Checking the resolved resonance region in EXFOR database

Transcription

1 Checking the reslved resnance regin in EXFOR database Gttfried Bertn Sciété de Calcul Mathématique (SCM) Oscar Cabells OECD/NEA Data Bank JEFF Meetings - Sessin JEFF Experiments Nvember 0-4, 017 Bulgne-Billancurt, France

2 1. Presentatin f the SCM activities Mathematical mdelling cmpany, established in 1995; Creates mathematical tls fr decisin help; Specialized in rbust mdelling; Main branches f activities: energy, envirnment, health, transprtatin, scientific assistance t large prjects Our wrk in nuclear sectr: Malfunctins in sensr netwrks; Outlier detectin, recnstructing missing infrmatin; Lking fr znes with highest risk; Evaluating the perfrmance f a netwrk f sensrs (e.g TELERAY); Taking int accunt the uncertainties in cmputatinal cdes.

3 . Objectives Crss-checking the experimental data (EXFOR) with the evaluated nes Prviding a list f suspicius data Ranking the entries t see which data are ptentially errneus and which are reliable Applying the wrk n mst nuclear data: Istpes and natural elements Threshld reactins, ismeric transitins, angular distributins, etc. Neutrn reactins. Taking the uncertainties f bth EXFOR and ENDF int accunt

4 3. Methdlgy in 016 Cmpute the distance between a curve (PENDF) and a set f pints (EXFOR) The distance is the interval between tw 95% vertical cnfidence intervals fr EXFOR and ENDF Cmpute the min distance ver the discretized hrizntal cnfidence interval Fig. 1. General principle f the methd Definitin f a Ranking value t identify the ptential prblems in EXFOR r ENDF: distance rati = max σ EXFOR, σ ENDF

5 4. Implementatin 1) Finding the right scale fr abscissa and discretizing it in 50 intervals ) Cnstructing the resnance indicatr as the relative variance 3) Cmputing the distance ratis fr each intervals: In a n-resnance interval: average f the pintwise distances In a resnance interval: difference between integral f EXFOR and ENDF

6 4. Implementatin 4) Averaging the ratis f the 50 intervals and cmputing the final ranking in A, B,, E 5) Cmpute the rank f the wrst single pint t detect single utliers (Fig. ) Fig.. Single pint aberrant in Carbn natural element

7 4. Implementatin This methd has limitatins in the resnance intervals Effect f reslutin bradening in regin f high variability: the crss-sectin measured is an averaging f the theretical crss-sectins at different energies

8 5. Results (016)

9 6. SCM s Methdlgy applied in RRR (017) Recver the reslutin functin in rder t: Cmpare PENDF and EXFOR in resnance regin Assess the shape f the reslutin functin (fr n_tof and GELINA entries) Verify if the reslutin changes with energy Detect islated sets f pints and utliers: impssibility t find a reslutin functin, abnrmally high reslutin, etc. Find missing peak in ENDF (r cntaminatin in EXFOR) Check nrmalizatin

10 6. SCM s Methdlgy applied in RRR (017) Discretize the energy dmain s that there are 50 resnance peaks in each energy bin Fr each energy bin: Checking Nrmalizatin by cmputing the rati between integral f EXFOR and PENDF Calculate the reslutin functin: the EXFOR curve is a mving average f the ENDF curve: find the cefficients x j f this averaging

11 6. SCM s Methdlgy applied in RRR (017) Discretize the energy dmain s that there are 50 resnance peaks in each energy bin Fr each energy bin: Crss-sectin (b) ENDF b a x a x a x 1 1,1 1 1, 1,3 3 b a x a x a x,1 1,,3 3 Energy (ev) x x x 1 3???

12 6. SCM s Methdlgy applied in RRR (017) Discretize the energy dmain s that there are 50 resnance peaks in each energy bin Fr each energy bin: Calculate the reslutin ΔE: hw spread is the reslutin functin is Check this value against resnance energy ΔE/E Is it an abnrmally high value? Des this rati change fr the different energy bins?

13 7. Finding a reslutin functin T find the cefficients x i, slving the system: n x jai, j bi, i 1,..., N j 0, 1,..., j 1 x j n b i is the crss-sectin f EXFOR a i,j crss-sectin f ENDF at energies arund EXFOR energy n the number f cefficients, N the number f EXFOR measures

14 7. Finding a reslutin functin Slving using the least squares methd T take int accunt uncertainties, use prbabilistic methd: Archimedes methd Allws t calculate fr each cefficient the expectatin (blue), and lwer/upper bunds (black) ΔE Calculate the uncertainty upn the reslutin t btain ΔE ± δ

15 7. Finding a reslutin functin Archimedes methd: 1. Generating a candidate reslutin functin, i.e a set f cefficients x j. At each EXFOR energy i Applying the bradening n the PENDF curve using the reslutin functin x j Cmparing this PENDF value t the EXFOR crss-sectin b i : define prbability p i t be arund b i using the uncertainty n each measure 3. Calculating the weight f the candidate slutin as Φ = p 1 p p N 4. Nrmalizing by the sum f the weights when generating all the slutins

16 7. Finding a reslutin functin Each candidate slutin has a prbability assciated Fr each candidate we can calculate the reslutin ΔE Eventually, we btain a prbability law upn the reslutin, and each cefficient x j It wrks als fr nn-linear systems and any kind f uncertainty (nt nly Gaussian)

17 7. Finding a reslutin functin Hw t generate the candidates slutins? Numerical example: b 1 = 10b with standard deviatin b, 95% prbability t be in [4; 16] b = 1b with standard deviatin 1b 95% prbability t be in [9; 15] We btain a system f inequalities: Crss-sectin (b) ENDF 4 9.1x 9.5x 10.x x 9.4x 11.3x Energy (ev)

18 7. Finding a reslutin functin These inequalities are the intersectin f half-spaces, and frm a cnvex space 4 9.1x 9.5x 10.x x 9.4x 11.3x We generate nly candidate slutins in this cnvex subspace by perfrming a randm walk in it Checking existence f a slutin t this system abve using simplex algrithm. N slutin culd mean: t small EXFOR uncertainties with respect t the distance with ENDF islated set f pints

19 8. Results Example f reslutin functin btained fr n_tof data (figure at right) Green line: ENDF Pink line: Bradened ENDF using cefficients n figure at right Blue: EXFOR Usually small reslutin (0.8% apprximately in the example abve)

20 8. Results Added cnstraint n the shape (cnvlutin f expnential and multiple gaussians as used in SAMMY cde) Adding such cnstraint ften leads t pr match between bradened ENDF and EXFOR

21 9. Data Data prcessed at rm temperature (Dppler bradening) Applied t large entries (TOF measurements frm GELINA and CERN) Reslutin functin defined n an interval energy f 50% arund the resnance energy Hrizntal shift between ENDF and EXFOR: recenter afterwards the reslutin functin btained t align ENDF t EXFOR.

22 10. Find missing peak Case 1: cntaminatin frm anther istpe in EXFOR

23 10. Find missing peak Case 1: cntaminatin frm anther istpe in EXFOR

24 10. Find missing peak Case : missing resnance in ENDF Methd t detect it: Bradening f each ENDF using the RF Fr each lcal maximum in EXFOR, calculate the distance EXFOR/ENDF If large distance, cunt the number f resnance peaks arund this peak fr each evaluatr If there is disagreement between the evaluatrs n the number f peaks: reprt JEFF? Peak fr ENDF but nt fr JEFF

25 10. Find missing peak Case : missing resnance in ENDF One mre example ENDF (OK) TENDL (??)

26 11. Find prblem in nrmalizatin First case: integrals dn t match, n ambiguity Smething wrng independently f reslutin Secnd case: is the vertical shift due t nrmalizatin prblem r reslutin bradening? Can we say it visually? N, t verify: check the existence f a reslutin functin having sum equal t ne? yes: the shift is due t reslutin effect n: the shift is due t a nrmalizatin prblem

27 1. Change in reslutin Is there a change in reslutin ΔE at a certain energy?

28 1. Change in reslutin Energy <0eV (green line) Energy >0eV

29 1. Change in reslutin Take int accunt relative reslutin ΔE/E The rati ΔE/E remains the same at left and right Energy 5 50 ev Energy ev

30 1. Change in reslutin Plt fr each energy bin, the reslutin btained. Fr tw different entries: Entry #1: N change in reslutin Entry #: Change in reslutin at 1 MeV

31 13. Find utliers After crrectin fr reslutin bradening, pintwise cmparisn allws t detect utliers in resnance regin (n_tof data): subentry 33.

32 13. Find utliers Check als situatins f strange reslutin functin r impssible t calculate: Generally, decreasing when away frm the center f the distributin

33 14. Other remark Is there a physical cnstraint n the reslutin functin that shuld be added? Why shuld be Gaussian? Different reslutin functins can lead t the same result (pink and red)

34 15. Cnclusin This wrk allwed t cmpare the ENDF and EXFOR in the reslved resnance zne Checking missing peak in ENDF Detecting islated sets f pints and ptential utliers Assessing the reslutin functin fr n_tof and GELINA data per energy bin and hw the reslutin changes with energy