Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft L. Mercatali, FZK/IRS IP EUROTRANS...

Forschungszentrum Karlsruhein der Helmholtz-Gemeinschaft

L. Mercatali, FZK/IRS IP EUROTRANS Training CourseSantiago de Compostela (Spain), June 7-10, 2006

On the accuracy in the theoretical prediction of neutron induced reaction

cross-sections above 0.1 MeV

Luigi [email protected]

Forschungszentrum Karlsruhe / Institute for Reactor Safety

2nd IP EUROTRANS Internal Training Course“Nuclear Data for Transmutation: Status, Needs and Methods”

Santiago de Compostela (Spain), June 7-10, 2006



IP-EUROTRANS

DM5: NUDATRA (NUclear DAta for TRAnsmutation)

Improvement and assessment of the simulation tools and associated uncertainties for ADS transmuters and its associated fuel cycle

The activity is essentially focused on the evaluated nuclear data libraries and reaction models for materials in transmutation fuels, coolants, spallation targets, internal structures, and reactor and accelerator shielding, relevant for the design and optimisation of the Generic ETD and XT-ADS

FZK contribution is related to:

WP5.1 Sensitivity Analysis and Validation of Nuclear Data and Simulation Tools



Background Nuclear data libraries are mainly focused on neutron induced reaction cross-

sections up to 20 MeV. At present there is a significant effort to extend the energy range of the library up to 200 MeV in order to comply with recent developments in transmutation research with ADS’s. This extension is not trivial because of the increasing number of open channels. In addition, the scarcity of experimental data at intermediate energies requires to rely extensevely on model calculations

Results of model calculations should be provided together with the associated uncertainties

Arjan Koning has shown that it possible (in principle) to generate a complete covariance matrix for all neutron-induced reactions using random variations of nuclear model paramenters (via a Monte Carlo algorithm), following the original idea of D. Smith (ANL)



Background (cont’d) Several open issues related to the approach of D. Smith:

1. Actual distribution of the model paramenters (Gaussian, …?)

2. Parameters correlations not only within one model, but also within paramenters of different models that have the same effect on a calculated quantity

3. Uncertainty due to nuclear models

4. How to disentangle uncertainties due to the models with the ones due to the model parameters

Comparison of massively calculated cross-sections against all the experimental data of the periodic table of elements would be needed in order to use the average deviations from experiments to assess the most pessimistic uncertainties for unmeasured reaction channels



Background (cont’d)

)def(j,i

)num(j,i

)par(j,i

(mod)j,i MMMM

1. uncertainties of the model parameters

2. errors due to numerical implementation

3. deficiencies of the model

H. Leeb et. al., Covariances for Evaluations Based on Extensive Modelling, Proc. ND2004, Santa Fe (USA)

K

1i2(exp)

i

2N21i

(mod)i

(exp)i2

)(

)]a,...a,a,E([

m

j(mod)j

nm

N

1m,n n

i(mod)ipar

j,i a

)E(

a

)E(M

Minimization2



Background (cont’d)

Mean model error extracted from the reproduction of observable not included in the evaluation

)E()E()u(CM jcalcji

calci

2j,i

)def(j,i

K

kk

K

kkk

w

uw

u

1

1

2

2

)(

)(

(mod)

k

(exp)k

(mod)k

ku

2

(exp)k

(mod)k

kw

; ;

Ci,j obtained by intuition



Assessment of the predictive power of modern nuclear models

Comparison between experimental cross-sections and theoretical predictions

Calculations performed with the state of the art of nuclear models and simulation tools:– GNASH, TALYS, ALICE/ASH, HMS/ALICE, EMPIRE, MCNPX

Goals:

1. Provide recommendations on the best combinations of theoretical models and codes to optimize the accuracy of the simulations (as for different energy groups, as for different nuclides, as for different channels)

2. Comparison of nuclear models on a large variety of materials (from C up to transuranics) to improve the systematics of the model parameters



Experimental data

Processing of EXFOR via FORTRAN coding and X4TOC4 code:

– All target nuclei with 13 ≤ Z ≤ 83

– Initial neutron energy above 0.1 MeV

– All (n,xnypzα) reactions

Data excluded:

– Out-dated and superceded measurements

– Targets containing natural mixtures of isotopes

– Reactions with metastable products

– Data averaged for a wide range of neutron incident energies

– (n,γ), (n,np), (n,nd) and (n,3He) reactions

– Identical data



Experimental data (cont’d)

25 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

1200

1400

Nu

mb

er

of

me

asu

rem

en

tsN

um

be

r o

f m

ea

sure

me

nts Mass distribution

Mass number (A)

0 10 20 30 40 50 60 700

500

1000

1500

2000

2500

3000

3500

Energy distribution

Incident neutron energy (MeV)

Total experimental points (Z,A,E): 17937

Energy range: 0.1÷64.4 MeV

Points with projectile energy > 20 MeV: 615

Reactions available:

(n,n’), (n,p), (n,α), (n,t), (n,2n), (n,nα), (n,2p)

(n,pα), (n,2α), (n,3n), (n,4n)

other reactions noted in EXFOR as (n,x)



Calculations

TALYS and ALICE/ASH codes– Nuclear reaction simulations in the range 1 keV ÷ 200 MeV

– Neutrons, protons, deuterons, tritons, helions, alphas and photons

– All open reaction channels covered

Uncertainty assessment on the use of different phenomenological and microscopic nuclear level density models

j Π

tot ΠJ,E,ρEρ

Numbers of nuclear levels per MeV around an excitation energy E



Nuclear level density calculation with TALYS and ALICE/ASH

Symbols Model for nuclear level density calculation Code Input variable

IST(1)Fermi gas model with the energy dependent nuclear level density parameter a(U) without explicit description of the collective enhancement*

TALYS

ldmodel=1

IST-CFermi gas model with a(U) with explicit description of the rotational and vibrational enhancement* ldmodel=2

G Microscopic calculations using the HF-BCS approach ldmodel=3

FG Fermi gas model with a=A/9*

ALICE/ASH

ldopt=0

IST(2)Fermi gas model with the energy dependent nuclear level density parameter a(U)* ldopt=4

SF Superfluid nuclear model ldopt=5

* at low energy of the excitation the “constant temperature” model is used.



Data Treatment

21

2

1

1

N

iexpi

calci

expi

NH

N

iexpi

calci

NR

1

1

N

iexpi

calci

expi

ND

1

1

21

1

21

10

N

i

calci

expi )log()log(

NF

N

1ii

N

1i

2

calci

expi

calci

i2

w

w

)u(L

Deviation factors can be provided as for single target nulide, energy, channel or groups of these



FactorsTALYS ALICE/ASH

IST (1) IST-C G FG IST (2) SF

Target nuclei with atomic mass number 27 ≤ A < 120

H 10.33 29.34 12.01 17.50 31.38 14.88

R 1.25 1.57 1.27 1.06 0.78 1.01

D 0.50 1.06 0.56 0.56 0.68 0.56

F 2.10 2.97 2.15 2.93 22.39 3.76

L 0.13 0.55 0.18 0.29 0.60 0.24

Number of points 14467 14441 14466 14313 14277 14304

120 ≤ A ≤ 209

H 10.45 36.39 15.31 6.15 7.38 5.44

R 1.32 1.77 1.38 1.03 0.84 0.95

D 0.50 0.95 0.58 0.36 0.42 0.34

F 2.03 2.41 2.08 2.19 4.42 2.49

L 0.27 0.77 0.44 0.14 0.29 0.13

Number of points 2829 2829 2829 2823 2773 2818

All nuclei with 27 ≤ A ≤ 209

H 10.35 30.60 12.61 16.18 28.87 13.78

R 1.26 1.60 1.29 1.05 0.79 1.00

D 0.50 1.05 0.57 0.53 0.64 0.52

F 2.09 2.88 2.14 2.81 18.31 3.55

L 0.14 0.59 0.21 0.29 0.60 0.23

Number of points 17296 17270 17295 17136 17050 17122



ReactionTALYS ALICE/ASH

IST (1) IST-C G FG IST (2) SF

Targets with atomic mass number 27 ≤ A < 120

(n.n’) 12.77 12.48 12.79 13.00 16.71 13.00

(n.2n) 13.56 14.94 13.32 31.48 60.77 22.62

(n.3n) 13.35 3.04 15.27 11.62 6.24 11.67

(n.p) 8.22 28.07 9.31 10.93 19.38 12.74

(n.α) 7.91 44.57 13.76 10.71 11.23 10.50

(n.t) 20.52 30.62 21.04 5.12 5.70 5.09

Others 7.20 4.83 7.98 9.98 15.62 10.52

All reactions 10.33 29.34 12.01 17.50 31.38 14.88

120 ≤ A ≤ 209

(n.n’) 2.17 2.62 2.22 2.11 5.68 2.52

(n.2n) 3.81 4.33 3.96 5.09 7.60 4.94

(n.3n) 4.65 4.76 5.22 12.49 10.92 5.98

(n.p) 17.80 23.60 18.29 32.81 6.99 6.53

(n.α) 11.56 96.20 33.74 5.45 6.64 5.66

(n.t) 41.81 103.70 42.07 4.03 4.08 4.03

Others 4.80 4.56 5.63 9.04 8.88 6.91

All reactions 10.45 36.39 15.31 6.15 7.38 5.44

H



Representation by A

50 100 150 2000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.050 100 150 200

0

20

40

60

80

100

R f

acto

r

Mass number (A)

H f

acto

r

IST (1) IST-C G

TALYS

50 100 150 2000.0

0.5

1.0

1.5

2.050 100 150 200

0

20

40

60

80

100

R f

act

or

Mass number (A)

H f

act

or

FG IST (2) SF

ALICE/ASH



TALYS and ALICE/ASH: Best performances by A

20 40 60 80 100 120 140 160 180 200 2200

5

10

15

20

25

30

H f

acto

r

Mass number (A)

TALYS, IST (1) ALICE/ASH, SF

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

20115151 10128

R f

acto

r

Mass Number (A)

TALYS, IST (1) ALICE/ASH, SF



Factors ENDF/B-VI.8 FENDL-2/A JEFF-3/A JENDL-3.2 JENDL-3.3

Targets with atomic mass number 27 ≤ A < 120 (Best nuclear model H=10.33, TALYS IST-1)

H 8.13 76.26 7.05 24.42 8.28

R 1.09 2.17 1.23 1.83 1.69

D 0.26 1.34 0.44 1.02 0.88

F 1.48 2.10 1.91 2.05 2.03

L 0.06 0.87 0.06 0.43 0.08

Number of points 10497 12591 12542 13802 13516

120 ≤ A ≤ 209 (Best nuclear model H=5.44, ALICE/ASH SF)

H 14.12 6.29 6.10 7.45 7.40

R 1.34 1.14 1.11 1.19 1.19

D 0.54 0.33 0.26 0.38 0.38

F 2.30 2.03 1.94 2.22 2.22

L 0.41 0.14 0.14 0.19 0.19

Number of points 1693 2571 2548 1836 1902

Evaluations vs. experiments



H- minimization procedure

18 20 22 24 26 28 30

0

20

40

60

80

100

120

Cro

ss S

ectio

n (m

b)

Energy (MeV)

Exp. Calc. Mod.

FactorTALYS Code

JEFF-3.0/AIST1 Corrected

(n,p) reaction

H 9.63 5.31 6.97

Exp. Points 6216 6216 614

(n,) reaction

H 7.96 4.77 6.34

Exp. Points 3846 3846 4375



Ongoing and future activities Uncertainty assessment for proton induced reaction cross-section up to the

highest energy for ADS applications (~ 1 GeV)

The processing and the simulations of all (p,xnypzα) reactions up to 150 MeV is completed → ~ 19300 experiments

20 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

1200

1400

Num

ber

of m

easu

rem

ents

Mass number (A)

Mass distribution

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 1500

200

400

600

800

1000

1200

1400

1600

Nu

mb

er

of

me

asu

rem

en

ts

Incident proton energy (MeV)

Energy distribution



Extension of the assessment to transuranics target nuclei

Investigation of the performance of different tools:

– EMPIRE, MCNPX (Bertini, ISABEL, INCL4, CEM2k models combined with pre-equilibrium exciton models and with evaporation Dresner and ABLA model)

Creation of a new activation library for proton induced reaction cross-sections based on the recommendations coming from the above analyses

Covariance studies via Leeb’s and Smith’s approaches

Global integral deviation factor:

Ongoing and future activities (cont’d)

ii

i fwf

Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft L. Mercatali, FZK/IRS IP EUROTRANS...

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