1. Nuclear Reaction Data assessing the best knowledge Helmut LEEB Working Group on Nuclear Physics and Nuclear Astrophysics Atominstitut, TU Wien, Austria H. Leeb October 7, 2016 1

2. Research Topics 2 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006  Bayesian Evaluation Technique - development of evaluation methods including model defects - general considerations on Peelle‘s Pertinent Puzzle - formulation of evaluation technique for differential data - novel formulation of General Least Square Technique for large number of observables - development of general Bayesian evaluation code GENEUS  Nuclear Reaction Theory and Calculations - semimicroscopic  -nucleus optical potentials for astrophysics - adaptive R-matrix method for light nuclei - breakup reactions at high energy - development of reaction code GECCCOS  Neutron cross section measurements at n_TOF@CERN - (n,  ) and (n,f) cross section measurements (nuclear astrophysics, nuclear technology) - neutron reaction measurements involving charged particles (n,p), (n,  ) - development of diamond detectors  Specific Topics in Quantum Mechanics - ultracold neutrons in the gravitational field - supersymmetric quantum mechanics - phase determination in neutron reflectivity

3. Bayesian Evaluation Technique 3 Evaluation Process Model DataExperimental Data Evaluated Data H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

4. Bayesian Statistics 4 Bayes Theorem (1761): aposteriori distribution distribution of para- meters taking a-priori and experimental info Evidence normalisation likelihood Experimental information apriori distribution provides the apriori knowledge, e.g. the nuclear model H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

5. Linearized Bayesian Update 5 Assumption of normal distributions for experimental uncertainties, model parameters likelihood assumed Sensitivity Matrix: H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

6. General Problem: Underestimate of error bands Example n- 181 Ta: total cross section 6 Evaluation of total n- 181 Ta cross section only  The posterior is syste- matically lower  Uncertainties too small H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

7. Novel Evaluation Concept: Statistically consistent Treatment of Model Defects 7 Standard Evaluation: Experiment vector Model vector Uncertainty vector of experiment Model defect Extended Evaluation: Concept of non-perfect model can be applied in many fields of physics, e.g. optimizing Skyrme forces, etc. PhD thesis of Georg Schnabel (TU Wien, June 2015) described by Gaussian process H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

8. Evaluation of total n- 181 Ta cross section 8 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

9. Differential elastic cross sections: without model defects 9  (n,el) at 8.03 MeV – without model defects H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

10. Differential elastic cross sections: with model defects 10  (n,el) at 8.03 MeV – with model defects H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

11. Modified Update Scheme 11 Basic Idea: The observables obtained by model calculations are not mutually independent; they are generated of a set of parameters p of dimension K << L. It is sufficient to generate mean values and covariances only from N model calculations with K < N << L with parameters sets {p i, i=1,…,N}. G. Schnabel, H.L, Nucl. Data Sheets 123, 196 (2015) Each vector summarizes the L observables evaluated by nuclear models with parameter set p k. using vector of dimension M Important: this procedure avoids the explicit calculation of the prior covariance matrix H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

12. Generalized Modified GLS for large Scale Evaluation 12 Starting point: Combine all sampling vectors G. Schnabel, H.L., submitted W 0 is an N x N matrix Recursion procedure: with The N x N matrix W i and the N-dimensional vector to- gether with the L-dimensional vector and L x N matrix U allows the full updating. The prior matrix A 0 must not be calculated. H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

13. Description of Data – Prior Determination 13 Intermediate energies: Statistical model calculations (GNASH, EMPIRE, TALYS) optical potentials, level densities, precompoud factors, fission barrier, … Resonance regime: R-matrix (SAMMY, REFIT, CONRAD, …; EDA,AZURE,AMUR,..) pole and widths parameter, matching radius, … R-matrix Statistical model Coupled-channel calc Preequilibrium model fission model …. Observables cross sections (integral,differential), spectra, fission yields, … A common evaluation must be on the basis of observables H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

14. Adaptive R-Matrix Approach 14 GOAL: Extension of the Bayesian evaluation method to light nuclei with emphasis on an almost continuous transition between resonance regime and energies beyond. Numerical implementation and inclusion into GENEUS. Resonance regime R-matrix calculations SAMMY, CONRAD, REFIT Basic R-matrix code EDA E statistical model calculations TALYS, EMPIRE, GNASH strongly overlapping resonances TALYS R-Matrix regime Concept of Evaluation Approach capability of large scale calculations required E F F D O C – 1 2 8 7 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

15. 8. Application Standard R-matrix 15 Problem with Matching Radius: Frequently R-matrix fits, especially for light nuclei, are performed with un- physically small matching radius With incompleteness in pole terms, the matching radius becomes a convergence parameter Thus association of the pole parameters with physics of resonances is problematic E F F D O C – 1 2 8 7  tot [mbarn] Energy [MeV] H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

16. 16 Coarse manual fit: Match.Radius a=7 fm Background plus 30 pole terms partial waves J  1/2 +, 1/2 -, 3/2 +, 3/2 -, 5/2 +, 5/2 -, 7/2 +, 7/2 -, 9/2 +, 9/2 - sufficient up to 15 MeV E F F D O C – 1 2 8 7 8. Application Actually used Background + Pole Terms  tot [mbarn] Energy [MeV] H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

17. n_TOF@CERN: 2 nd Experimental Area 17 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006 The 2 nd experimental area EAR2 is particularly well suited for (n,f) measurements (n,f) cross sections of actinides, e.g. ang. Distributions PPACS developed by IPN

18. Development of a diamod CVD detector for (n,  ) measurements 18 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006 Ch. Weiß, et al., NIM A 732 (2013) 190

19. Experiments with strong involvement of the Austrian Team 19 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006 Simultaneous measurement of 233 U(n,  ) and 233 U(n,f) PhD thesis of Michael Bacak The Austrian n_TOF Team: Atominstitut: E. Jericha, E. Griesmayer, H. Leeb, M. Bacak Cividec: E. Griesmayer, Ch. Weiß*, P. Kavrigin* Univ. Wien: A. Pavlik The (n,  ) cross section measurement for light isotopes gas targets: 16 O, 10 B, 12 C, 14 N, 19 F Team TU Wien Students of TU Wien

20. International Research Projects 20 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006  ANDES, Euratom Project 6 th FWP  CHANDA, Euratom Project 7 th FWP  ENSAR European Infrastructure Project  ESF Eurocores Project EXNUC  F4E Project on Nuclear Data Files  F4E Framework Partnership Agreement – Specific Grants 1+2  Matching Grants, Austrian Academy of Sciences – Fusion Research  Measurement of (n,  ) cross sections of light gaseous targets at n_TOF application at the Austrian Science Foundation in preparation  Nuclear Data Project at Eurofusion in preparation for 2017

21. Master and PhD students since 2010 21 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006 Master Students Stefan Gundacker Georg Schnabel Brigitte Hasenberger Thomas Srdinko Bendikt Raab (current) PhD Students Denise Neudecker (staff member, Los Alamos) Georg Schnabel (PostDoc, CEA Saclay) Verena Kleinrath (PostDoc, Los Alamos) Thomas Srdinko (current) Michael Bacak (current)

22. Outlook 22 H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006 Physics Further development of the adaptive R-matrix method for light nuclei R-matrix technique for 3-body exit channels, e.g. (n,np) unitary R-matrix formulation for capture channels Development of Techniques for the calculation of breakup reactions reformulation of LIT method for breakup channels Code Developments Further extension of the reaction code GECCCOS implementing further reaction mechanisms (transfer reactions) generate a more user-friendly interface Completion of the general evaluation code system GENEUS simultaneous conistent evaluation of isotope groups and reactions implementation of recent developments to generate a data base system

23. 23 Thank you for your attention H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

24. Gaussian Processes 24 The a-priori knowledge on model error:  idea about quality  idea about structure Definition of Gaussian Processes: Consider space F of function f: R d  R.  (.) assigns to each f a probability density for all f in F.  (.) induces a Gaussian process if for any set of {x i }, i=1,…,N the associated function values {f(x i )} i=1,…,N follow a multivariate normal distribution H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

25. Gaussian Processes: Example 25 Example: squared exponential covariance function  =20% and = 50 MeV  =10% and = 20 MeV H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

26. Marginal Likelihood Maximization 26 Prior covariance matrix of the model defect vector is given by the covariance function k(E,E‘) of the Gaussian process. Marginal likelihood: Maximizing the marginal likelihood H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

27. 27 Motivation Nuclear Data Files generated by various evaluation techniques should provide consistent and continuous sets of reaction data including integrated and differential cross section data, spectra, isotope production rates, etc. Demands from the user community: Extension of the neutron energy range from 20 MeV to 200 MeV Inclusion of uncertainty information – covariance matrices Generation of evaluated libraries for several light projectiles ( ,p,d,  ) Consequences triggered by these demands: Extension to higher energies only via use of nuclear models to compensate for lack of data Techniques needed to combine experimental and theoretical knowledge Development of techniques providing reliable uncertainty estimates H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006

28. Origin of the Problem n- 181 Ta total cross section 28 T HE O RIGIN OF THE P ROBLEM The prior covariance matrix contains the features of the original model solutions which are not independent from energy have vanishing probability Aposteriori uncertainties too small prior covariance matrix eigenvalues eigenvectors H. Leeb Nuclear Reaction Data - assessing the best knowledge NuPECC Meeting Vienna,, 7.10.2006