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Unfolding Beta Decay Using Bayesian Network and Total Absorption Spectroscopy

Explore the use of Bayesian networks and TAS in unfolding beta decay measurements, discussing applications and challenges. Learn about the TAS inverse problem, Bayesian network parameters, inference algorithms, and the potential inclusion of gamma intensities. See how advanced algorithms and tools like genetic inference can improve data analysis in nuclear spectroscopy.

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Unfolding Beta Decay Using Bayesian Network and Total Absorption Spectroscopy

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  1. E. Nácher The bayesian network of Total Absorption Spectroscopy and Machine Learning unfolding algorithms E. Nácher, J.L. Taín ... for the Gamma ray & neustron spectroscopy group Instituto de Física Corpuscular, CSIC - UV

  2. E. Nácher Outlook of the talk • Introduction: beta decay measurements • The TAS inverse problem • The TAS bayesian network • Summary and Conclusions

  3. E. Nácher Beta decay measurements • b-decay is an important source of nuclear structure information. • From direct measurements one can obtain half-lives, energy levels, beta intensity distributions (b feeding)…  Applications: decayheat in nuc. tech., neutrino spectrafor non-proliferation Parentnucleus • Measuring the b feeding distribution is far from being trivial!! T1/2 E4 b g E3 Qb E2 g g E1 g Daughternucleus

  4. E. Nácher Beta decay measurements Medium mass and heavy nuclei: large level density at high energy. b+ AZ real feeding • Very fragmented feeding distr. andg-deexcitation pattern. apparentfeeding g • HPGe arrays fail to detect systematically the upper part of the g-cascade resulting in a wrong feeding and B(GT) distr. AZ-1 HPGe HPGe g1’ g1 g2

  5. E. Nácher

  6. 27/5/19 E. Nácher 7 Total Absorption Spectroscopy (TAS) bfeeding E2 NaI g2 E1 g1 g1 g2 bfeeding N E2 E Ideal case

  7. N X-ray detector EC E2 E N Positron detector b+ E2 E 2 photons (511 keV) back to back Unfolding algorithm (EM) Ib E2 E 27/5/19 E. Nácher 8 Total Absorption Spectroscopy (TAS) NaI g1 g2 Real case

  8. E. Nácher The TAS Inverse Problem • The number of counts detected in channel j relates to the beta feeding to level ithrough the linear equation: fi : Feeding to energy level “i” dj : Counts in channel“j”of thespectrum Rij : Response Function (matrix) to thedecay

  9. E. Nácher The TAS Inverse Problem No way to measure Rij!! • Stat. Model for the lev. dens. & br’s • Geant4 for the detector response • The number of counts detected in channel j relates to the beta feeding to level ithrough the linear equation: • We have used the EM algorithm so far to unfold the data: Calculation of Rij from individual g’s and b’s: D. Cano, J.L. Taín, NIM A430 (1999) 333 Study of the EM and others applied to TAS: J.L. Taín, D. Cano, NIM A571 (2007) 728

  10. E. Nácher The TAS Bayesian Network f1 fn f2 … parameters to estimate: ‘unknown causes’ joint probability distribution (JPD): Rij d1 d2 dm … observables: ‘known effects’ direct probability: di = SRijfj Genetic (score & search) inverse probability: inference  learning BN Exp-Max, Genetic (score & search), Markov Chain MC…

  11. E. Nácher The TAS Bayesian Network f1 fn br1 br2 f2 brk … … d1 d2 dm I1 I2 Il … … Mq M1 M2 … • add new observables: gamma intensities • add the br’sto the network…, • not so easy, theyaffectdirectlytheRij dynamic BN • - addthemeasuredmultiplicities

  12. E. Nácher Summary & Conclusions • TheTAS inverseproblemcan be wellrepresentedwith a BayesianNetwork, and the usual inferencealgorithms of thesenetworks can be appliedto solveit. • So farthe EM algorithm has beenused, butwe are implementing a geneticalgorithmnowforalpha (simpler) spectroscopy and soonforTAS. • Gamma intensities and multiplicitiesmust be part of theanalysis, theymust be added to thespace of observables (already done withtheintensities). Thisdoesnotincreasethedimensionorcomplexityof theproblem "toomuch". • Withgreatercalculationpower (Artemisa) one can considerintroducingthebranching ratios as part of theproblem and thesolution. Evensimulate new MC response functions in eachiteration ?? Thisdoesincreasethedimension and complexityof theproblem "considerably".

  13. E. Nácher Thanks for your attention!!

  14. E. Nácher The Response Function

  15. E. Nácher The Response Function b-decay of 24Na: test bench for our simulations

  16. E. Nácher Study case: 186Hg decay Statistical model: -Level densities: Goriely et al. Phys. Rev. C, 78 (2008) HFB + combinatorial (RIPL3) 320 positive parity levels 1-3 MeV -Gamma branchings: Axel-Brink hypothesis E1, M1 & E2 from giant resonances ? 0+ ENSDF  G4RadioactiveDecay Event generator including the ‘unknown’ part: D. Jordánet al., NIM A828 (2016) 52

  17. E. Nácher Some other TAS results • Reactor decay heat and related issues • A. Algora, D. Jordan et al, Phys. Rev. Lett. 105 (2010) 202501

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