1. 19 March 2009Thomas Mueller - Workshop AAP09 1 Spectral modeling of reactor antineutrino Thomas Mueller – CEA Saclay Irfu/SPhN

2. Thomas Mueller - Workshop AAP092 19 March 2009 Purpose of these simulations Provide the reference antineutrino energy spectrum emitted by reactor with:  Control of the systematics  Gain in sensitivity Oscillation analysis: Double Chooz, Daya Bay Feasibility of nuclear reactor monitoring:  Power measurement  Non-proliferation studies (IEAE) The Nucifer project: CEA-DSM/Irfu-DAM & IN2P3  see M. Fallot’s talk

3. Thomas Mueller - Workshop AAP093 19 March 2009 Computation of reactor antineutrino spectrum fissions / s ν / fissions P th : total thermal power α i : fraction of power per fuel assembly f i k : fraction of fissions per fissile isotope and fuel assembly N ν k : neutrino E spectrum per fission for isotope « k » Reactor data Relevant degree of freedom is fuel assembly (~200 in one core) of 17x17 fuel rods Subject of this talk

4. Thomas Mueller - Workshop AAP094 19 March 2009 Antineutrino energy spectra references Information on the antineutrino flux from 235 U, 239 Pu & 241 Pu obtained through conversion of experimentally measured β spectra:  K. Schreckenbach et al., Phys. Lett. B160, 325 (1985) [ 235 U]  A. A. Hahn et al., Phys. Lett. B218, 365 (1989) [ 239 Pu & 241 Pu] No measurements for 238 U (11% of total ν rate) but theoretical calculations:  P. Vogel et al., Phys Rev C24, 1543 (1981)  H. V. Klapdor and J. Metzinger, Phys. Lett. B112, 22 (1982) Measurements of 238 U β spectrum is ongoing by K. Schreckenbach & N. Haag (PhD thesis) @ München (Germany)

5. Thomas Mueller - Workshop AAP095 19 March 2009 From Schreckenbach’s measured β spectra… β spectra from fission products in thermal-neutron induced fission of 235 U, 239 Pu and 241 Pu have been measured on line @ ILL research reactor using electromagnetic spectrometer BILL Very accurate electron reference data from 2 to 8 MeV:  Negligible statistical error → less than 1% up to 7 MeV  Negligible calibration error → momentum resolution of Δp/p ~ 3×10 -4  Normalization error → ~ 1.8%

6. Thomas Mueller - Workshop AAP096 19 March 2009 … to converted ν spectra For each measured β spectrum, neutrino was obtained using a conversion procedure:  Fit of the β spectrum with 30 virtual β branches  Conversion of these branches into neutrino branches through energy conservation  Sum of the 30 neutrino branches to obtain the final spectrum The conversion procedure induces a 1.8 to 3% additional error « Accurate conversion can be obtained only if […] the optimum nuclear charge Z is independently known as a function of the endpoint energy E 0 » P. Vogel, Phys. Rev. C76 (2007)

7. Thomas Mueller - Workshop AAP097 19 March 2009 Microscopic approach Fission yields JEFF3.1 / MURE Fission products ENSDF + BESTIOLE ex: branch of 13 B Microscopic approach: study of systematic effects / estimation & propagation of all sources of errors

8. Thomas Mueller - Workshop AAP098 19 March 2009 Comparison with Schreckenbach No free parameter ! Good global agreement between simulation and experiment Same mean energy Example of 235 U:

9. Thomas Mueller - Workshop AAP099 19 March 2009 Relative comparison Pandemonium effect → TAGS measurements (Greenwood, Tengblad) Very short-lived high-Q β unknown nuclei → GS to GS approximation, gross-theory, toy-models  we cannot control residues better than few % R = (S sim -S exp ) / S exp

10. Thomas Mueller - Workshop AAP0910 19 March 2009 Revisiting Schreckenbach’s conversion procedure (1) Starting point: all experimental data i.e. ENSDF database + TAGS measurement (blue curve) 95% of the experimental spectrum is reproduced The remaining part is fitted using virtual branches  Improvement from more physics input (~10000 β branches) Fit with 4 virtual β branches

11. Thomas Mueller - Workshop AAP0911 19 March 2009 Correction beyond Fermi theory of β decay  QED corrections  Weak magnetism  Higher order Coulomb Microscopic approach: more physics inputs e.g. true endpoint E 0 & nuclear charge distribution Z  Better implementation of the corrections Revisiting Schreckenbach’s conversion procedure (2) effective corrections

12. Thomas Mueller - Workshop AAP0912 19 March 2009 Consequences on neutrino residues Systematic +2% bias below 6 MeV Important for oscillation analysis Important for flux to power comparison Oscillation range

13. Thomas Mueller - Workshop AAP0913 19 March 2009 Principle of the crosschecks Several methods have been tested to confirm this + 2% bias The goal is to fit Schreckenbach electron data by « tweaking » database’s parameters and to check the consequences on neutrino residues 3 independent methods: 1)BR → BR × ( 1 + α i ) 2)E 0 → E 0 × ( 1 - αE 0 + βE 0 2 ) 3)BR modifications + GS constraints Requirements:  Reduce set of parameters  Only few % modification in physical distributions

14. Thomas Mueller - Workshop AAP0914 19 March 2009 Comparison of the different methods Can achieve < 1% electron residues with few % modifications 4 independent methods are stable @ level of Schreckenbach’s error bars + 2% bias in neutrino residues is confirmed !

15. Thomas Mueller - Workshop AAP0915 19 March 2009 Conclusions Preliminary error budget  Schreckenbach normalization ~ 1.8%  Conversion procedure ~ 1%  Corrections to Fermi theory of β decay < 0.25% / MeV Systematic bias of + 2% below 6 MeV Next:  Final systematics studies  Off-equilibrium effects

16. Thomas Mueller - Workshop AAP0916 19 March 2009 Back up: The pandemonium effect Overestimation of the high energy part of the spectrum due to experimental technique - detection in coincidence of an electron and a photon Solution: TAGS measurements with a 4π-detector

17. Thomas Mueller - Workshop AAP0917 19 March 2009 Back up: Results for 239 Pu