NUCLEAR DATA REQUIREMENTS FOR DECAY HEAT CALCULATIONS FISSION YIELDS

Slide serial no 2 © 2002 IAEA NUCLEAR DATA FOR DECAY HEAT CALCULATIONS - THERMAL AND FAST NEUTRON FISSION ====== Derivation of N i (t) through inventory codes - wide range of radionuclides and stable nuclides -  : total neutron absorption, (n,  ) and (n,2n) cross sections of actinides

Slide serial no 3 © 2002 IAEA NUCLEAR DATA FOR DECAY HEAT CALCULATIONS

Slide serial no 4 © 2002 IAEA 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).

Slide serial no 5 © 2002 IAEA 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, when A = A + 1 and Z = Z - 1 Equation can be solved if the independent yields are known. A, Z, I

Slide serial no 6 © 2002 IAEA 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.

Slide serial no 7 © 2002 IAEA 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 IAEA-TECDOC-1168, IAEA Vienna (2000).

Slide serial no 8 © 2002 IAEA Fission product chain yields from 235 U fission

Slide serial no 9 © 2002 IAEA Mass distribution curves in the thermal-neutron induced fission of 229 Th, 233 U, 235 U and 239 Pu

Slide serial no 10 © 2002 IAEA Available experimental data: fractional independent 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 fast neutron-induced fission of 233 U, PhD thesis, Université Aix- Marseille

Slide serial no 11 © 2002 IAEA 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 fast neutron-induced fission of 233 U, PhD thesis, Université Aix- Marseille

Slide serial no 12 © 2002 IAEA 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), able to represent COMPLETE mass distributions for a fissioning system.

Slide serial no 13 © 2002 IAEA Various Gaussian curves fitted to mass distributions of fission processes: thermal-neutron fission of 235 U, and high-energy neutron fission of 238 U

Slide serial no 14 © 2002 IAEA Various Gaussian curves fitted to mass distributions of fission processes: thermal-neutron fission of 239 Pu, 242m Am and 249 Cf, and spontaneous fission of 252 Cf

Slide serial no 15 © 2002 IAEA Various Gaussian curves fitted to mass distributions of fission processes: thermal-neutron fission of 249 Cf, and spontaneous fission of 252 Cf

Slide serial no 16 © 2002 IAEA NUCLEAR CHARGE DISTRIBUTIONS Two empirical models to determine a large fraction of fission yields that remain unmeasured Z p 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 _ _

Slide serial no 17 © 2002 IAEA Z p MODEL Z p -model parameters are either constant or linear functions of A except  Z F z  z F N   Z apart from distributions close to symmetry, when the width parameter changes abruptly twice (  z ); even-odd proton and neutron factors equal 1.0 (F Z and F N ), and  Z function undergoes a dramatic zig-zag transition.

Slide serial no 18 © 2002 IAEA Z p functions for thermal fission of 235 U Solid lines calculated by L.S., red.  2 = 3.6(0.7) Dashed lines from systematics, red.  2 = 6.6(0.6)

Slide serial no 19 © 2002 IAEA FRACTIONAL INDEPENDENT YIELDS (FI) FI(A, Z) = (0.5) [ F(A) ] [ N(A) ] [ erf (V) - erf (W) ] where V = Z(A) - Z p (A)  2 [  z (A) ] and W = Z(A) - Z p (A)  2 [  z (A) ] Z p (A H ) = A [ Z F /A F ] +    Z p (A L ) = A [ Z F /A F ] +    where A = A F - A H H Hc L L

Slide serial no 20 © 2002 IAEA FRACTIONAL INDEPENDENT YIELDS (FI) For Z For N F(A) = [ F z (A) ] [ F N (A) ] even even F(A) = [ F z (A) ] /[ F N (A) ] even odd F(A) = [ F N (A) ] / [ F z (A) ] odd even 1 odd odd [ F Z (A) ] [ F N (A) ] F(A) = 1.00 near symmetry  (A  )  z (A), F z (A) and F N (A) depend on A and the region in which A falls. F(A) =

Slide serial no 21 © 2002 IAEA Peak parameters for A(140)

Slide serial no 22 © 2002 IAEA Z p MODEL PARAMETERS 229 Th(T) 232 Th(F) 233 U(T) 235 U(T) 238 U(F) 238 U(14 MeV) 238 Np(T) 239 Pu(T) 242 Am(T) 249 Cf(T) 252 Cf(SF) All of the model parameters can only be determined with confidence for 235 U(T). Parameters over specific regions for fission reactions can be estimated through equation: PM = P(1) + P(2)(Z F -92) + P(3) (A F - 236) + P(4)(E* ) P(1) etc determined by least squares from PM values determined by least squares for individual fission reactions.

Slide serial no 23 © 2002 IAEA A MODEL Gaussian width parameters are close to an average  of  (defined as the global average) for 47 Ag and 42 Mo - 50 Sn pair Values for 48 Cd and 43 Tc - 49 In pair are considerably larger, implying formation by more than one process -better fit with two Gaussian functions (each with  of  P

Slide serial no 24 © 2002 IAEA Thermal fission of 235 U – A p model near symmetry: single Gaussian curve

Slide serial no 25 © 2002 IAEA Thermal fission of 235 U – A p model near symmetry: two Gaussian curves

Slide serial no 26 © 2002 IAEA ISOMERIC FISSION YIELDS Equations derived to calculate fractional independent isomeric yields (f iiy ) for a high-spin isomeric state and for a low-spin isomeric state. Comparisons of experimental data with calculated f iiy values have furnished recommended values for the spin distributions: J rms of 6.50; J nuc of 6.00 for odd-mass nuclides J rms of 6.00; J nuc of 1.00 to 2.00 for even-mass nuclides Alternative model based on energy of gamma rays.

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Slide serial no 28 © 2002 IAEA 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

Slide serial no 29 © 2002 IAEA EVALUATED FISSION YIELD LIBRARIES (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.

Slide serial no 30 © 2002 IAEA EVALUATED FISSION YIELD LIBRARIES (3) CENDL 10 yield sets A new expansive evaluation is underway

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Slide serial no 32 © 2002 IAEA 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 (Z p 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

Slide serial no 33 © 2002 IAEA 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.

Slide serial no 34 © 2002 IAEA FISSION YIELDS: STATUS 2002 On-going IAEA-CRP: Fission product yield data required for transmutation of minor actinide nuclear waste, 1998 – 2002  Further development of models and systematics for fission yields.  Study of systematic trends in experimental data for mass and charge distribution in fission – produce set of suitable equations.  Theoretical studies of fission cross sections.  Methodology and tools for fission yield evaluations. Models and systematics need to be tested – benchmark exercise.

Slide serial no 35 © 2002 IAEA YCALC G. 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 LINKS YCALC