.8 – 8] MeV
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© F. Durillon, animea
Contributing
Nuclei
Detection reaction enhances the contribution of high energy b-transitions:
- Lot of very unstable nuclei, high above valley of stability
- Short lived, reach equilibrium fast w.r.t. experiment time scale
 Reference fission spectra approach favored w.r.t. ab initio approach.
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Evolution Along a Reactor Cycle
Typical evolution of the isotopic
composition of a commercial rector
At Pth= constant, 239Pu fission leads to 60%
less detected neutrinos than 235U fission.
ak [%]
Burnup [MWd/t]
2000 4000 6000 8000 10000 12000 14000
239Pu
ON
238U
Refueling with fresh 235U
70
60
50
40
30
20
10
0
0
235U
ON
241Pu
Total Spectrum:
S(E, t) = åak (t) Sk (E)
k = 235U, 238U, 239 Pu, 241Pu
k
• Monitoring of reactor n flux with sensitivity to plutonium content.
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Fission Spectra uncertainties
& Non-proliferation
• Non proliferation relies on
evolution of the neutrino rate
along a reactor cycle; Relative
variations and/or reference anchor
point.
• In the case of converted spectra,
the normalization and shape
uncertainties are mostly correlated
for all fissioning isotopes  their
impact is suppressed.
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73 kg of 239Pu
removed
V. Bulaevskaya and A. Bernstein, nucl-ex/1009.2123
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Re-evaluation of
Reference Spectra
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ILL data: reference b- Spectra
Emitted b spectra per fission
Magnetic BILL
spectrometer
eTarget foil
(235U, 239Pu, 241Pu)
in thermal n flux
ILL research reactor
(Grenoble, France)
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A. A. Hahn, K. Schreckenbach et al.,
Phys. Let. B218,365 (1989)+ refs therein
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b- n Conversion
1- Need to break down the total e- spectrum into single b-branches
 fit the data with 30 virtual branches:
2- Convert each virtual e- branches to n branches
3- Sum all converted n branches to get total n spectrum
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Theory of b-decay
Fermi theory:
N b (W ) = K p (W -W0 ) F(Z,W ) CShape (W )
F
2
2
Fermi Shape factor
function of forbidden
Phase
space
•
•
•
•
W = total energy
W0 = end-point
p = momentum
Z = Nuclear charge
Corrections:
Nb (W ) = NbF (W ) L0 (Z,W) S(Z,W ) C(Z,W) Gb (Z,W ) (1+ dWM W )
Finite size of nuclear
electric charge
Screening of
Atomic e-
Finite size distrib.
QED
of decaying
radiative
neutron
correction
Weak
magnetism
n branch obtained by replacing: WW0-W, GbGn
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Corrections to Fermi theory
n spectrum corrections
Example of a
single branch
with
Z=46
A=117
E0=10 MeV
b spectrum corrections
P. Huber
• Total fission spectra is a sum over a quasi continuous end-point distribution
 +/- cancellation at low E, adds up at high E.
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Re-evaluation of Converted Spectra
T. A. Mueller et al., Phys. Rev. C83,054615 (2011)
• Initiated by the need of accurate prediction for the far detector of Double Chooz
• Maximize the use of nuclear
data: 90% of the total b spectrum
is described by the sum of
measured b-decays * Fission
yields.
Nuclear Data
• Use virtual branches only to fill
the remaining 10% gap.
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Re-evaluation of Converted Spectra
T. A. Mueller et al., Phys. Rev. C83,054615 (2011)
• True distribution of Z from all b-decays of databases.
• Apply all corrections at the branch level instead of an effective global slope.
0.1
0.05
0
-0.05
-0.1
2
Corrections applied at branch level
3
4
5
Old effective correction
6
“true” Z distribution from
nuclear databases
7 8
E (MeV)
• Combined effect at low and high energy leading to a global +3% shift
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Reactor Anomaly
G. Mention et al., Phys. Rev. D83, 073006, 2011
New
Oscilation to
sterile n?
Atmospheric
Oscilation
Solar
Oscilation
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Confirmed by Complementary Work
P. Huber, Phys. Rev. C84, 024617(2011)
• Revisit conversion procedure of ILL data with minimal use of nuclear data.
New conv. with “extra correction”
New conv. P. Huber
New conv. T.A. Mueller et al.
ILL conversion
•
•
•
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Confirms global increase of predicted spectrum
Fixes remaining oscillations of first re-evaluation
Extra slope correction
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Two Predictions in Agreement
The two published predictions contain the same physics.
Difference in global slope is now understood:
• L0 correction not properly implemented in Mueller et al. re-evaluation.
• Different expressions of C(Z,W) term.
(
f
- f
ILL
)
/
f
ILL
0.12
Revised Mueller et al.
Huber, Phys. Rev. C84, 024617 (2011)
0.14
0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
2
Mueller et al., Phys. Rev. C83, 054615 (2011)
3
4 5 6
En [MeV]
7
8
T.A. Mueller, D. Lhuillier
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Updated Reactor Anomaly
White paper: K. N. Abazajian et al. , hep-ph/1204.5379
Reactor + Gallium anomaly
7% deficit
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~4% from reactors
1% from tn, 1% from off-eq
1% from previous deficit
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Normalization Uncertainty
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Normalization of ILL data
• Dominant systematic error : 1.8 % (1 s)
• Absolute calibration via internal conversion electron lines of known partial
cross section per neutron capture
• Correlated across all energy bins of all isotopes
directly propagates into the converted antineutrino spectra.
115In(n,
g)116mIn &
113Cd(n,g)114Cd
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207Pb(n,
g)208Pb : absolute normalization
: relative normalization
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Independent
Norm. at 2% level?
2. 10-2 b/fission in 250keV bin centered on 6 MeV:
• The required few 106 fissions could be recorded
with less intense neutron source (away from reactor
 background reduction).
10-1
10-2
-3
10
10-4
0
• Same calibration using internal conversion line +
Precise counting with evt by evt fission tagging?
n rate (a.u.)
2
4
• Magnetic design for e- detection in large solid angle,
and well controlled energy resolution.
6
0 to 25h30
1h to 25h30
2h to 25h30
3h to 25h30
4h to 25h30
5h to 25h30
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E (MeV)
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6h to 25h30
8
Potential large impact on reactor anomaly…
7h to 25h30
• No off-equilibrium corrections
21
Shape Uncertainty
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Weak Magnetism
Approximate expression neglecting nuclear structure:
dWM »
4 mp - mn CV
´ E » 0.48% / MeV ´ E
3 M N CA
Measurement of dWM through transitions in isobaric analog states:
CVC symmetry
Magnetic dipole M1 g decay width
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dWM
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Weak Magnetism
dWM »
4 mp - mn CV
´ E » 0.48% / MeV ´ E
3 M N CA
, assume 100% error
Experimental
slope in good
agreement for
transitions with
low ft values
Contribution of
large ft’s in fission
neutrino spectra?
P. Huber, Phys. Rev. C84, 024617(2011)
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Weak Magnetism
Relative contribution
• High log(ft) values have a sizeable contribution to fission n spectra across all E range
(reflects the large contribution of forbidden decays)
• CVC still valid for very large ft transition which have tiny overlap of wave functions in
b-decay?
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Weak Magnetism
Total Relat Syst (%)
10
8
6
4
2
0
-2
-4
-6
2
4
Total systematics
Nominal dAwm
4*dAwm
3
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 Upcoming data from DayBay, Reno
and Double Chooz near detectors
have the potential to confirm the
current shape uncertainty!
5
6
7
Evis (MeV)
 Reanalysis of Bugey3 data may
already constrain the weak magn
slope at this level.
-8
-10
 A factor 4 increase of dWM would
compensate the +4% deviation
from ILL spectra, but also induce a
large negative tilt.
• Estimated shape uncertainty with ~3.5 105
accumulated neutrinos, dEscale = 0.5% and
~4% 9Li background.
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Shape Uncertainty
239Pu / 235U
0.9
0.8
0.7
0.6
0.5
0.4
0.3
WM+Z+Stat
10
8
WM+Z
2
6
4
2
0
-2
-4
-6
-8
-10
Error (%)
2
4
ILL conversion
3
WM
4
New Conversion
3
5
5
6
7
8
En (MeV)
6
7
8
n Kinetic E (Mev)
• Correlated across all energy bins and isotopes
 favorable to non-proliferation and oscillation search
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New Data
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Updated Ab Initio Predictions
• Correct for Pandemonium effect by using Total Absorption g-ray
Spectrometry (TAS)
• Short list of fission products contributing by more than 4% to 2-6MeV bins.
A. Algora et al., Phys. Rev. Lett. 105, 202501 (2010)
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Updated Ab Initio Predictions
M. Fallot et al. , nucl-ex/1208.3877
• Inclusion of 7 new Tc, Mo and Nb
isotopes.
• Sizeable correction of predicted
spectra  within ±10% of new
converted spectra.
• Analysis and new measurements
on-going.
• Same uncertainties on slope factors
beyond databases systematics.
• Toward a competitive prediction of
absolute normalization?
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New 238U data
New 238U data @ FRMII reactor,
Munich
• Anchor point of 235U measurement:
- Background well understood.
- Comparison to ILL spectrum cancels
most uncertainties.
n flux
Natural U foil
b
MWC
Plastic
Scintillator
N. Haag, K. Schrekenbach et al.
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New 238U Data
• N. Haag Ph.D. thesis to be published by end of this year.
• Final measurement of 238 U ranges from 2.0 MeV to 6.5 MeV with relative
errors of 5% - 15%
• Spread of ab Initio flux predictions in the ±10% range
Possible update of the reactor anomaly at 1% level with sligthly improved
total uncertainty
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Conclusions
 Demonstrated bias in the conversion procedure of the ILL data.
 +4% increase of detected rate is confirmed by two independent
works.
 +1% off-equilibrium correction of reactor simulation
+ 1% updated neutron life-time
+ 1% previous mean shift with old spectra
 ~7% deficit of the reactor anomaly
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Conclusions
 Application to reactor surveillance:
- Main uncertainties are common to all isotopes suppressing
their impact on relative monitoring
- Short baseline oscillations to be tested soon. n rate at one
location is affected through U-Pu shape difference only.
 Challenging independent Xcheck of spectra normalization
 New data coming soon to consolidate the current error
budget:
- 238U Spectrum from FRM II
- New shape envelope to be measured by near detectors of
currently running reactor experiments.
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Back Up Slides
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Complementary Approaches
Conversion of total b spectra
Ab initio calculations
Complete simulation of core evolution
Total b spectra of fissile isotopes
measured at ILL in the 80’s
- Fuel loading, geometry, n-capture and
fission physics
 Fission product inventory
 Accurate reference electron spectra
Conversion to antineutrinos
Description of all b-decays
- Use of “virtual” b-branches
- Fermi theory + corrections
- Control of approximations
- Nuclear databases
- Fermi theory + corrections
- Nuclear models
 b and n total spectra from some 104
b-branches.
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 Reference n spectra per isotope to be
combined with prediction of fissions
rates.
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Ingredients
Sum of all fission
products’ activities
Sum of all β-branches
of each fission product
Theory of βdecay
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Status of Spectra Rate
Final difference with respect to ILL n spectra :
 Global rate increase
 Linear trend with slope ≤1%/MeV enhances this increase in detected rate
Emitted Flux
Detected Rate
Shift (%)
Signif. (s)
Shift (%)
Signif. (s)
235U
2.4
3.7
3.7
2.4
239Pu
2.9
3.9
4.2
2.8
241Pu
3.2
4.0
4.7
3.0
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Finite Size Correction of Weak
Interaction
Different expressions of C(Z,W) term:
P. Vogel, Phys. Rev. D29, 1918 (1984).
D. Wilkinson, Nucl. Phys. Inst. and Meth. A 290, 509 (1990)
(Huber-Mueller) /
Mueller
0.04
0.02
0
-0.02
-0.04
2
4
Relative Dif erence induced by C(Z,W)
3
5
6
7
8
En (MeV)
• Include the envelope of various calculations as extra uncertainty?
• Would reach ~2% at 7 MeV.
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Uncertainties
10
8
6
4
2
0
-2
-4
-6
-8
-10
Conversion of b spectra
Error (%)
2
WM+Norm+Z+Stat
WM+Norm+Z
4
WM+Norm
WM
3
 Finite size corrections could be further
studies by combining nuclear model
and lepton scattering data. Not
dominant uncertainty.
5
6
7
8
n Kinetic E (Mev)
 Normalization:
- Common to all predictions.
- Currently 1.8% at 1 s.
- A new measurement should target 1%.
Not likely to happen.
Quadratically stacked errors
 Current treatment of weak magnetism neglect the nuclear structure.
- Dominant shape uncertainty, 100% error assumed.
- Underestimated uncertainty?
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Shape Evolution Along a Reactor Cycle
• Expected shape rotation on top of flux reduction
• But significant measurement requires very large statistics on month time scale.
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Total Reactor Spectrum
S(W, t)tot = åa k (t)Sk (W ) , k = 235U, 238U, 239 Pu, 241Pu
k
ak = fission fraction, Sk(W)=Reference spectrum
Half way through:
• Prediction of ak(t)
•
238U
couldn’t be measured at ILL because it undergoes fission in fast
neutron flux.
• Extrapolation of the ILL spectra to commercial reactors?
Ab initio approach addresses it all
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Ab initio
• Build as complete as possible nuclear database
coupled to MCNP Utility for Reactor Evolution (*)
 full core inventory
•
235U
spectrum matches the ILL data at ~10% level
•
238U
prediction 10% higher than previous estimate
Phys. Rev. C83,054615 (2011)
ENSDF only
Pandemonium corr.
Add gross theory
Deviation from Vogel et al.,
Phys. Rev. C24, 1543 (1981)
• Total error in the 10-20% range. Dominated by
systematics of nuclear databases.
(*) http://www.nea.fr/tools/abstract/detail/nea-1845.
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Ab initio
Study of relative spectrum variations to reach equilibrium
Off-eq. correction as computed by the MURE
 ILL reference data are photos of b
decays after 12-36h irradiation time.
 Long-lived isotopes, dominant at low
energy, keep accumulating over
several weeks.
 Sizeable correction to ILL data in
[53] = Chooz paper
below 3 MeV; +1% total detected flux
See poster 146, A., Reactor and antineutrino spectrum calculation for the Double
Chooz first phase result
C. Jones et al. arXiv:nucl-ex/1109.5379v1
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Error Budget
235U
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Phys. Rev. C83,054615 (2011)
239Pu
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241Pu
45
Error
Budget
Phys. Rev. C84, 024617(2011)
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Bugey
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