Update of uncertainty file in the EAF project J. Kopecky 1 and R.A. Forrest 2 1 JUKO Research, the Netherlands 2 EURATOM/UKAEA Association, Culham, UK FENDL Vienna

Scope of the presentation ● History of EAF uncertainties ● EAF-2007 status ● Current actions and updates for EAF-2009 ● Conclusions

History of EAF uncertainties ● EAF-2 (1991) - Use of error factors derived from 14.5 MeV systematic to assess the overall uncertainty for most of the reactions. These factors indicate the accuracy estimate only.

History of EAF uncertainties (cont.) ● EAF-3 (1992) – Uncertainty file (in the ENDF-6 MF = 33 format) for all reactions in a 1 group (threshold reactions [E th –20MeV]) and 2 groups (non-threshold reactions [ eV –EH–20MeV]) structure. The uncertainty values adopted correspond to the error factor f = 1 + , where  is the relative error (  2 is actually stored in the file) in the cross section . In this case the best estimate of the cross section uncertainty is  /f <  <  f.

MF33 from EAF-3

Error factors (EAF-3) Used for all reactions

History of EAF uncertainties (cont.) ● EAF-4 (1995) ● The uncertainty file contained more information for (n,  ) and (n,f) reactions. These were given in 3 groups (10 -5 eV – EL – EH– 20MeV]) rather than the 2 groups used previously.  (th) and I  are used for respective energy groups as an experimental information. ● Estimates for data with no experimental information :

History of EAF uncertainties (cont.) ● Experimental uncertainties for threshold reactions (EAF data set of recommended single  (14.5 MeV) data points) were used to replace the generic values adopted from 14.5 MeV systematic. This 14.5 MeV experimental variance is used for the entire energy range of the excitation function, and because no information on uncertainties at other energies has been used, an uncertainty value of  = 3  exp has been adopted if  < 0.25.

History of EAF uncertainties (cont.) ● EAF-97 (1997) - New treatment of uncertainties for split reactions has been adopted. If experimental values of partial cross sections are known their uncertainties are adopted. However, in general for uncertainties of cross sections to ground and isomeric states an uncertainty factor of the branching ration (f b ) of 1.3 has been adopted when the branching is derived from BR systematic. ● By definition  m = b  and  g = (1-b) . Thus the uncertainty in  m is given by and  =f-1 and  b=f b -1. Thus.

History of EAF uncertainties (cont.) ● EAF-99 (1999) - EAF-2001 (2001) - EAF-2003 (2003) - The corresponding uncertainty files for reactions supported with experimental data includes visual estimates based on all EXFOR data points covering broader energy regions. Three energy groups have been applied also for non- threshold (n,p) and (n,  ) reactions with LEA treatment below EH.

Error factors (EAF-97 – EAF-2003) Used for all reactions with no experimental support

History of EAF uncertainties (cont.) ● EAF-2005 – The upper energy extended to 60 MeV by adding a new energy group (20 – 60 MeV). The new error factors have been adopted using the assumption of f 20 MeV. ● Threshold reactions: E th 20MeV 60MeV E th 20MeV 60MeV

Uncertainties – non-threshold reactions EL EH EL 20MeV 60MeV  (th)  I  or 0.5  exp  or 0.5

EAF-2007 status (exp. data) ● Error factors based on experimental data -The experimental variance is adopted from both EXFOR as well the EAF internal data base and is used for the entire energy range of the excitation function. This uncertainty has been estimated visually from the data scatter around the library excitation curve from cross section plots or from growing data base of experimental integral validations.

EAF-2007 status (no exp.) ● Error factors with no experimental data (based on  (14.5 MeV) systematic - These factors quantify how well the systematic of  (14.5 MeV) fits the experimental data. They are used in the generation of the uncertainty file if no experimental data are available and the adopted library data agree with  (14.5 MeV). They are assumed to be representative for the whole energy range above E th and the conservative values are applied. ● Error factors f without systematic - If no cross section systematic is available, the results of graphical treatment of calculations or adopted data (e.g. SACS analysis) and the educated conservative guess of the accuracy of the calculation (upper limit) are applied. ● Error factors f > 20 MeV - If no experimental data are available to estimate f, the same uncertainty is adopted as the uncertainty of the energy group just below 20 MeV.

Error factors EAF-2007 Used for all reactions with no experimental support

References prior EAF-2009 ● J Kopecky, D Nierop and RA Forrest, Uncertainties in the european activation file EAF-3.1, ECN-C— (March 1994). ● RA Forrest, J Kopecky, Statistical analysis of cross sections, Fusion Eng. and Design, 82(2007) 73. ● RA Forrest, J Kopecky, AJ Koning, Detailed analysis of (n,p) and (n,  ) reactions in the EAF-2007 and TALYS-generated libraries, Fusion Eng. and Design, 83(2007) 614. ● RA Forrest, J Kopecky, AJ Koning, Revisions and improvements of neutron capture cross sections for EAF-2009 and validation of TALYS calculations, UKAEA FUS 546 (March 2008). ● RA Forrest et al., Validation of EASY-2007 using integral experiments, UKAEA FUS 547 (April 2008). ● Graphical comparison of all EAF-2007 Score =1-6 reactions, corresponding TALYS calculations (if TALYS not adopted) with experimental data (J Kopecky – private information).

Actions and updates for EAF-2009 Standard treatment ● Complete revision of  (exp) values is in progress. 1. Threshold reactions. Several new rules shall be applied and new error factors proposed based on TALYS validations, SACS analysis and studies and comparisons against experimental data. ► If  (Eth-20 MeV) < 0.1 the value has been increased to 0.1. ► If  (Eth-20 MeV) < 0.2 the value of  ( MeV) is specially treated for excitation curves with dominant cross section part above 20 MeV. Further the starting energy of the last energy group (20 MeV) has been made free, in order to better cover the the shape of the excitation curve. The use of C/E (integral data) for cross section improvements is added. ► The uncertainty visual estimate shall be applied to account for the energy range of experimental data in the shape of calculated excitation curves (see next slide). ► Details for threshold reactions are described together with relevant plots in EAF-Doc-48 to be released in December 2008.

Uncertainty ranges 1,2 – weak arguments 3,4,(5) – strong arguments for  

Uncertainty ranges - a dream situation -

Uncertainty ranges Combination of sources EXP  max SACS TALYS predictive power SACS E max  max  1/2x TALYS validation

TALYS predictive power for major threshold reactions (references) ● Since EAF-2007 includes 65,565 reactions and only about 1750 are supported by experimental information, the test of predictive power with TALYS calculated data is of great importance. For validation of TALYS calculations see: ● RA Forrest, J Kopecky, Statistical analysis of cross sections, Fusion Eng. and Design, 82(2007) 73. ● RA Forrest, J Kopecky, AJ Koning, Detailed analysis of (n,p) and (n,  ) reactions in the EAF-2007 and TALYS-generated libraries, Fusion Eng. and Design, 83(2007) 614. ● RA Forrest, J Kopecky, AJ Koning, Revisions and improvements of neutron capture cross sections for EAF and validation of TALYS calculations, UKAEA FUS 546 (March 2008). ● J Kopecky, TALYS validation plots, private communication.

TALYS predictive power for major threshold reactions (cont.) ● Neutron emission channels: For (n,n′), (n,xn), (n,n′p), (n,n′  ) reactions the shape of calculated cross sections is in good agreement with the trend of experimental data and the shape of the excitation curves is considered good. ● Charge particle emission channels: ► A similar conclusion was made for (n,p), (n,d), (n,  ) reactions with two specific cases to look at manually. The FWHM of (n,p) reaction in the transitional range with 0.08 < s < 0.12 and  max of (n,  ) reaction to check with SACS analysis. ► (n,t) data are now in a good agreement. ► (n,h), (n,2p) reactions are the experimental data (especially activation measurements) probably often overestimated due to the interference of competing reactions from elemental or isotopic impurities.

SACS  ½ (n,p) supported by EXFOR data Ca-43 Ti-47 Co-59 Zn-66 Fe-58 Ni-62 Cu-65 Zn-67, Pd-102,Sn-112 Transition range

(n,  ) EAF-2009 (preliminary) Ir-194m

(n,t) agreement

(n,He-3) problem

Actions and updates for EAF-2009 (cont.) Standard treatment ► Details for threshold reactions are described together with relevant plots in EAF-Doc-48 to be released in December Non-threshold reactions. Complete revision of  (exp) values shall be performed again with improved rules and new error factors based on TALYS validations, SACS analysis and agreements with experimental data: ► Details will be described together with relevant plots in EAF- Doc-49 to be released by April 1, Uncertainties with TALYS. The uncertainties for a limited number of important targets will be obtained by applying a Monte Carlo method to the TALYS nuclear reaction code.

Error factors (EAF-2009) – in progress * - good fit with experimental data & - shape problems close to the threshold # - shape problem > 20 MeV for (n,p) and  (max) for (n,  )

TALYS Monte Carlo calculation (A. Koning) ● The uncertainties are obtained by applying a Monte Carlo method on the TALYS nuclear reaction code. In the fast neutron range, a number of model parameters (between 20 and 30) are varied. These parameters concern: ► the optical model ► the level density model ► pre-equilibrium parameters ► gamma-ray model parameters ● They are randomly varied following a normal distribution, centered at the default TALYS parameter values, with a default standard deviation. These two values (mean and standard deviation) are obtained from a global fitting procedure so that a default TALYS calculation is rather close to experimental data from F-19 to Bi-209.

TALYS Monte Carlo calculation From the scatter of (n,  ) curves after 100 runs the average, error bars and all covariance matrix elements can be derived.

MF33 of EAF-2009 for special targets TALYS calculations

Selection of important reactions for TALYS uncertainties ● Importance diagrams with factor > 1 (90% of activation) used to select a number of reactions for most materials includes 5105 reactions. ● Daughter nuclide Importance H1(n,g)H2 |H3 5 H2(n,g)H3 |H3 5 He3(n,p)H3 |H3 5 He4(n,2n)He3 |H3 5 Li6(n,p)He6 |He6 3 Li6(n,a)H3 |H3 5 Li7(n,na)H3 |H3 5 Li7(n,g)Li8 |Li8 5 Li7(n,d)He6 |He6 5 Be10(n,na)He6 |He6 3 Be10(n,g)Be11 |Li8, Be11 5 Be10(n,t)Li8 |Li8 3 Be10(n,nta)H3 |H3 1 Be9(n,nt)Li6 |He6 2 Be9(n,g)Be10 |H3, Li8, Be10, Be11 5 …… etc

Selection of important reactions for TALYS uncertainties ● From the previous list of important reactions a selections has been made for reactions on important targets for materials relevant to present fusion applications. This resulted in the following targets: Li6,7; Be9,10; B10,11; C12-14; N14,15; O16-18; F19, Sc45,46,48; Ti46-50; V49-51; Cr50,52-54; Mn54,55; Fe54,56-59; Co57-60; Ni58-64; Cu63,65; Nb91-95; Mo92,94- 98,100; Ta177,179,180m-182; W ; Re , Os184, ,192,193; Pb ; Bi and Po210. ● This selection amounts to 100 isotopic targets and all reaction channels shall be calculated. The calculation will be performed in 1, 2 and 5 MeV energy steps for data for energy regions <20MeV, 20-30MeV and 30-60MeV, respectively. The results will be used to overwrite the existing error factors for these reaction channels.

EAF v TALYS uncertainties Good agreement!

EAF v TALYS uncertainties EAF uncertainty smaller – use of experimental data near threshold

Conclusions ● A thorough revision and extension of the uncertainty data for EAF-2009 by a combination of an improvement of error-factor approach and TALYS Monte Carlo calculation will be performed. This will result in a new high-quality uncertainty file in MF33 format. ● The derivation of energy dependent error factors, based on TALYS Monte Carlo calculations, will be considered to replace the single-value (energy independent) factors f. ● Use the results of the recent TENDL-2008 library and especially the future TENDL-2009 release.