1. Recent re-Evaluation of Reactor n Flux
D. Lhuillier – CEA Saclay
Based on:
Phys. Let. B218,365 (1989)+ refs therein
A. A. Hahn, K. Schreckenbach, W. Gellently, F. von Feilitzsch, G. Colvin, B. Krusche
Phys. Rev. C83, (2011)
T.A. Mueller, D. Lhuiller, M.Fallot, A. Letourneau, S. Cormon, M. Fechner, L. Giot, T. Lasserre, J. Martino, G. Mention, A. Porta, F. Yermia
Phys. Rev. C84, (2011)
P. Huber
D. Lhuillier
SNAC Blacksburg

2. Reactor Anomaly Phys. Rev. D83, 073006, 2011 Reactor + Gallium
G. Mention, M. Fechner, T. Lasserre, M. Cribier, Th. Mueller D. Lhuillier, A. Letourneau
Reactor + Gallium
Average = ± (c2=19.6/19)
D. Lhuillier
SNAC Blacksburg

3. n spectrum emitted by a reactor
The prediction of reactor ν spectrum is the dominant source of systematic error for single detector reactor neutrino experiments
Thermal power, δPth <1%
Fraction of fissions from isotope k, δak=few %
E released per fissions of isotope k, δEk≈0.3%
ν spectrum per fission
This work !
Reactor data
Nuclear databases
Reactor evolution codes
D. Lhuillier
SNAC Blacksburg

4. n spectrum emitted by a reactor=
S all fission products
D. Lhuillier
SNAC Blacksburg

5. The guts of Sk(E) Sum of all fission products’ activities
Sum of all β-branches of each fission product
Theory of β-decay
D. Lhuillier
SNAC Blacksburg

6. Corrections to Fermi Theory
See P. Vogel’s talk
Correction
Physics
Size
Error Gn
Real&virtual g emmision by charged fermion lines
Small L0
Coulomb field from finite size nucleus
~% MeV-1
CW*
Weak interaction inside a finite size nucleus S
Screening of nuclear charge by atomic electrons
dWM
Weak magnetism
Assumed 0.5% MeV-1, could be large
100% relative error (?)
*: not implemented before P. Huber’s work
D. Lhuillier
SNAC Blacksburg

7. Corrections to Fermi Theory
Example with Z=46, A=117, E0=10 MeV,
Effect on fission spectra results from the sum over quasi continuous end-point distribution
P. Huber
D. Lhuillier
SNAC Blacksburg

8. Complementary approaches
Integral measurements of e- spectra
Nuclear Data
Sum of all fission products’ activities
fission product inventory (t)
U & Pu fission rates (t)
Reference e-spectrum for each isotope to be converted to n spectrum
Sum of all β-branches of each fission product
Build total spectrum from sum of β-branches
Complete β-decays schemes (ENSDF)
β-strength (Greenwood et al.)
Total β spectrum per nucleus (Rudstam et al.)
Masses (Qb)
Nuclear models …
Theory of β-decay
Corrected Fermi theory
ab-inito
Mixed
Effective
D. Lhuillier
SNAC Blacksburg

9. The ILL electron Data “Anchor point”
See K. Schreckenbach’s talk
Total electron spectra from the b-decays of 235U, 239Pu and 241Pu fission products.
Target foil
(235U, 239Pu, 241Pu)
in thermal n flux
High
resolution spectrometer
ILL research reactor
(Grenoble, France) e-
Accurate e- measurements
@ ILL in Grenoble ( ):
High resolution magn. Spectrometer
Calibration by extensive use of reference internal conversion electron lines
Normalization syst 1.8%
Unique reference to be met by any other measurement or calculation
D. Lhuillier
SNAC Blacksburg

10. Normalization of ILL e- data
Dominant error of e- data
Correlated across all energy bins of all isotopes
Relies on well known/checked n-g cross sections (conversion lines).
207Pb(n, g)208Pb
115In(n, g)116mIn
113Cd(n,g)114Cd
D. Lhuillier
SNAC Blacksburg

11. e- n conversion Fission product level b-branch level
Exact conversion requires complete knowledge from fission yield down to b-transition between parent ground (or isomeric)-state and daughter states
b-branch level
Fission product level
Lot of relevant quantities: Z, A, End-points, Jp, nuclear matrix elements, branching ratios, fission yields, life time… but scarce data as E0 increases
D. Lhuillier
SNAC Blacksburg

12. Conversion of reference e- spectra
1- Fit total e- spectrum with a sum of 30 effective b branches determined by iterative method (instead of ~10,000+ real branches)
2- Convert each effective e- branches to ν branches
3- Sum all converted ν branches to get total ν spectrum
K. Schreckenbach et al., Phys. Lett. 99B, 251 (1981).
D. Lhuillier
SNAC Blacksburg

13. ILL n spectra Emitted Interacting
Reference spectra over the last 25 years
D. Lhuillier
SNAC Blacksburg

14. Stack of quadratic sum of 235U errors:
ILL n spectra
Stack of quadratic sum of 235U errors:
Conversion error from envelop of numerical
studies
Correction to Fermi theory in the effective
branches:
What Z? : Mean fit on nuclear data Z=f(E0)
- Effective Coulomb + Weak magn. Correction:
Can we do better ?
D. Lhuillier
SNAC Blacksburg

15. Ab initio Approach
BESTIOLE code: build up database of ~ 800 nuclei and b-branches
MURE evolution code: inventory of fission products
All data from ENSDF (b-branches) and JEFF (fission yields) databases +
Complementary measurements of fission products spectra to tag and replace pandemonium candidates
Unmeasured nuclei described by gross-theory (JENDL database) + our own model based on ENSDF mean fits.
Residues w.r.t. reference ILL e- data
 95+/-5% of the spectrum reproduced but still not meeting required precision
D. Lhuillier
SNAC Blacksburg

16. Ab initio Approach
Stack of quadratic sum of 238U errors
First propagation of all ENSDF quoted errors + correlations.
Demonstrate that uncertainty on shape factors has ≤1.5% impact on total spectrum.
Total error dominated by (rough) estimate of syst of nuclear databases in the 10-20% range.
D. Lhuillier
SNAC Blacksburg

17. Relative change of n spectrum w.r.t. infinite irradiation time
Ab-initio approach
RELATIVE off equilibrium effect
Relative change of n spectrum w.r.t. infinite irradiation time
ILL reference data are photos of b emission after 12-36h irradiation time.
Long-lived isotopes contribute to a significant fraction of the low energy part of the n spectrum and keep accumulating over several weeks.
 Sizeable correction to ILL data in the low E range.
ILL conditions
D. Lhuillier
SNAC Blacksburg

18. 238U reference spectrum
No measurement of total b-spectrum available yet – requires fast n flux
Updated prediction using the ab-initio approach ~10% above previous calculations, with uncertainties in the 10-20% range.
Deviation from Vogel’s spectrum, Phys. Rev. C24, 1543 (1981)
D. Lhuillier
SNAC Blacksburg

19. 238U reference spectrum
Upcoming results from 238U irradiation in fast neutron flux of FRMII reactor – Munchen.
New conversion procedure to be applied on e- data.
See K. Schreckenbach’s talk
D. Lhuillier
SNAC Blacksburg

20. New Mixed Approach Ratio of Prediction/ Reference ILL data
Th. Mueller et al, Phys. Rev. C83, (2011)
Ratio of Prediction/ Reference ILL data
ILL electron data anchor point
Fit of residual: five effective branches are fitted to the remaining 10%
 Suppresses error of full ab initio approach
“true” distribution of all known β-branches describes >90% of ILL e- data  reduces sensitivity to virtual branches approximations
Corrections to Fermi theory applied on all b-branches
D. Lhuillier
SNAC Blacksburg

21. New Mixed Approach
+3% normalization shift with respect to old ν spectrum
Residuals to ILL e-
Residuals to ILL n
Similar result for all isotopes
NB: this +3% shift is above the IBD threshold, the total integral of emitted spectrum
remains unchanged (1 e- and 1 nu emitted per decay)
D. Lhuillier
SNAC Blacksburg

22. Consistency Check
Define “true” e- and n spectra from reduced set of well-known branches from ENSDF nuclei data base. “Perfect knowledge” of both e and n spectra.
Apply exact same OLD conversion procedure to true e- spectrum.
Compare the converted n spectrum to the true one.
Converted spectrum 3%
below true ν spectrum
 ILL analysis leads to a 3% bias w.r.t. the true ν spectrum
D. Lhuillier
SNAC Blacksburg

23. Origin of the 3% shift E <4 MeV
Effective linear correction of ILL data
replaced by correction at b-branch level:
and
Effective correction “à la ILL”
New conversion at branch level
Correct a bias. Assume 100% syst error.
Still the correction at branch level neglects all effects of nuclear structure. Uncertainty could be larger than 100%?
D. Lhuillier
SNAC Blacksburg

24. Origin of the 3% shift E >4 MeV Mean fit of nuclear charge
doesn’t reflect accurately enough the true Z distribution
D. Lhuillier
SNAC Blacksburg

25. Correlation matrix of the 4 isotopes
Error Budget
Stack of quadratic sum of 235U errors
Correlation matrix of the 4 isotopes
D. Lhuillier
SNAC Blacksburg

26. What we learned Mixed approach: Revisit conversion procedure:
ILL conversion procedure have 2 independent biases (~1.5% each in total detected rate):
- Low energy: correction to Fermi theory should be applied at branch level.
- High energy: mean Z fit is not accurate enough.
Combination of all “well known” nuclear data can provide a good proxy for neutrino spectra (~90% of experimental spectrum described)
Revisit conversion procedure:
Apply all above
Complementary approach, minimizing the use of nuclear data
 P. Huber, Phys. Rev. C84, (2011)
D. Lhuillier
SNAC Blacksburg

27. Conversion with virtual branches
Bias
Spectrum conversion problem is mathematically ill-posed
Total spectra built from JEFF (fission yields) and ENSDF (b-spectra) nuclear databases already known to be a good proxy for real reference spectra.
 Allow complete numerical studies to determine the size of potential bias for given number of branch and binning.
D. Lhuillier
SNAC Blacksburg

28. Conversion with virtual branches
Statistical uncertainty
Fluctuate b-spectrum by the variance of the actual data
 Determine the envelope of converted spectra.
D. Lhuillier
SNAC Blacksburg

29. Mean nuclear charge
Demonstrate that proper weighting by fission yield and branching ratio
when fitting the mean nuclear charge cures the conversion bias at high energy.
Quite robust with respect to approx of poorly known nuclei.
D. Lhuillier
SNAC Blacksburg

30. Well Established deviation from ILL spectra
New conv.
New conv. with simple b-shape
Mixed-approach
ILL inversion
Confirms global increase of predicted spectrum
Fixes remaining oscillations of mixed-approach prediction
Extra deviation at high energy from more complete correction to Fermi theory (weak interaction in the finite volume of the parent nucleus).
D. Lhuillier
SNAC Blacksburg

31. Weak Magnetism , assume 100% error
Experimental slope in good agreement for transitions with low ft values
Contribution of large ft’s in fission neutrino spectra?
D. Lhuillier
SNAC Blacksburg

32. Weak Magnetism Preliminary Preliminary
Relative contribution
Preliminary
Preliminary
High log(ft) values have a sizeable contribution to fission n spectra across all E range
(reflects the large contribution of forbidden decays)
No obvious argument can reject a substantially larger dWM contribution or error
Better constraint from analysis of experimental reactor spectra?
D. Lhuillier
SNAC Blacksburg

33. Experimental Constraints on global slope factor
Rovno
evts
Compare shape distortion of dWM with available experimental shape information
Rovno data, courtesy V. Sinev
Bugey 3, Chooz, … data to be added
Upcoming data from Reno, Daya Bay and Double Chooz near detectors.
Relative errors
Uncertainty on E scale ?
D. Lhuillier
SNAC Blacksburg

34. Experimental Constraints on global slope factor
This test: assume predicted and Rovno spectra in perfect agreement and compare the error envelope with the distortion induced by an increasing dWM correction
Position of this crossing point might depend on the conversion procedure (Mixed approach used here)
A 4 times larger dWM would compensate the 3% flux increase.
Preliminary
 Existing+upcoming data might be able to provide constraint at the “reactor anomaly level”.
D. Lhuillier
SNAC Blacksburg

35. <Residue> in [2-8] MeV <Flux ratio> in [2-8] MeV
Conclusions
Normalization
ILL electron data are high quality data
Common systematic error to all converted n spectra
+3% bias of conversion to anti-n spectra:
~1.5% from better nuclear charge distribution
~1.5% from implementation of corrections at the branch level
Current error on total detected rate ~ 2%
But unsolved issues from
weak magnetism correction
Emitted
<Residue> in [2-8] MeV
Detected
<Flux ratio> in [2-8] MeV
235U
+3.0%
+2.5%
239Pu
+3.5%
+3.1%
241Pu
+4.3%
+3.7%
238U
+6.2%
+7.8%
D. Lhuillier
SNAC Blacksburg

36. Conclusions Shape  Compile data:
Improved shape correction and control of conversion error from P. Huber’s recent work.
Large weak magnetism correction would show up in reactor data as a slope.
 Compile data:
Existing (upcoming) spectral data collected at reactors might bring stringent enough constraint on the shape to clarify the situation.
Expected new 238U reference data from FRMII.
Bugey-4 measurement provides an accurate absolute anchor point as well as upcoming near detector data (DC, Reno, Daya Bay)
 No impact on q13 search.
D. Lhuillier
SNAC Blacksburg

37. Outlook Reactor anomaly:
About half of the effect is independent on new spectra normalization:
Mean value of all measurements was already below
Off-eq effects, neutron life-time are well established corrections.
Anomaly analysis should be updated using new P. Huber’s results and experimental shape constraints.
See T. Schwetz’s talk
D. Lhuillier
SNAC Blacksburg

38. Backup Sides
D. Lhuillier
SNAC Blacksburg

39. Pandemonium Measurements of b-decay scheme based on b-g coincidence  
Z N A
Z-1N’
det drops
fast with E +
difficult analysis
of continuum
Under (over)-estimation of the low (high) E part of the spectrum
- Missed g are attributed to GS transition.
 New measurements using total Absorption Gamma Spectrometers (only sensitive to the total energy of the g decay chain)
D. Lhuillier
SNAC Blacksburg

40. Bugey
D. Lhuillier
SNAC Blacksburg

41. Error Budget
235U
239Pu
241Pu
D. Lhuillier
SNAC Blacksburg

42. Error Budget Phys. Rev. C84, 024617(2011) D. Lhuillier
SNAC Blacksburg

43. 4th neutrino hypothesis
Combine all rate measurements, no spectral-shape information
Fit to anti-ne disappearance hypothesis
allowed
Absence of oscillations disfavored at 98.6% C.L.
excluded
area
D. Lhuillier
BLV Gatlinburg

44. 1981 ILL measurement
Reactor at ILL with almost pure 235U, 8.76 m away from compact core
Reanalysis in 1995 by part of the collaboration to account for overestimation of flux at ILL reactor by 10%... Affects the rate only
Large errors, but a striking oscillation pattern is seen by eye ?
1981
D. Lhuillier
BLV Gatlinburg

45. Combined Rate+Shape contours
Including original Bugey-3 & ILL Energy Spectra constraints
D. Lhuillier
BLV Gatlinburg

46. Reactor Rate+Shape + Ga + (MB)
The no-oscillation hypothesis is disfavored at 99.8% CL
D. Lhuillier
BLV Gatlinburg

47. Unique potential to detect new oscillations
A 144Ce Source Experiment
M. Cribier et al., arXiv: , submitted to PRL.
Activity : 50.0 kCi (1.85 PBq)
Mass: 15.7 g
(1.4 kg all Ce isotopes)
Heat released: 373 W
Unique potential to detect new oscillations
D. Lhuillier
BLV Gatlinburg