nuclear data requirements for decay heat calculations fission yields

NUCLEAR DATA REQUIREMENTSFOR DECAY HEAT CALCULATIONS

FISSION YIELDS

Slide serial no 2© 2002 IAEA

NUCLEAR DATA FOR DECAY HEAT CALCULATIONS- THERMAL AND FAST NEUTRON FISSION

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Derivation of Ni(t) through inventory codes

- wide range of radionuclides and stable nuclides

- : total neutron absorption, (n,) and (n,2n) cross sections of actinides


NUCLEAR DATA FOR DECAY HEAT CALCULATIONS

Fka , - e f f e c t i v e g r o u p - a v e r a g e d f i s s i o n c r o s s s e c t i o n o f a c t i n i d e a i n t h e k t h n e u t r o n g r o u p ,

Aji , - t o t a l n e u t r o n a b s o r p t i o n c r o s s s e c t i o n o f f i s s i o n p r o d u c t i ,

,,n

ji - ( n , ) c r o s s s e c t i o n o f f i s s i o n p r o d u c t i ,

nnji

2,, - ( n , 2 n ) c r o s s s e c t i o n o f f i s s i o n p r o d u c t i ,

ikaY , - i n d e p e n d e n t y i e l d s f o r f i s s i o n p r o d u c t i ,

i - d e c a y c o n s t a n t ( s ) o f f i s s i o n p r o d u c t i ,

kkk ,, - b r a n c h i n g f r a c t i o n s f o r , - a n d + d e c a y t o n u c l i d e Z , A ,

iii EEE ,, - m e a n a l p h a , b e t a a n d g a m m a e n e r g y r e l e a s e s p e r d i s i n t e g r a t i o n o f n u c l i d e i .


DEFINITIONS:

(1) Independent fission yield (%)

Number of atoms of a specific nuclide produced directly per 100 fission reactions.Excludes radioactive decay of precursors

Y(A, Z, I) = Y(A) f(A,Z) R(A, Z, I)

- Y(A) is the total sum of independent yields (before delayed- neutron emission) of all the fission products of mass number A;- f(A, Z) is the fractional independent yield of all isomers of

(A, Z);- R(A, Z, I) is the fraction of (A, Z) produced directly as isomer I (ie., isomeric yield ratio).


DEFINITIONS:

(2) Cumulative fission yield (%)

Number of atoms of a specific nuclide produced directly and via decay of precursors per 100 fission reactions:

Cu(A, Z, I) = Y(A, Z, I) b(A, Z, I A, Z, I). Cu(A, Z, I)

Most fission products undergo - or IT decay, and hence A = A

Complications arise for - delayed-neutron decay, whenA = A + 1 and Z = Z - 1

Equation can be solved if the independent yields are known.

A, Z, I


DEFINITIONS:

(3) Chain yield (%)

Number of isobars of a specific mass produced in 100 fission reactions.

Ch(A) is sum of all stable or long-lived cumulative yields for a given mass chain.

Complications arise from - delayed-neutron decay.

(4) Mass (number) yield (%)Sum of all independent yields of a particular mass chain in 100 fission reactions.


1970s to 2002

Key Issues and Developments:

(1) measured yields have increased significantly;

(2) need isomeric yields for decay heat calculations;

(3) energy dependence of fission yields;

(4) development of new measurement techniques;

(5) development of models to determine unmeasured yields.

IAEA-CRP: Compilation and evaluation of fission product yield nuclear data, Final report of a Co-ordinated Research

Project 1991-1996. IAEA-TECDOC-1168, IAEA Vienna (2000).


Fission product chain yields from 235U fission


Mass distribution curves in the thermal-neutron induced fission of229Th, 233U, 235U and 239Pu


Available experimental data: fractional independent yields forthermal and fast fission spectra, high-energy neutron-induced fission,and spontaneous fission

Galy, J. (1999) Investigation of the fission yields of the fastneutron-induced fission of 233U, PhD thesis, Université Aix-Marseille


Available experimental data: cumulative and chain yields for thermal and fast fission spectra, high-energy neutron-induced fission, and spontaneous fission.

Galy, J. (1999) Investigation of the fission yields of the fastneutron-induced fission of 233U, PhD thesis, Université Aix-Marseille


MASS DISTRIBUTIONS

Serendipity - variable number of Gaussian functions to represent the mass distributions of different fission reactions and neutron energies.

Th to Es ( Z = 90 to 99 )

neutron excitation energies < 20 MeV

Wahl (1988) Atomic Data and Nuclear Data Tables, 39(1), 1 - 156.

able to represent COMPLETE mass distributions for

a fissioning system.


Various Gaussian curves fitted to mass distributions of fission processes:thermal-neutron fission of 235U, and high-energy neutron fission of 238U


Various Gaussian curves fitted to mass distributions of fission processes:thermal-neutron fission of 239Pu, 242mAm and 249Cf, and spontaneous fission of 252Cf


Various Gaussian curves fitted to mass distributions of fission processes:thermal-neutron fission of 249Cf, and spontaneous fission of 252Cf


NUCLEAR CHARGE DISTRIBUTIONS

Two empirical models to determine a large fraction of fission yields that remain unmeasured

Zp model: distribution of fractional independent yields with Z for each A of primary fission products

A model:distribution of independent yields with A for each Z of primary fission products, where A is the average mass number of the precursor primary fragments that give products with A by prompt-neutron emission

A = A + A

where A is the average number of prompt neutrons emitted to form fission products for each mass number A.

p

_

_


Zp MODEL

Zp-model parameters are either constant or linear functions of A except Z

Fz

zFN

Z

apart from distributions close to symmetry, when the width parameter changes abruptly twice (z);even-odd proton and neutron factors equal 1.0 (FZ and

FN), and Z function undergoes a dramatic zig-zag transition.


Zp functions for thermal fission of 235USolid lines calculated by L.S., red. 2 = 3.6(0.7)Dashed lines from systematics, red. 2 = 6.6(0.6)


FRACTIONAL INDEPENDENT YIELDS (FI)FI(A, Z) = (0.5) [ F(A) ] [ N(A) ] [ erf (V) - erf (W) ]

where V = Z(A) - Zp (A) + 0.5 2 [ z (A) ]

and W = Z(A) - Zp (A) - 0.5

2 [z (A) ]

Zp (AH) = A [ ZF/AF ] +

Zp (AL) = A [ ZF/AF ] +

where A = AF - A

H H

Hc

Hc

L

L


FRACTIONAL INDEPENDENT YIELDS (FI)

For Z For NF(A) = [ Fz (A) ] [ FN(A) ] even even

F(A) = [ Fz (A) ] /[ FN(A) ] even odd

F(A) = [ FN (A) ] / [ Fz(A) ] odd even1 odd odd

[ FZ (A) ] [ FN(A) ]F(A) = 1.00 near symmetry

(A)z(A), Fz(A) and FN(A) depend on A

and the region in which A falls.

F(A) =


Peak parameters for A(140)


Zp MODEL PARAMETERS229Th(T)232Th(F)233U(T)235U(T)238U(F)238U(14 MeV)238Np(T)239Pu(T)242Am(T)249Cf(T)252Cf(SF)

All of the model parameters can only be determined with confidence for 235U(T).

Parameters over specific regions for fission reactions can be estimated through equation:

PM = P(1) + P(2)(ZF -92) + P(3) (AF - 236) + P(4)(E*- 6.551)

P(1) etc determined by least squares from PM values determined by least squares for individual fission reactions.


A MODEL

Gaussian width parameters are close to an average of

(defined as the global average) for 47Ag and 42Mo - 50Sn pair

Values for 48Cd and 43Tc - 49In pair are considerably larger,implying formation by more than one process - better fit with two Gaussian functions (each with of

P


Thermal fission of 235U – Ap model near symmetry: single Gaussian curve


Thermal fission of 235U – Ap model near symmetry:two Gaussian curves


ISOMERIC FISSION YIELDS

Equations derived to calculate fractional independent isomeric yields (fiiy) for a high-spin

isomeric state and for a low-spin isomeric state.

Comparisons of experimental data with calculated fiiy values have furnished recommended values for the

spin distributions:

Jrms of 6.50; Jnuc of 6.00 for odd-mass nuclides

Jrms of 6.00; Jnuc of 1.00 to 2.00 for even-mass nuclides

Alternative model based on energy of gamma rays.


Nuclide fiiy(high) Nuclide fiiy(high)experimental calculated experimental calculated

79Ge 1.00 ± 0.11 0.829 127In 0.87 ± 0.06 0.81481Ge 0.70 ± 0.06 0.835 127Sn 0.90 ± 0.11 0.62682As 0.17 ± 0.07 0.597 128In 0.30 ± 0.07 0.19083Se 0.89 ± 0.07 0.816 128Sn 0.11 ± 0.07 0.20984Br 0.30 ± 0.04 0.504 128Sb 0.61 ± 0.06 0.19284Br 0.38 ± 0.04 0.504 129In 0.76 ± 0.07 0.815

90R b 0.58 ± 0.05 0.659 129Sn 0.43 ± 0.06 0.62190R b 0.90 ± 0.01 0.659 130Sn 0.13 ± 0.02 0.21299Nb 0.06 ± 0.14 0.819 130Sb 0.45 ± 0.11 0.190113Ag ~1.00 0.847 132Sb 0.20 ± 0.02 0.190115Ag ~1.00 0.846 132Sb 0.19 ± 0.03 0.190116Ag ~1.00 0.391 133Te 0.78 ± 0.04 0.590117Ag ~1.00 0.848 133Te 0.57 ± 0.04 0.590118Ag 0.44 ± 0.10 0.388 133Te 0.61 ± 0.08 0.590119Cd 0.39 ± 0.20 0.724 133I 0.07 ± 0.02 0.140120Ag 0.85 ± 0.15 0.382 133Xe 0.75 ± 0.04 0.603121Cd 0.89 ± 0.11 0.730 134Sb 0.19 ± 0.05 0.279123Cd 0.68 ± 0.02 0.614 134I 0.20 ± 0.02 0.183123In 0.94 ± 0.11 0.817 135Xe 0.65 ± 0.04 0.575123Sn 1.00 ± 0.28 0.627 136I 0.79 ± 0.14 0.391124In 0.86 ± 0.80 0.215 138Cs 0.58 ± 0.08 0.392

125Cd 0.66 ± 0.08 0.614 146La 0.06 ± 0.03 0.391125In 0.88 ± 0.08 0.813 148Pr 0.12 ± 0.03 0.660126In 0.42 ± 0.17 0.215 148Pm 0.71 ± 0.06 0.388

Experimental and calculated fractional independent yields of the high-spin isomers of nuclides formed in the thermal-fission of 235U


EVALUATED FISSION YIELD LIBRARIES

(1) US ENDF/B-V1

Increased from 10 to 60 yield sets.

Corrections have been applied.

Models to estimate unmeasured yields.

England and Rider (1994) Los Alamos National Laboratory Report LA-UR-

94-3106.



(2) UKFY2 (and UKFY3)

39 yield sets.

Important short-lived fission products are missing from UK decay data files: correction terms applied to independent yields

of UKFY2 so that recommended chain yields are obtained.

Decay-data evaluations have recently been undertaken to avoid

this problem.

Mills (1995) PhD thesis, University of Birmingham James et al (1991a, 1991b and 1991c)

AEA Technology Reports AEA-TRS-1015,1018 and 1019

New evaluation underway (UKFY3/JEFF-3) based on recent developments (IAEA TECDOC-1168), and specific decay-data evaluations previously omitted from database.



(3) CENDL

10 yield sets

A new expansive evaluation is underway


Fissioning US ENDF/ B-VI UKFY2 (JEF-2.2) CENDLNuclide S T F H S T F H T F H

227Th229Th232Th

xx

x x x x x231Pa x232U233U234U235U236U237U238U

xx

x

xxxxxx

xxxx

x

x

x

xxxx

x

x

x

x

x

x x

x

x

x237Np238Np

x x xx

x xx

xx

238Pu239Pu240Pu241Pu242Pu

xxxx

xxxxx

xx

x

xx

x

xxxxx

x

x

x

241Am242mAm243Am

xx

x

x

x xxx

xxx

242Cm243Cm244Cm245Cm246Cm248Cm

x

xx

x

x

xxx

xx

x

xxxx

xxx

249Cf250Cf251Cf252Cf

x

x

x

xx

253Es254Es

xx

254Fm255Fm256Fm

x

xx

Evaluated fission yield libraries, 2000


FISSION YIELDS: 2000/01

(1) International network of co-operation between fission yield experts :

- clean-up of data bases,- model development,- share evaluation procedures.

(2) Empirical models (Zp and A ) - reliability from thermal to 15 MeV neutrons.

(3) Computer programs : - correlations and covariance matrices.

(4) Complete fission yield data sets.

(5) IAEA-TECDOC-1168

p


FISSION YIELDS: PROBLEMS 2000/01

(1) Models and systematics incapable of generating accurate and reliable fission yield estimates at different neutron energies.

More experimental data are required.

(2) Isomeric yields - inadequate model when insufficient experimental data are available.

More experimental data are required.


FISSION YIELDS: STATUS 2002

On-going IAEA-CRP: Fission product yield data required fortransmutation of minor actinide nuclear waste, 1998 – 2002

1) Further development of models and systematics for fission yields.

2) Study of systematic trends in experimental data for mass and

charge distribution in fission – produce set of suitableequations.

3) Theoretical studies of fission cross sections.4) Methodology and tools for fission yield evaluations.

Models and systematics need to be tested – benchmark exercise.


YCALCG. Grommes, H. O. Kling and H. O. Denschlag

Program to calculate mass yields or fractional independent and

cumulative yields for 12 fission reactions

Results can be displayed as tables and graphs

University of Mainz Website

http://www.kernchemie.uni-mainz.de

LINKS YCALC

nuclear data requirements for decay heat calculations fission yields

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