Reactor models and the reactor
anomaly
Patrick Huber
Center for Neutrino Physics – Virginia Tech
Neutrino Oscillation Workshop 2014
Conca Specchullia, Italy
September 7-14, 2014
P. Huber – p. 1
Fission yields of β emitters
N=50 N=82
Z=50
235U
239Pu
stable
fission yield
8E-5 0.004 0.008
P. Huber – p. 2
Neutrinos from fission
235U + n → X1 +X2 + 2n ,
with average masses of X1 of about A=94 and X2 ofabout A=140. X1 and X2 have together 142 neutrons.
The stable nuclei with A=94 and A=140 are 9440
Zr and14058
Ce, which together have only 136 neutrons.
Thus 6 β-decays will occur, yielding 6 ν̄e. About 2will be above the inverse β-decay threshold of1.8 MeV.
P. Huber – p. 3
Neutrinos from fissionFor a single branch energy conservation implies aone-to-one correspondence between β and ν̄spectrum.
However, here there are about 500 nuclei and 10 000individual β-branches involved; many are far awayfrom stability.
Direct β-spectroscopy of single nuclei never will becomplete, and even then one has to untangle thevarious branches.
γ-spectroscopy yields energy levels and branchingfractions, but with limitations, cf. pandemoniumeffect Hardy et al., 1977.
P. Huber – p. 4
β branches
P. Huber – p. 5
β-spectrum from fission
235U foil inside the HighFlux Reactor at ILL
Electron spectroscopywith a magnetic spec-trometer
Same method used for239Pu and 241Pu
For 238U there is a recentmeasurement by Haag et
al. 2013.
Schreckenbach, et al. 1985.P. Huber – p. 6
Extraction of ν-spectrum
The total β-spectrum is a sum of all decay branches
Nβ(Ee) =
∫dE0Nβ(Ee, E0; Z̄) η(E0) .
with Z̄ effective nuclear charge and η(E0), theunderlying distribution of endpoints
This is a so called Fredholm integral equation of thefirst kind – mathematically ill-posed, i.e. solutionstend to oscillate, needs regulator.
This approach is the basis for “virtual branches”Schreckenbach et al., 1982, 1985, 1989 and is used in themodern calculations as well Mueller et al. 2011, Huber
2011P. Huber – p. 7
Virtual branches
æ æ æ æ æ
7.0 7.2 7.4 7.6 7.8 8.0 8.210-6
10-5
10-4
10-3
10-2
Ee @MeVD
coun
tspe
rbi
n
E0=9.16MeV, Η=0.115
æ
æ
æ
æ
æ
7.0 7.2 7.4 7.6 7.8 8.0 8.210-6
10-5
10-4
10-3
10-2
Ee @MeVDco
unts
per
bin
E0=8.09MeV, Η=0.204
æ
æ
æ
æ
æ
7.0 7.2 7.4 7.6 7.8 8.0 8.210-6
10-5
10-4
10-3
10-2
Ee @MeVD
coun
tspe
rbi
n
E0=7.82MeV, Η=0.122
1 – fit an allowed β-spectrum with free normalization η and
endpoint energy E0 the last s data points
2 – delete the last s data points
3 – subtract the fitted spectrum from the data
4 – goto 1
Invert each virtual branch using energy conservation into a
neutrino spectrum and add them all. e.g. Vogel, 2007P. Huber – p. 8
Corrections to β-shape
There are numerous correction to the β-spectrum
0 2 4 6 8 10-10
-5
0
5
10
EΝ @MeVD
Siz
eof
corr
ectio
n@%D
∆WM
L0
CS
GΝ
∆WM - weak magnetismGΝ - QED radiative correctionC - weak finite sizeL0 - QED finite sizeS - screening by s-electrons
Many of these correction depend on the nuclearcharge Z, but Z is not determined by the β-spectrummeasurement.
For forbidden decays many of these corrections arenot known – potentially large uncertainty
P. Huber – p. 9
Result for 235U
ILL inversionsimple Β-shape
Huber, 2011Mueller et al., 2011
2 3 4 5 6 7 8-0.05
0.00
0.05
0.10
0.15
EΝ @MeVD
HΦ-Φ
ILLL�Φ
ILL
Huber, 2011
Shift with respect to ILL results, due to
a) different effective nuclear charge distributionb) branch-by-branch application of shape corrections
Results for 239Pu and 241Pu similar.
P. Huber – p. 10
The reactor anomaly
Distance (m)10
210
310
0.6
0.8
1.0
1.2
Previous data
Daya Bay
World Average
Exp. Unc.σ1-
Flux Unc.σ1-
Data
/ P
red
ictio
n
Previous average
R = 0.943 +- 0.008 (exp.)
Daya Bay’s reactor flux
previous short baseline
Daya Bay R = 0.947 ± 0.022
Daya Bay, preliminary, 2014
The increase in predicted neutrino fluxes, triggered are-analysis of existing reactor data
And this was found by Mueller et al., 2011, 2012 –where are all the neutrinos gone? P. Huber – p. 11
Contributors to the anomaly
6% deficit of ν̄e from nuclear reactors at shortdistances
• 3% increase in reactor neutrino fluxes
• decrease in neutron lifetime
• inclusion of long-lived isotopes (non-equilibriumcorrection)
The effects is therefore only partially due to the fluxes,but the error budget is clearly dominated by the fluxes.
P. Huber – p. 12
A priori calculations
Energy (MeV)
2 4 6 8 10 12 14 16
/MeV
/fiss
ion
eν
-1210
-910
-610
-310
110
U238
Energy (MeV)
2 4 6 8 10 12 14 16
-12
-9
-6
-3
110
U235
/MeV
/fiss
ion
eν
-1210
-910
-610
-310
110
Pu239
2 4 6 8 10 12 14 16
-12
-9
-6
-3
110
Pu241
/MeV
/fiss
ion
eν
Energy (MeV)
2 4 6 80.8
1
1.2 P. HuberSummation method /
Rat
io
Energy (MeV)2 4 6 8
0.8
1
1.2 P. HuberSummation method /
Rat
io
Energy (MeV)
2 4 6 80.8
1
1.2 P. HuberSummation method /
Rat
io
Energy (MeV)
Fallot et al., 2012
Updated β-feeding func-tions from total absorptionγ spectroscopy (safe frompandemonium) for the iso-
topes: 102,104,105,106,107Tc,105Mo and 102Nb
The calculation for 238Uagrees within 10% withmeasurement of Haag etal.
Still a 10-20% discrepancywith the measured totalβ-spectra.
Next steps?P. Huber – p. 13
Weak magnetism & β-spectra
Nuclear structure effects can be summarized by the
use of appropriate form factors FNX .
The weak magnetic nuclear, FNM form factor by virtue
of CVC is given in terms of the analog EM formfactor as
FNM (0) =
√2µ(0)
The effect on the β-decay spectrum (in alloweddecays) is given by
1 + δWMW ≃ 1 +4
3M
FNM (0)
FNA (0)
W
P. Huber – p. 14
What is the value of δWM?
Three ways to determine δWM
• impulse approximation – universal value
0.5%MeV−1
• using CVC – FM from analog M1 γ-decay width,FA from ft value
• direct measurement in β-spectrum – only veryfew, light nuclei have been studied. In those casesthe CVC predictions are confirmed within(sizable) errors.
Overall, good agreement with naive expectationsexcept for handful of nuclei → hint to non-trivialnuclear structure effects
P. Huber – p. 15
WM in forbidden decays
2 4 6 8
Eν(MeV)
0.9
0.95
1
1.05
1.1
1.15
k(E
ν)/k
(Eν) o
rig
ina
l
Treat all transitions as allowed GT
Treat all non-unique forbidden transitions as [Σ,r]0-
Treat all non-unique forbidden transitions as [Σ,r]1-
Treat all non-unique forbidden transitions as [Σ,r]2-
Approximate upper bound forthe flux error due to forbiddendecays.
Hayes et. al, 2013 point out thatin forbidden decays a mixture ofdifferent operators are involved,and that while for many of theindividual operators the correc-tions can be computed, the rel-ative contribution of each opera-tor is generally unknown.
My interpretation: it is the WM which is the leadingcause for the large combined uncertainty they find.
P. Huber – p. 16
The 5 MeV bump
see also talks by S.B. Kim, J. Crespo Anadon, J.-C. Peng
•
•
•
Seen by all three reactor experiments
Tracks reactor power
Seems independent of burn-up P. Huber – p. 17
Explanations?
Direct summation of latest ENSDF database,assuming allowed beta-spectrum shapeDwyer and Langford, 2014
]-1
fiss
ion
-1)
[MeV
ν S
(E×
νσ
0.1
0.2 Nuclear Calculation
Conversion, Huber-β
Conversion, Mueller-β
Antineutrino Energy [MeV]2 3 4 5 6 7 8
) ν(E
con
v.- β
) / S
νS
(E
0.8
0.9
1
1.1RENO
Double CHOOZ
]-1
fiss
ion
-1)
[MeV
e-S
(E
-310
-210
-110
1
U235
Nuclear Calculation
BILL measurement
Electron Kinetic Energy [MeV]2 3 4 5 6 7 8
)e-
(EB
ILL
) / S
e-S
(E
0.8
0.9
1
1.1
This direct summation, as all other direct summations,does not agree with the Schreckenbach totalbeta-spectrum.
P. Huber – p. 18
Another explanation?
2 4 6 8
Eν(MeV)
0.9
0.95
1
1.05
1.1
1.15
k(E
ν)/k
(Eν) o
rig
ina
l
Treat all transitions as allowed GT
Treat all non-unique forbidden transitions as [Σ,r]0-
Treat all non-unique forbidden transitions as [Σ,r]1-
Treat all non-unique forbidden transitions as [Σ,r]2-
Hayes et. al, 2013, shown isthe relative shift between beta andneutrino spectra
For certain operators there is afeature at 5 MeV resulting fromthe ensemble of all decays.
It has not been quantitatively shown that theseforbidden decays can both reproduce theSchreckenbach data and the neutrino data.
P. Huber – p. 19
Summary
Fission has been an important neutrino source formore than 60 years
Fission neutrinos are understood at the 5% level
Recent 3% increase in fluxes confirmed by twoindependent analyses assuming allowed beta-spectra
Many complicated questions related to forbiddendecays arise – not obvious how theory can help
The 5 MeV bump is most likely due to nuclearphysics, although a quantitative explanation ismissing at the moment
P. Huber – p. 20
Backup Slides
P. Huber – p. 21
CVC at workCollect all nuclei for which we
• can identify the isospin analog energy level
• and know ΓM1
then, compute the resulting δWM . This exercise hasbeen done in Calaprice, Holstein, Nucl. Phys. A273 (1976)
301. and they find for nuclei with ft < 106
δWM = 0.82± 0.4%MeV−1
which is in reasonable agreement with the impulse
approximated value of δWM = 0.5%MeV−1. Our
result for ft < 106 is δWM = (0.67± 0.26)%MeV−1.
P. Huber – p. 22
CVC at workDecay Ji → Jf Eγ ΓM1 bγ ft c bγ/Ac |dN/dE|
(keV) (eV) (s) (% MeV−1)
6He →6 Li 0+→1
+3563 8.2 71.8 805.2 2.76 4.33 0.646
12B →12 C 1+→0
+15110 43.6 37.9 11640. 0.726 4.35 0.62
12N →12 C 1+→0
+15110 43.6 37.9 13120. 0.684 4.62 0.6
18Ne →18 F 0+→1
+1042 0.258 242. 1233. 2.23 6.02 0.8
20F →20 Ne 2+→2
+8640 4.26 45.7 93260. 0.257 8.9 1.23
22Mg →22 Na 0+→1
+74 0.0000233 148. 4365. 1.19 5.67 0.757
24Al →24 Mg 4+→4
+1077 0.046 129. 8511. 0.85 6.35 0.85
26Si →26 Al 0+→1
+829 0.018 130. 3548. 1.32 3.79 0.503
28Al →28 Si 3+→2
+7537 0.3 20.8 73280. 0.29 2.57 0.362
28P →28 Si 3+→2
+7537 0.3 20.8 70790. 0.295 2.53 0.331
14C →14 N 0+→1
+2313 0.0067 9.16 1.096 × 10
90.00237 276. 37.6
14O →14 N 0+→1
+2313 0.0067 9.16 1.901 × 10
70.018 36.4 4.92
32P →32 S 1+→0
+7002 0.3 26.6 7.943 × 10
70.00879 94.4 12.9
P. Huber – p. 23
What happens for large ft?Decay Ji → Jf Eγ ΓM1 bγ ft c bγ/Ac |dN/dE|
(keV) (eV) (s) (% MeV−1)14C →14 N 0
+→1+
2313 0.0067 9.16 1.096× 109
0.00237 276. 37.614O →14 N 0
+→1+
2313 0.0067 9.16 1.901× 107
0.018 36.4 4.9232P →32 S 1
+→0+
7002 0.3 26.6 7.943× 107
0.00879 94.4 12.9
Including these large ft nuclei, we have
δWM = (4.78± 10.5)%MeV−1
which is about 10 times the impulse approximatedvalue and this are about 3 nuclei out of 10-20...
NB, a shift of δWM by 1%MeV−1 shifts the totalneutrino flux above inverse β-decay threshold by
∼ 2%.
P. Huber – p. 24