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