Reactor Neutrino Flux and Spectra

Patrick Huber

Center for Neutrino Physics – Virginia Tech

Neutrino Geoscience 2015

Institut de physique du globe de Paris

June 15 – 17, 2015

P. Huber – p. 1

Why care?

This requires a very precise understanding of thereactor neutrino signal below 4 MeV.

P. Huber – p. 2

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. 3

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 9440Zr and

14058 Ce, which together have only 136 neutrons.

Thus 6 β-decays will occur, yielding 6 ν̄e. About 2will be above inverse β-decay threshold.

How does one compute the number and spectrum ofneutrinos above inverse β-decay threshold?

P. Huber – p. 4

β branches

P. Huber – p. 5

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.

P. Huber – p. 6

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 recent measure-ment by Haag et al., 2013

Schreckenbach, et al. 1985.P. 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

Reactor antineutrino fluxes

ILL inversionsimple Β-shape

our result1101.2663

2 3 4 5 6 7 8-0.05

0.00

0.05

0.10

0.15

EΝ @MeVD

HΦ-Φ

ILLL�Φ

ILL

PH, 2011

Shift with respect to ILL results, due to

a) different effective nuclear charge distributionb) branch-by-branch application of shape corrections

P. Huber – p. 9

Non-equilibrium corrections

Mueller, et al., 2011

only 2 dozen isotopeswith t1/2 > 12 h above

inverse β-decay thresh-old

Extra shift due to long-lived isotopes in core

a) small nuclear physics uncertainty in β-decayb) depends on detailed fuel history

P. Huber – p. 10

Spent nuclear fuel

Daya Bay Near DetectorLing Ao Near DetectorDB+LA Far Detector

2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.005

0.010

0.015

Energy @MeVD

RatioHSF�co

reL

1 day10 days365 days

1.5 2.0 2.5 3.0 3.5 4.00.00

0.05

0.10

0.15

Energy MeV

Ratio

SFcore

Extra shift due to long-lived isotopes in SNF

a) small nuclear physics uncertainty in β-decayb) depends on detailed fuel history

P. Huber – p. 11

Recent neutrino measurementsIn Daya Bay, RENO and Double Chooz, the distanceis such that all sterile oscillations are averaged away –no confusion between nuclear physics and newphysics

The statistics in the Daya Bay near detectors is around1 million events

In combination, this should provide a good test of ourability to compute reactor fluxes

P. Huber – p. 12

The 5 MeV bump

•

•

•

Seen by all three reactor experiments

Tracks reactor power

Seems independent of burn-upP. Huber – p. 13

Explanations?

Direct summation of latest ENSDF database,assuming allowed beta-spectrum shapeDwyer and Langford, 2014

This direct summation, as all other direct summations,does not agree with the Schreckenbach totalbeta-spectrum. P. Huber – p. 14

Another explanation?

2 4 6 8

Eν(MeV)

0.9

0.95

1

1.05

1.1

1.15

k(E

ν)/k(E

ν) ori

gin

al

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

Forbidden beta decays showa strong nuclear structuredependence

For certain operators thereis a feature at 5 MeV resultingfrom the 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. 15

Non-linear effects100Tc is not made as afission product

It can not be fed bythe A=100 decay chainsince it ends at stable100Mo.

99Tc + n →100Tc

neutron capture can pro-

duce 100Tc!100Tc in turn has a beta decay with an endpoint of3.2028 MeV, well above inverse-beta decay threshold.

P. Huber – p. 16

Non-linear effectsIn a neutrino from a fission fragment

nν ∝ nfission ∝ σfissionρfissileφn ,

with φn being the neutron flux density and ρfissile is thenumber density of fissile atoms. In particular

nν/nfission = const.

For neutron capture on 100Tc, the situation is different,to first order in φn we have

nTc100 ∝ ρTc99σnφn ∝ σfissionρfissileφn︸ ︷︷ ︸

=ρTc99

σnφn ∝ φ2n

that is nν/nfission ∝ φ!

P. Huber – p. 17

Non-linear effectsRelevant isotopes need to have a large fission yieldand a reasonable cross section for production bycapture and a beta decay energy above inverse betadecay threshold.

100Tc 104Rh 110Ag 142Pr

Fission Yields

235U 0.061316 0.031033 0.00028765 0.058554

239Pu 0.061843 0.069481 0.016732 0.052051

241Pu 0.056133 0.065384 0.029654 0.049

Eβ (MeV) 3.4 2.45 2.9 2.15

τ1/2 (sec) 15.54 42.3 24.6 68830

P. Huber – p. 18

Non-linear effects

Higher order effects yield a dependence on the

neutron flux density of φ0.5n .

P. Huber – p. 19

Low-energy corrections

Need to know

Non-equ. – 25%SNF – 50%Non-linear – 50%

others fine, if no(further) surprises

Statistics corresponds to 10 years of JUNO running.With these assumptions the statistical and systematicerrors are approximately the same.

P. Huber – p. 20

Summary

• Reactor are very complex neutrino sources

• Many corrections at the 1-5% level at lowenergies

• Non-linear correction presented for the first time⇒ high-flux reactors are not good proxies

In combination a systematic uncertainty (withreasonable assumptions) of 1–1.5% below 4 MeV

Suitable near detectors could reduce the systematicuncertainty to negligible levels – 1 ton at 90 m fromreactor has the same rate as 20 ton at 400 m fromreactor.

P. Huber – p. 21