Conclusions concerning the delayed neutron data for the major actinides

Progress

in NUC/MU Energq., Vol. 41. No.

Pergamon

0 2002

Elsevier

Science 0 I49-

www.elsevier.comflocate/pnucene

1-4. pp. 391-412, 2002 Ltd. All rights reserved Punted in Great Bntain

I9701026

ccc front

matter

PII: SO149-1970(02)00020-3

CONCERNlNG

CONCLUSIONS THE DELAYED NEUTRON THE MAJOR ACTINIDES

ANTONIO D’ANGELO’

DATA

FOR

and JOHN L ROWLANDS”

* ENEA/Ca.saccia. S.P. 101. P.O.Box 2400. 00100 Rome. Italy. (danpelo(~~:a.Fn~~,i~.enea.it ** RI. South Court Avenue. Dorchester DTI 2DA. United Kingdom. lrowtand~J_lOaol.com)

ABSTRACT The conclusions which relate to the delayed neutron yield data for “?J, *‘*U and 239Pu recommended for use in calculations of the effective delayed neutron fraction, &, in conventional thermal and fast reactors, as described in the present issue of Progress in Nuclear Energy, are summarised and discussed. 0 2002 Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION The recommended data presented in the papers published in the present volume are summarised and compared with the delayed neutron data currently in use. Tuttle’s 1975 and 1979 evaluations of total yields, together with Keepin’s 6 group parameters representing the time dependence, are still widely used and a comparison between these, the data in the current nuclear data libraries, and the present recommendations for the primary isotopes, 235U, 238U and 239Pu, might be of most interest. It 1~ also appropriate to consider what further work is needed.

In the overview paper in the present volume (D’Angelo, 2002) the programmes of measurement and evaluation of delayed neutron data carried out during the past decade have been comprehensively reviewed and, in particular, the work which has been co-ordinated by Subgroup 6 of the OECD NEANSC Working Party on International Evaluation Co-operation has been summarised. At the level of the data for individual fission product isotopes, the measurements and associated evaluations of decay constants, Pn values and fission product yields have significantly improved the database. These measurements and evaluations are being incorporated in the fission product yield and radioactive decay data files in the major nuclear data libraries, such as ENDF/B, JEFF and JENDL. Developments are being made to the measurement facilities and techniques at several laboratories and the accuracy of the microscopic data is expected to continue to be improved. Refinements are also being made to the theoretical models used to calculate unmeasured data. Intercomparisons between the data in the different libraries have been carried out by an IAEA Co-ordinated Research Programme, (Lammer, 2000).

391

392

A. D’Angelo and J. L. Rowlands

Although the accuracy of the data for individual decade, for &calculations reliance must still be neutron emission data for the major isotopes and fl& and time-dependent effects. Indeed, it is by measured values of fl& that the data most suitable

fission product isotopes has improved during the past placed on the macroscopic measurements of the delayed the validation of the data using reactor measurements of adjusting the yield data to improve the agreement with for &calculations is obtained.

2. THE PROGRAMMES OF BETA-EFFECTIVE MEASUREMENTS The paper in the present volume by Okajima et al (2002) describes the /&measurements which have been made in the fast reactor benchmark series of experiments carried out in the fast critical facilities MASURCA (France) and FCA (Japan). These programmes differ from previous measurements in that in each assembly several different techniques were used and different teams carried out the measurements. Two assemblies were studied in MASURCA, one uranium fuelled (R2) and the other fuelled with uranium/plutonium (ZONA2). Both assemblies had a significant contribution to & from *‘?J. Three assemblies were studied in FCA. The value of fl& measured in FCA XIX.1 was predominantly sensitive to the 235U yield, and in XIX.3 to the plutonium yield. The value measured in XIX.2 was about equally sensitive to plutonium and 238U. These five assemblies were designed to provide reference values of /!& suitable for validating the delayed neutron data for 235U,238Uand 239Pu in fast reactor spectra. The groups which participated in these experiments were: CEA/Cadarache (France), IPPE/Obninsk (Russia), JAERI (Japan), KAERI (Korea), LANL (USA) and Nagoya Univ. (Japan). The techniques used were: Cf source Noise Rossi-cr Modified Bennet Nelson Number The benchmark measurements provide an insight into the accuracy of the different methods. Two groups carried out measurements using the Cf source technique. The values of&rthey measured in MASURCA R2 differ by a surprising 5%, the estimated uncertainty being a standard deviation of? 3%. The derivation of the value of/&, from the parameters which are measured involves calculated correction factors, such as the relationship between the measured fission rate and the average fission rate in the reactor (although these calculated factors can be adjusted on the basis of a comparison between measured and calculated fission rate scans). Jeff can be written in the form Pm.Pc, where Pm denotes the measured part and PC the calculated part. In the case of the two Cf source measurements made in R2 the values of Pm differ by 4% and PC by 1%. The two Cf source measurements made in ZONA2 are in better agreement, the values of Pm differing by 2% and PC by 1% givingJ’,Jvalues which differ by 3%. In the FCA series of experiments two teams again made measurements. In this case the same values of PC were used by both teams and the Pm values differed by 4% in XIX-l, and by 2% in XIX-2 and XIX-3. The mean values differ from the means of all the measurements by 2% to 3%. Bearing in mind that there are additional sources of error common to all the Cf source measurements made in a core an uncertainty estimate of f 3% for this technique is perhaps optimistic. The Rossi-alpha measurement made in R2 comprised measurements made at two different reactivity levels and gave values which differ by 3%. There are additional sources of error common to both measurements, arising from both the measured and calculated factors. A measurement was also made in FCA XIX-l and it gave a value 4% higher than the mean value of the measurements made in this core. Again an uncertainty estimate of + 3% seems optimistic (and a much smaller uncertainty has been assumed in the study made by Fort et al, 2002).

Conclusions

393

Measurements made using the noise technique can be compared with the mean values of the measurements made in a core using the different techniques and the agreement is consistent with an estimated uncertainty of about f 2.5%, provided that there are not errors common to all of the techniques. (The Diven factor is common to all excepting the Cf source technique and it introduces an uncertainty in measured,&values of about f 1.3%.) We note, however, that a much smaller uncertainty than this figure off 2.5% is attributed to the value of&-derived by noise measurements made in the thermal spectrum MISTRAL cores (k 1.6%) studied in the EOLE facility at Cadarache (Litaize and Santamarina, Cadarache, 2001). Further intercomparisons of the different techniques would be helpful in giving confidence in the use of the earlier measurements made in SNEAK and ZPR, and the associated uncertainty estimates, where a single technique (Cf source or noise) was used. The papers in the present volume by Okajima et al (2002) and by Fort et al (2002) show that the agreement between the measured and calculated&-values is good for the benchmark series, within about * 3% for the data in the current nuclear data libraries, ENDFBVI, JEF-2.2 and JENDL-3.2, (although it should be noted that the calculations made by Fort et al use an adjusted version of the JEF-2.2 cross-section library). However, the ENDF/B-VI yield data underestimate the&f values measured in the MOX fuelled SNEAK and ZPR cores which have a high dependence on 238U. Several measurements have been made in thermal spectrum systems. In the EOLE facility at Cadarache the uranium fuelled system, MISTRAL-I, and the MOX fuelled system, MISTRAL-2 have been studied and the uncertainty estimates for these Jr/ measurements are small, + 1.6%. These results have been included in the adjustment study carried out by Fort et al. Measurements were made in Japan in the 1980s in the SHE series of experiments (Kaneko et al, 1988) and these resulted in values for the 23?J delayed neutron fraction having an estimated uncertainty of f 1.2%. Measurements have also been made in the TCA facility in Japan and the measurement made in a uranium fuelled system has been included in the adjustment study carried out by Sakurai and Okajima (2002). This & measurement has an estimated uncertainty of 2.2% and the value appears to be significantly lower than that derived from the SHE series of measurements. There appears to be a difference of about 2% between the older (SNEAK and ZPR) measurements of & and the benchmark series of measurements. Further intercomparisons of techniques, and measurements made on cores similar to the older cores would be helpful in understanding this difference and would also give confidence in the high accuracy which has been assigned to the recent thermal reactor measurements.

3. THE ENERGY DEPENDENCE OF DELAYED NEUTRON YIELDS The measurements of &made on reactor facilities do not provide information on the energy dependence of yields (other than the difference between the average values for thermal spectrum and fast spectrum systems). Some assumptions about the energy dependence are required to interrelate the results for different systems and to extrapolate from the measured values to systems with different spectra. In his 1979 paper, Tuttle discussed the incident neutron energy dependence of total delayed neutron yields. He represented the energy dependence for 233U, 235U and 239Pu as linear in energy in the intervals 0 to 3 MeV, 3 to 7 MeV, 7 to 11 MeV and 11 to 14.5 MeV, with increases in the range to 3 MeV of about 5% for 235U and 233Pu, and 10% for 233U. These increases are followed by decreases by about 30% from 3 to 7 MeV. The evidence in support of these variations for 23?J and 239Pu in the energy range up to 3 MeV isn’t strong. The linear fit to the monoenergetic measurements by Krick and Evans (1972) in the range 0.05 to 1.75 MeV imply the following increases in a 1 MeV interval:

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lncreare in total vield in a 1 MeV interval (Krick and Evans) U-233 2.2% (+0.6%) U-235 0.6% (+I .O%) IQ-239 2.0% (*OS%) If these figures could be accepted as applying to the energy range horn 0 to 3 MeV one could conclude that the difference between the thermal spectrum and fast reactor spectrum averaged values for these isotopes is less than about 1%. However, Tuttle didn’t use this conclusion in his evaluation of thermal and fast spectrum values but he averaged them independently. Thus he obtains the following differences between the thermal and fast spectrum values: Difference between thermal and fast snectrum averaged values in Tuttle (I 979) U-233 9.6% (56.5%) U-235 3.2% (*3.7%) Pu-239 0.2% (*6.5%) In the case of 2’9Pu a much larger uncertainty is associated with the thermal vaiue (&6%) than the fast spectrum value (*2.5%) and the uncertainty on the thermal value could be reduced if one had confidence in the energy dependence deduced from the Krick and Evans measurements. In producing the JEF-2.2 evaluations for 235Uand 239Pu Fort and Long (1989) calculated the energy dependence using the theoretical model of Lendel et al (1986). The resulting differences between the thermal and fast spectrum averaged values are then small, about 0.3%. This is in contrast to the differences obtained in summation calculations. Jn their calculations Wilson and England (2002) obtain for 235Ua fast spectrum value 6.3% higher than the thermal value, and for 239Pu a value 12% lower. These results are in contrast with the results of the summation calculations carried out by Mills (1999). He used the JEF-2.2 decay data and fission yields and obtained fast spectrum yields 12% larger than the thermal yields for both ‘35U and 239Pu. These summation calculation results suggest that there are discrepancies in the relationship between thermal and fast spectrum fission product precursor yields. Direct measurements of the energy dependence of yields could help in improving the relationship. We note the work of lsaev et al (2002) analysing the energy dependent measurements of time dependence in terms of the energy dependence of precursor yields. Piksaikin et al (2002~) have made measurements at several energies up to about 5 MeV for 235Uand 237Np. The measurements for 235U at 0.742 MeV and in the range 3.27 to 4.80 MeV show a decreasing yield, the values at 3.27 and 3.80 MeV being about 4% lower than the value at 0.742 Mev, the uncertainties on the individual values being about f 6%. Measurements have been made recently at IPPE of the energy dependence of the total yield in fission of 238U in the energy range l-5 MeV. In the range 3 to 5 MeV the yield is approximately constant but the value at about 1 MeV is about 20% lower, suggesting that the yield increases significantly with increase in energy below about 3 MeV. An alternative explanation is that the value measured at 1 MeV is below the threshold and is different in character from the fission above threshold. The measurements of Krick (1970) and Cox (1974) are more consistent with the yield being constant between about 1.5 and 5 MeV. The earlier measurements of Cox and Whiting (1970) suggest a possible increase with increasing energy but are equally consistent with a constant value in this energy range. An increase in yield with increase in energy is also obtained by the IPPE group ou the basis of a systematics method developed at IPPE. This is based on a correlation of the total yield with the mean halflife of the delayed neutrons. More accurate measurements in the energy range 1.5 to 3MeV would be helpful in resolving this uncertainty. There is another effect which has been studied more recently and this Fort and Long (1989) included a is the variation of the total yield through the resonance region. calculation of this effect in their JEF-2.2 evaluations. More recently Ohsawa and Oyama (1999 and 2002) have calculated the effect for 235U and find variations of up to about 2%, with dips at the energies of

Conclusions

395

resonances. In the calculations made by Fort and Long the variations in vd were anticorrelated with those in vp whereas Ohsawa and Oyama find a positive correlation. Fort et al (2002) consider that their earlier calculations should be reviewed and probably revised. Clearly, measurements of these energy dependent effects would be helpful but difficult to carry out. Broad resolution measurements through the resonance range would be valuable. For 238U we note that the energy dependence given in JENDL-3.2 (also adopted in JEF-2.2) results in a reactor spectrum averaged value about 2.5% below the value in the energy range up to 3.5 MeV (this being constant in the file). The energy dependence in ENDFB-VI results in a reactor spectrum averaged value about 3% lower than the (constant) value in the energy range up to 4 MeV. The energy dependence at present adopted in the evaluated files has a greater effect for 23sU than for 23?J and 239Pu because of the higher mean energy of the fission rate spectrum for 238U. Piksaikin et al (2002b) have made measurements of the time dependence of delayed neutron emission as a function of incident neutron energy for 23sU, 238Uand 239Pu. The energy ranges of the measurements are: 2.85 eV to 5 MeV for 23?J and 239Pu, 1 to 5 MeV for 238U. They calculate the average half-life, CT>, of the precursors and find that this parameter decreases linearly with incident neutron energy, the percentage changes per MeV being: -0.95% + 0.05% per MeV for 235U, - 1.9% + 0.13% per MeV for 239Pu, -1.3% + 0.22% per MeV for 238Uin the range 3-5 MeV. Piksaikin et al (2002a) have also investigated the relationship between total yields (at “fast” energies) and average half-lives and have found these to be correlated for isotopes of one element. The relationship is of the form: vd = exp(a + b.ln) and, for the examples given (Th, U, Pu, Am), vd decreases with increasing values of (r>. It was found in these investigations by Piksaikin et al., that the above expression can be applied to the relationship between the energy dependence of the total delayed neutron yield, vd(E”), and the energy dependence of the average half-life of delayed neutron precursors (E,), in the energy range up to 3 MeV. On the basis of this approach they obtain the following values for the increase in V@,,) in a 1 MeV interval: Increase in total yield in a 1 MeV interval (Piksaikin et al.) U-233 2.50% (*0.85%) U-235 1.50% (+0.96%) Pu-239 4.90% (*1.36%) The variation for 233Uis similar to that measured by Krick and Evans. For ‘35U and 239Puthe variation ,s about 2.5 times larger, although within the range of the standard deviations for 23sU. Piksaikin et al. have preliminary indications from direct measurements which support this correlation based estimate of the energy dependence for 239Pu. More accurate measurements of the energy dependence, as well as studies of the possible variations through the resonance range, are needed to clarify the uncertainties in incident neutron energy dependence. The recommended time dependent data are given in 8 groups, with the same set of group half-lives for all energies and isotopes. The values are given at thermal energy, fast energy and high energy. Piksaikin et al (2002b) point out that the incident neutron energy dependence they find for (r> justifies linear interpolation in energy being used to calculate the group relative abundances for a particular reactor fission rate energy spectrum from the values given at thermal and fast energies.

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4. EVALUATIONS

OF TOTAL DELAYED NEUTRON YIELDS

4.1. Total delaved neutron vield evaluations in the JEF-2.2. ENDF/B-VI and JENDL-3.2 libraries The total yield evaluations for 239Pu and 235U included in JEF-2.2 were carried out by Fort and Long (1989) and used Lendel’s semi-empirical model. The calculated energy derndent data for 235U were normalised to the thermal value recommended by Kaneko et al (1988). For 23 Pu the normalisation was to the fast spectrum value of Tuttle (1979). The second chance, third chance etc. fission were normalised to values derived using the systematics of Waldo et al (198 1). In ENDF/B-VI and JENDL-3.2 a simple form of energy dependence has been adopted for 235U, 238U and 239Pu, corresponding to values for first chance, second chance and third chance fission which vary linearly in energy throughout each of the ranges. This form of energy dependence follows the approach adopted by Tuttle (1979). The data adopted in ENDF/B-VI for 235Uand 239Pu are the ENDF/B-IV evaluations by Cox (1974) and, for 238U, a (1978, unpublished) evaluation by Kaiser and Carpenter. The values are constant in energy below 4 MeV, decrease linearly in energy up to 9 MeV and then remain constant to higher energies. The 238U evaluation has a value below 4 MeV which is close to Tuttle’s (1979) recommended fast spectrum value of 0.0439. Table 1. Delayed neutron yield data in ENDF/B-VI. Energy (eV) U-235 dn yield U-238 dn yield Pu-239 dn yield

1.OE-5 0.0167 0.044 0.00645

4.OE+6 0.0167 0.044 0.00645

9.OE+6 0.009 0.026 0.0043

2.OE+7 0.009 0.026 0.0043

The 235U and 23gPu data in JENDL-3.2 vary linearly between thermal and about 3 MeV whereas the yield data for 238U are constant below 3.5 MeV. The data for 239Pu are Tuttle’s incident neutron energy dependent values (which are not precisely consistent with his thermal and fast spectrum values). One notes that the value for 238Ubelow 3.5 MeV is 9% higher than the value in ENDFIB-VI, whereas the values for 235U and 239Pu at thermal energies are both about 4% lower. The JENDL-3.2 data for 238U have also been adopted in JEF-2.2.

Conclusions

397

Table 2. Delayed neutron yield data in JENDL-3.2.

4.2. A~~measurements studies of Fort et al (2002) and Sakurai and Okaiima (2002) 4.2. I. The scope of the adjustment

- the

studies.

In his study presented in 19?0 D’Angelo analysed the fi~measurements made in a series of SNEAK and ZPR fast critical assemblies, 4 SNEAK assemblies (Fischer, 1977) and 6 ZPR assemblies (M&night, Internal ANL document) to derive improved fast spectrum averaged yields. In 1997 this study was extended by D’Angelo and Filip to include the measurements made in the two MASURCA cores, R2 and ZONA2. The more recent studies by Fort et al have generalised the approach by treating the energy dependence and adjusting the yield values in 5 energy groups. In addition to the systems analysed by D’Angelo and Filip two of the three FCA XIX fast reactor cores (cores -1 and -3) have been included, together with 3 thermal reactor systems (SHE-8, MISTRAL- 1 and MISTRAL-2). The measured /&values have also been revised by Fort et al. In particular the Diven factors used in the derivation of the measured values for the ZPR cores and for the earlier interpretation of measurements made in R2 and ZONA2 have been revised. These are then consistent with the values used in the interpretation of the XIX cores. The spatial fission rate distributions involved in the interpretation of the R2 and ZONA2 measurements have also been revised and are based on calculations made using the ERALIB 1 data set. These distributions are then consistent, in the data used, with the calculated fin values with which the measured values are compared. The uncertainties in the measurements have also been reassessed and the correlations between the uncertainties in the different measurements made in the same core and in different cores have been treated. The ERALIBl data set, which has been used by Fort et al to calculate the fluxes and reaction rates, is a CEA development of a JEF-2.2 based cross section set, adjusted on the basis of an ailalysis of integral measurements. Because the measured’ values are being compared with values calculated using the ERALIBl adjusted cross-section set it is considered that no allowance need be made for uncertainties in the fission rate calculations used in deriving the measured and calculated values of &. All of the calculated values are within f3% of the measured values (or within 1 s.d. of the measured value when the discrepancy is larger than 3%). The comparisons therefore give confidence (at the 3% level) in the use of JEF-2.2 yield data. The adjustments, and the estimates of the accuracy of the adjusted data, depend on the estimated uncertainties in the measured values of fl& in the calculations of relative fission rates and delayed neutron importances, in the unadjusted delayed neutron data and in the energy dependence of the total yields. Different assumptions about the uncertainties could result in different adjustments and associated accuracy estimates. Fort et al have used Lendel’s model to calculate the energy dependence for 23?J and 23?‘u and to estimate the uncertainty in this energy dependence.

A. D’Angelo

398

and J. L. Rowlands

The 5 group values before and after adjustment in the study by Fort et al are as follows: Table 3. Total delayed neutron yields before adjustment (JEF-2.2 data), and the assumed uncertainties adopted by Fort et al.

Group Group Group Group Group

1 2 3 4 5

0- 1OkeV 10 - 500 keV 0.5 - 4 MeV 4-7MeV 7-20MeV

U-235 1.654E-2 I? 3.0% 1.656E-2 + 3.0% 1.68 1E-2 + 4.0% 1.539E-2 f 6.0% 1.127E-2 + 7.0%

U-238 4.8 l OE-2f 6.0% 4.830E-2 f 6.0% 4.809E-2 + 7.0% 4.438E-2 f 9.0% 3.567E-2 + 10.0%

Pu-239 6.47 lE-3 f 4.0% 6.414E-3 + 4.0% 6.579E-3 f 5.0% 6.085E-3 + 7.0% 3.797E-3 f 8.0%

Table 4. Total delayed neutron yields after adjustment and the associated uncertainties. -_____ U-235 U-238 Pu-239 0- 10keV Group I 1.62lE-2 f 1.3% 4.810E-2 f 5.9% 6.495B-3 f 1.7% Group 2 10 - 500 keV 1.663E-2 + 1.6% 4.808E-2 + 5.9% 6.535E-3 + 2.6% 0.5 - 4 MeV Group 3 1.687E-2 I&C 3.5% 4.818E-2 + 2.4% 6.659E-3 -I 4.1% Group 4 4-7MeV 1.538E-2 f 5.9% 4.430E-2 + 8.4% 6.115E-3 f 6.8% 7-20MeV Group 5 l.l27E-2 !I 6.9% 3.544E-2 + 9.8% 3.800E-3 + 7.9% Table 5. Percentage adjustments

Group 1 Group 2 Group 3 Group 4 Group 5

0- 10keV 10 - 500 keV 0.3 - 4 MeV 4-7MeV 7 - 20 MeV

U-235 -2.00% +0.43% +0.33% -0.05% -0.02%

U-238 +o.oo% -0.02% +O.18% -0.18% -0.64%

Pu-239 +0.38% +1.88% +1.21% +0.49% +0.09%

From these five group values we can calculate corresponding thermal and fast reactor spectrum averaged values. The unadjusted spectrum averaged values given in Table 7 are mean values for the systems studied by Fort et al (see the thesis by V. Zammit-Averlant, 1998). Table 6. Group sensitivities for the chosen systems.

I 1+0.4% ) +1.5% / +o.l% 1 +o.l% Average change 1 -2.0% The percentage changes to these spectrum averaged values have been calculated by weighting the percentage adjustments given in Table 5 with the sensitivity coefficients of &r values (for a chosen system) to changes in the group yields, as given by V. Zammit-Averlant in her thesis and, for MISTRAL2, by 0 Litaize (private communication).

Conclusions

399

The choice of fast spectrum system for weighting the 23?J 5 group data has a significant effect on the calculated value of the averaged change. It depends on the sensitivity to the group 1 adjustment, below lOkeV, which is mainly determined by the fit to the thermal spectrum systems (MISTRAL-l and SHE-g). The 0.4% increase in the group 2 value is perhaps partly to compensate for this 2% decrease below 10 keV, which affects several of the fast spectrum systems. We note that the changes, resulting from the adjustments, for the uranium fuelled fast spectrum systems included in the study by Fort et al, are as follows: ZPR U9 +0.4%, SNEAK 9Cl +0.20%; MASURCA R2 +0.09%, FCA XIX-1 -0.77%, ZPR UFeRef -0.31%, these last two systems being fuelled with highly enriched uranium. Such a strong variation in the values seems unphysical and is a consequence of this step change in the yield by about 2.6% at 10 keV. In what follows it is assumed that there is no significant change to the fast spectrum averaged yield for 23?J. The unadjusted and adjusted values calculated in this way are given in Table 7. Table 7. Thermal and fast reactor fission rate spectrum averaged values.

JEF-2.2 Change Adjusted Uncertainties proposed by Fort

U-235 thermal

U-235 fast

0.01654 f 3.0% -2% 0.01621 f 1.3% + 1.8%

0.01658 Ik 3.0% +0.0% 0.01658 f 1.6% I!I 1.9%

U-238 fast 0.0468 + 6.5% +o. 1% 0.0469 + 2.4% + 4.0%

Pu-239 thermal 0.00647 * 4.0% +0.4% 0.00650 f 1.7% + 2.2%

Pu-239 fast 0.00646 f 4.0% +1.5% 0.00656 f 2.6% -k2.1%

These spectrum averaged values depend on the a~sumed@sion rate spectrum for the reactor. For the ,sy.stems studied by Fort et al there is a variation about these JEF-2.2 (unadjusted) value.7 of about M. I% for 235U and ‘3’Pu and a variation of about 21% for 23xU. For the adjusted value.7 the variation i.s larger because of the broad group structure used to calculate the adjustments. The associated uncertainiy estimates are al.70 approximate. In particular the uncertainties of the adjusted value.7 have been calculated without the use of covariance matrices. We should also note that there could be additional sources of uncertainty which should be taken into account and thejgures in the row entitled “Uncertainties proposed by Fort et al” reflect their estimates of the eflects of these additional sources of uncertainty.

We should note that the changes to the 235U, 5 group yield values result in a significant change in the variation of the yield with energy, between thermal and the range 10 to 500 keV, a variation of +2.6%. For 239Puthere is a change from a variation of -0.9% to +0.6%. If we are justified in saying that changes of less than about 0.5% are not significant then we can interpret the results, obtained by Fort ei al, as confirming the 23RUdata in JEF-2.2 (and JENDL-3.2) and also confirming the 235U fast spectrum data and the 23s?u thermal spectrum data. The only changes which are indicated as significant are the 2% reduction in the 235U thermal value and the 1.5% increase in the 239Pu fast spectrum value. The uncertainty estimates given in Table 7 associated with the adjusted values are the values corresponding to the 5 group adjustments given in Table 4. As we have seen above Fort ef al have in most cases increased these uncertainties to allow for other sources and these values are given in the bottom row of Table 7. An even higher value is given by them for the uncertainty in the U-238 yield in a thermal reactor spectrum, f 5.6% (compared with f 4.0% for the average yield in a fast reactor spectrum).

400

A. D’Angelo and J. L. Rowlands

4.2.2. Thermal spectrum averaged values. The change which has been proposed by Fort et al to the 235Uthermal spectrum averaged value is based on the measurements made in the SHE-8 and MISTRAL-l programmes (although some of the fast spectrum systems have a significant sensitivity to the energy range below 10 keV, which is treated as a single energy group, group I).

SHE-8 MISTRAL- 1

Measured 696 789.7

s.d. % 4.6% 1.6%

Calculated 694.2 808.2

(E - C)/C % 0.26% -2.29%

The JEF-2.2 delayed neutron yield evaluation for ?J was normalised at thermal energies to the value of beta recommended by Kaneko et al (1988). This value was based on an analysis of the SHE programme of measurements and had an estimated uncertainty of f1.2%. It is not surprising, therefore, that calculation is in agreement with the value measured in SHE-g. The adjusted yield value depends on the relative weights given to the JEF-2.2 thermal value, (+3.0%), to the SHE-8 measurement, (f4.6%), and to the MISTRAL-l measurement (+_1.6%). This latter experiment has a much higher weight in the fit, resulting in the proposed reduction of 2% in the 23?J thermal value. Confirmation of the need for a lower 23k thermal value is given by the delayed neutron yield adjustment study carried out by Sakurai and Okajima (2002). They included in their study a measurement made in a uranium fuelled thermal reactor core, built in TCA (Nakajima, 1999), together with the benchmark series of fast reactor spectrum systems (MASURCA R2 and ZONA2 and the FCA XIX cores). The analysis was made using the JENDL-3.2 nuclear data library. The thermal spectrum yield for 235U in JENDL-3.2 is 0.01600, which is 3.3% lower than the value in JEF-2.2. Even so, the C/E value for the /?=f measurement in the TCA core is 1.024. In their adjustment study Sakurai and Okajima reduce both the 235U yield (by 0.9%) and the 238U yield (by 3.08%) resulting in a 1.2% improvement in the agreement. The resulting adjusted value of the thermal yield for 23sU is 0.01586 (which is 2.2% lower than the adjusted value obtained by Fort et al). The adjustments made to the JENDL-3.2 yield data have been constrained by the form of the data representation. The data are represented at thermal, 3.3 MeV, 6.9 MeV and 13.5 MeV with a linear The adjustment study includes two uranium fuelled fast dependence between these energy points. spectrum systems, R2 and XIX-l, and the fief values for these systems will have their strongest dependence on the thermal value of the 235Uyield as a consequence of the adoption of this form of energy dependence. The resulting energy variation of the yield, the difference between the thermal and fast spectrum averaged values, is, as a consequence, much smaller than that found in the study by Fort et al. The MISTRAL-2 measurement is the only one for a MOX fuelled thermal spectrum system for which an analysis has been published and it has been included in the adjustment study carried out by Fort et al. This also has a high estimated accuracy.

MISTRAL-2

1 Measured [ 372.5

s.d. % 1 1.6%

1Calculated 1370.7

1 (E - C)/C % ( 0.49%

The adjusted thermal group value for 239Pu, 0.00650 +1.7%, obtained by Fort et al, is based on this result. There is also a dependence on the yield value for 238Uwhich is only marginally changed (+O.l%) in the fit. In addition there is also a significant sensitivity to the 24’Pu yield, which has a relatively large uncertainty.

Conclusions

401

The thermal value for 239Pu obtained in the adjustment study by Sakurai and Okajima is determined by the fast reactor systems included in the study. The thermal value for ‘?u before adjustment is 0.00622 + 6.5% and after adj~tment is 0.00638 f 3.6%, 2.0% lower than the value of 0.00651 f I .7% obtained by Fort et al. The results are essentially consistent. 4.2.3. Fast spectrum averaged values - the UPSURCA and FCA benchmark series of measurements. It is of interest to look at the results for the benchmark experiments as presented by Okajima et al (2002). Table 8. C/E values based on the /&-values calculated by Okajima et al(2002). ZONAZ -349 16 1.7% 42% U8, 48% Pug,

J3.2/J3.2 mod J3.2/ENDF/B-VI

1.008 1.016 1.021 1.028 1.011

XIX-1 742 *24 3.2% 94% u5

1 XIX-2 1 XIX-3 364 251 *9 &4 -..2.5% 1.6% 11% u5, 9% u5, 46% U8, 11%U8, 41% Pl19 77% Pu9

0.995 1.019 0.972 0.999 0.966

The J3.2iJ3.2 mod calculated values are the ones used in the adjusiment study carried out hy Sailurai calculations differ from the first set of values in the delayed neutron spectrum u.wd (ENDFiB-VI data are treatment of the heterogeneiry of the MSURCA cores - a very small e$fect. Tht3; also use earlier values for measured in R2 and ZONAZ (716 _+I6 and 3432 7). hefore the revbions io [he CEA measured values were

and Okajima. The used) and include a the mean & values mode by Fort et al.

The reaction rate calculations have been made using either a data set based on JENDL-3.2 (J3.2) or using ERALIBl (El). These have been combined with the delayed neutron yield data in JENDL3.2, ENDFIBVI or JEF-2.2. Comparing the J3.2/B-VI and the El/B-VI results we see the effects of using a different cross section set to calculate the reaction rates. The results are within about 1% of each other. We recall the fast spectrum averaged yield values:

JEF-2.2 ENDF/‘B-VI JENDL-3.2

U-235 fast 0.01658 0.01667 0.0161

U-238 fast 0.0468 * 0.0429 0.0471 *

Pu-239 fast 0.00646 0.00644 0.00627

f * The delayed neutron data for rrNU in JEF-2.2 were adoptedfro~i JENDL-3.2. The value of0.0468 i.?on averngefbr the corex studied by Fort et al. The value used by Okajima et al, starting from the same energy dependent data, is 0.0471. which corresponds to the 2’XUfission rate spectwm in lhe XIX cores.) It can be seen that the agreement of the &values is generally within about rt3% for the three different yield data sets. The ENDF~-VI yield data set gives larger ,&- values than the JENDL-3.2 data set except for ZONA2 and X1X-2. The larger values of the delayed neutron yields for 235Uand 239Pu in ENDFIB-VI are primarily responsible for this tendency. On the other hand, in the ZONA2 and XIX-2 cores, the larger yield values of ‘3sU in JENDL-3.2 give larger ,!?$values since the contribution of 238Uto the ,& value is

A. D’Angelo and J. L. Rowlands

402

about 45% in these cores. The C/E values obtained using the JEF-2.2 yield data are higher than for JENDL-3.2 because the yield values for 235Uand 239Pu are larger. The pattern of results suggests that reducing the 235U yield in B-VI and JEF-2.2 and increasing the 23sU yield in ENDF/B-VI would result in an improved agreement. We note that the study by Fort et al has indicated that a small increase in the JEF-2.2 23?J fast spectrum yield above 10 keV would improve the overall agreement, but this study has used the measurements made in an additional series of cores (SNEAK and ZPR). It has also used different values for some of the measurements made in the benchmark series of experiments (and, in particular, a higher mean value for the measurement in R2, when account is taken of the form of the covariance matrix) and, furthermore, the increase in group 2 could be a compensation for the 2% reduction in group 1 (below 10 keV). Sakurai and Okajima (2002) have made their adjustment study based on their analysis of the MASURCA (BERENICE) and FCA (XIX) benchmark series of measurements (together with the uranium fuelled thermal spectrum system studied in TCA). They have adjusted the total yield data in the JENDL-3.2 library. The yield data are given at 4 energy points with linear interpolation between these points. Based on the adjusted data of Sakurai and Okajima we calculate the following fast reactor spectrum averaged adjusted values, and percentage changes to the JENDL-3.2 values: Table 9. Fast reactor fission rate spectrum averaged values, based on the work of Sakurai and Okajima, compared with values based on the adjustments calculated by Fort et al.

JENDL-3.2

Change Adjusted Fort et al Difference (%)

U-235 fast

U-238 fast

0.0161 -0.8% 0.0160 + 1.8% 0.01658 + 1.6% 3.6%

0.0471 -3.1% 0.0456 + 3.6% 0.0469 f 2.4% 2.9%

The values are approximate because of the msumptions made about the derive the spectrum averaged va1ue.s. Thb could affect the value.7 for “‘U The uncertainty estimates are abo approximate. The covariance matrices Sakurai and Okajima and these should be used to calculate the uncertainty

Pu-239 fast 0.00627 __ 12.4% 0.00642 + 3.6% 0.00656 I? 2.6% 2.2% choice off&t reactor&ion rate spectrum used to and “‘Pu by about 0. I % and for 23xU by about I o/o. of the adjusted values have also been calculated by in a /$r calculation.

We note that the values corresponding

to the adjusted data of Sakurai and Okajima are lower than those corresponding to the adjusted data of Fort et al. The reasons for these differences lie in the differences in the treatment of the benchmark results, the assessment of uncertainties in the results and the inclusion of the SNEAK and ZPR measurements in the study carried out by Fort ef al. Even though the adjusted yield for 238U obtained by Sakurai and Okajima is a reduction of about 3% relative to JENDL-3.2 (and JEF-2.2) the adjusted value is about 6.3% higher than the ENDFiB-VI value. 4.2.5. The SNEAK and ZPR series of measurements. The additional uranium fuelled cores included in the studies by Fort et al are given in the following Table together with the two benchmark experiments (using the average of the measured values calculated by Okajima et an:

Conclusions

403

Table 10. Uranium fuelled fast spectrum systems.

ZPR UFe Leak

For these uranium fuelled cores there is a very good agreement for both the JEF-2.2 and ENDFBVI calculated values. The lower yield value in 238U in ENDFBVI gives the somewhat lower value for U9. The values of C/E for the two benchmark experiments, R2 and XIX-l, are higher than for the earlier measurements in SNEAK and ZPR, implying lower measured values of &in the benchmark cores. *Note, however, that the mean measured value for R2 calculated by Fort et al (using a different method to derive the individual measured values and uncertainties) is 2.6% higher. The fast spectrum averaged yield for 23?l is 2.9% lower in JENDL-3.2 than in JEF-2.2. The further reduction proposed in the JENDL-3.2 adjustment study is probably a consequence of the inclusion of the thermal spectrum measurement. There is no evidence from the fast spectrum measurements of a need to reduce the value by 0.8%, (noting also that the JENDL-3.2 adjustment study indicates a 3.1% decrease in the 238U yield value). Similarly there is no evidence from these results for an increase in the JEF-2.2 yield value for 23sIJ. In fact a reduction in the JEF-2.2 value would be more consistent with the FCA XIX-l measurement. However, the standard deviation is larger than the discrepancy in this case. There is no evidence to suggest that the discrepancies are energy dependent (other than the difference between the fast and thermal spectrum averages). There are some significant differences between the values of fief measured by the different groups participating in the benchmark experiments and this could indicate that the uncertainties on individual measurements should be increased. This would affect the relative weighting given to the benchmark experiments and the measurements made in the ZPR and SNEAK cores because only one measurement was made in each of the ZPR and SNEAK cores. For the additional plutonium fuelled core, ZPR PuCSS, there is also a good agreement for the JEF-2.2 and ENDFBVI yields. Again there is a tendency for the benchmark C/E value to be higher than for the ZPR measurement, and thus for the &rvalue measured in the benchmark core to be smaller. Table 11. Plutonium fuelled fast spectrum systems. Core

Relative contributions

ZPR PuCSS Benchmark XIX-3

98% Pu9 9%U5, 1 l%US, 77% Pu9

For the mixed plutonium-uranium

to &

Measurement s.d.(%) 2.3%

fuelled cores the El/JEF-2.2

EI/JEF-2.2 C/E values 0.993 l.tilO

El/B-VI C/E values 0.989 1.001

and El/ENDF/B-VI

/

results are as follows:

A. D’Angelo and .I. L. Rowlands

404

Table 12. Mixed Pu-U fuelled fast spectrum systems. COK SNEAK 7A SNEAK 7B SNEAK 9C2 ZPR CRef ZPR RSR Benchmark ZONAZ Benchmark XIX-2

This C/E valur for XIX-

Relative contributions

to &

Measurement s.d.(%) 8% U5,51% U8,39%Pu9 2.8% I l%U5, 59%U8, 28%Pu9 2.8% 4.6% 2.2% 2.2% I .7% 2.5% - Vl value

EI/JEF-2.2 C/E values 0.98 1 1.020

El/B-VI C/E values 0.947 0.977 0.923 0.953 0.944 0.966 (0.985)*

There is again good agreement for the JEF-2.2 yield data whereas there is strong evidence that the 23xU yield in ENDF/B-VI is too low. It is probably the measurements made in these SNEAK and ZPR cores which have resulted in the higher value for the yield in 238Ucalculated by Fort et al and the increase in the yield for ‘39Pu. Again there is a tendency for the C/E values for the benchmark measurements, ZONA2 and X1X-2, to be higher than those for the SNEAK and ZPR measurements. 4.3. A summary of recommended thermal and fast spectrum averaged vield values In Table 13 we compare thermal and fast spectrum averaged values of the delayed neutron yields derived from various sources. Following the values calculated from the data in JEF-2.2, JENDL-3.2 and ENDF/BVI the values recommended by Tuttle (1975 and 1979) and by Blachot et al (1990) are given. These are based on the direct measurements of total yields. It is not always clear for what mean energy the fast spectrum values given in an evaluation are defined. The fast reactor spectrum averaged values for 23?J and 239Pu (given above, for the evaluated data libraries) correspond to a mean energy of about 200 keV, but there is a wide variation in the mean energies of the different systems included in the adjustment studies. Also included in the Table are the fast reactor spectrum averaged values obtained by D’Angelo (1990) in an integral measurement adjustment study made to fit the SNEAK and ZPR measurements. The value obtained by Kaneko et al (1988) for 235U thermal, on the basis of the SHE integral measurements, is also given (beta = 0.00677 * 0.00008, and assuming vt = 2.4367 f 0.0005). This has a standard deviation of 1.2%. Some recent measurements of total yields have also been included in Table 13. These are the measurements made by Piksaikin et al, IPPE, (1997), Parish et al, Texas A+M, (1997), and Borzakov et al, Dubna, (2000) (the quoted values being based on these measurements with an adjustment for differences in energy so as to relate to 200 keV). Finally the table includes the values derived here from the adjusted data obtained in the studies carried out by Fort et al and by Sakurai and Okajima. Both adjustment studies, that by Fort et al and that by Sakurai and Okajima, have resulted in yield values for 238Usubstantially higher than the ENDF/B-VI data (9.3% k 2.4% and 6.3% + 3.6% higher, respectively), the weighted average value being 0.0465. This has been chosen as the recommended value. Reductions to the ‘35U thermal yield value are proposed both by Fort et al and by Sakurai and Okajima, based on their analyses of the MISTRAL-l and the TCA measurements, respectively. In deriving an average of these adjusted values we have also included the higher value derived by Kaneko et al (1988) on the basis of the SHE programme of measurements. (This has been given a low weight in the adjustment study carried out by Fort et al and has not been taken into account in the study made by Sakurai and Okajima.) In this way we get an average yield of 0.0162. We note that this is consistent with the yield measurement made by Parish (1997), who obtained the value 0.0159 f 2.5%. The

Conclusions

difference

between

the values

obtained

405

by Fort et al and by Sakm-ai and Okajima

for the fast reactor

spectrum yield in 23?J is larger, 3.6% (the values being 0.01658 + 1.6% and 0.0160 I!I 1.8%, respectively). This could be partly because of the independent evaluation of the R2 and ZONA2 measured &values and associated uncertainties in the study by Fort et al and the use of an earlier interpretation of the measured values in the adjustment study by Sakurai and Okajima. The recommended value is the weighted average, 0.0163. Table 13. Thermal and fast reactor spectrum averaged values.

Piksaikin (1997) Parish (1997) 0.0159 f2.5% Borzakov( 1997) Piksaikin (2002) ____ Sakurai and 0.01586 + 1.8% Okajima (2002) Fortetal*** 0.01621 f 1.3% (2002) Recommended values Percentage difference from Tuttle (1979)

0.0168 +S%** 0.0167 f4.8% 0.00686*5%

0.0160 f 1.8%

~~ ~~ 0.0461 + 3.9%** 0.0456 f 3.6%

0.00638 + 3.6%

0.00642 f 3.6%

0.01658 + 1.6%

0.0469 + 2.4%

0.0065 1 + 1.7%

0.00656 + 2.6%

0.0162

0.0163

0.0465

0.00650

0.0065 1

0%

-2.6%

+5.6%

43.4%

13.2%

(* The delayed neutron data for “‘U in JEF-2.2 Here adoptedji-om JENDL-3.2. The value of0.0468 is an average for the cores studied by Fort et al. The value used by Okajima et al, starting from the Same energy dependent data, is 0.0471. which is the average value for the FCA XX cores.) (** The “‘Ufast value quotedfor Piksaikin et al (1997) is the value meautred at 1.165 MeV (0.01709) reduced by 1.9% on the assumption of a rate of increme of 2% per MeV below thb energ-y (Tuttle’s estimate of the variation). The “‘l_J value of Pibaikin et al (2002~) is an average for the range 3-5 Me V) (*** The uncertainties given here are relative and do not take into account allsources qf‘uncertainty.)

The & measurement made in MISTRAL-2 gives confidence in JEF-2.2 calculations made for MOX fuelled~thermal reactor systems. The thermal yield value for 239Pu obtained by Fort et al is 0.0065 1 + 1.7%. The thermal yield value obtained in the adjustment study of Sakurai and Okajima, 0.00638 + 3.6%, is determined by the fast reactor systems included in the study. Their value is 2.0% lower than the value obtained by Fort et al. but is essentially consistent with the unadjusted JENDL3.2 value of 0.00650, which has been chosen as the recommended value. The fast reactor spectrum averaged yield values derived for 239Pu from the results of the two adjustment studies, 0.00656 + 2.6% (Fort et al) and 0.00642 f 3.6% (Sakurai and Okajima) differ by 2.2%. The recommended value is the weighted average, 0.0065 1.

406

A. D’Angelo and .I. L. Rowlands

The uncertainties given in the Table for the adjusted values corresponding to the 5 group data of Fort et al are not the final uncertainties proposed by Fort et al for the spectrum averaged values. They have increased the uncertainties (in most cases) to take account of other contributions to the overall uncertainty in the derived yield values. Sakurai and Okajima have given a covariance matrix for their adjusted data. Rather than derive estimated uncertainties for the recommended values it is proposed here simply that an uncertainty figure be given for the values of &,r calculated using these yield values. It is considered that using these recommended yield values an accuracy off 3% (1 s.d.) will be achieved in ,B& calculations for the major actinides in conventional reactors (to be combined with any additional sources of uncertainty due to relative fission rate and fission rate distribution calculations and calculations of the relative importances of delayed neutrons). It is interesting to recall the recommendations for the three major isotopes in thermal and fast reactor spectra made by Tuttle in 1979 (based on an evaluation of the measurements of total yields). The values recommended here are 0% to 3% smaller than Tuttle’s values for 235U, 3% to 4% larger for 239Pu and 5.6% larger for 2?J. Tuttle considered the possibility of a dependence on the chemical form of the fissioning isotope, with the yield being higher for an oxide fuel than for a metal fuel. This has not been examined further in the more recent studies. 4.4. The accuracy of &calculations

made for conventional

reactors using the recommended

yield data

The target accuracy which has been proposed for &calculations is k 3% (1 s.d.). We examine in the following paragraphs the reasons why we consider this target to be met for conventional thermal and fast reactors fuelled with uranium or mixed uranium-plutonium. It is more clearly met for fast reactors than for thermal reactors because there are fewer measurements of &available for validating the calculations for thermal systems. For uranium fuelled thermal spectrum systems three measurements (or programmes of measurement in the case of the SHE programme result) have been used to validate calculations, SHE-S (which is representative of the SHE programme), MISTRAL-l and the TCA uranium fuelled core. Using the recommended data we estimate the discrepancies between calculation and measurement (and the standard deviations of the measurements) to be: -2.2% t 1.2% (the s.d. of the mean value derived from the programme) SHE-8 MISTRAL-l +0.6% f 1.6% TCA (U mel) +3.2% f 2.2% The discrepancy between the yield data derived from the SHE programme and the TCA measurement needs to be understood. The discrepancy for the TCA measurement is beyond the 3% target. For MOX fuelled cores we have a direct calculation only for MISTRAL-2. thsdiscrepancy is: MISTRAL-2 -0.5% + 1.6%

Using the recommended data

It is reported that for the Uipu fuelled core studied in TCA there is agreement between measurement and the JENDL-3.2 calculation. The 239Puyield in JENDL-3.2 is 4.3% lower than the value recommended here. The discrepancy in the &value will depend on the fractional contribution of 239Pu,but the discrepancy could be -3%.

407

Conclusions

More measurements on thermal systems, and analyses of existing measurements, required degree of confidence in calculations for thermal systems.

are needed to give the

For fast spectrum systems there are many more measurements and the measurements are more consistent. The values of &rcalculated by Fort et al using JEF-2.2 yield values are within I s.d. of the measurement for all excepting 3 of the 19 fast spectrum measurements treated, and the measurement uncertainty is less than f 3% for most measurements. Relative to JEF-2.2 the recommended fast spectrum yields are reduced by 1.7% for 235U, reduced by 1% for 238U and increased by 0.8% for 239Pu. There is also the trend for the benchmark measurement to give values about 2 % lower than the SNEAK and ZPR series of measurements. We also recall that for R2 the measured value derived by Fort et al is about 2.6% hi her 4 than that derived by Okajima et al. We conclude that for fast spectrum systems fuelled with ?J, 23 U and 239Puthe &fvalue calculated using the recommended yields will have uncertainties of between f 2% and Y!z 3%.

5. TIME-DEPENDENT DATA The paper by Spriggs, Campbell and Piksaikin (1999) describes the work done to produce improved representations of the time dependence of delayed neutron emission. A key requirement for the new form of representation was that the time constants of the three longest lived dominant precursors should be explicitly represented, this being considered to be essential for an accurate representation of these longer periods in reactor kinetics. An 8 time group representation has been found to be satisfactory, an advantage of this new representation being that the time constants of the groups are the same for all isotopes and energies. Recommended data are provided for thermal and fast reactor spectra. Piksaikin et al (2000a) have measured the time dependence and studied the systematics of average half-life values. These results provide a useful guide when selecting the recommended measurement of the timedependent data. In particular, these measurements, and studies of reactor kinetics, support many of the Keepin’s sets of time-dependent data. The time-dependent data included in ENDF/B-VI are not supported. These were based on precursor summation calculations (Brady and England, 1989). The time-dependent data included in JEF-2.2 for 235U and 239Pu are also unsatisfacto~, being a combination of the Brady and England data and other sources (in fact these data were not intended for use in kinetics calculations but were linked to other items of data included in the files from other sources). Following a comprehensive review of all the measured data a selection was made. The measurements, associated group analyses, used to derive the recommended 8 group yields are as follows: U-235 U-235 U-238 Pu-239 Pu-239

Thermal Spectrum, fast: 0.624 MeV, Fast Spectrum, Thermal Spectrum, Fast Spectrum,

6-groups, 8-groups, 6-groups, 6-groups, s-groups,

and

Keepin et al. ( 1957) Piksaikin et al. (1997) Keepin et al. (1957) Keepin et al. (1957) Besant et al. (1977)

We note that for thermal reactor applications the recommended

data sets are based on Keepin et al (1957).

Since the evaluation work of Spriggs, Campbell and Piksaikin (1999) was completed there have been more measurements of time dependence and we note that the thermal spectrum data measured by Piksaikin et al (2002b) for 239Pu have much lower uncertainties than Keepin’s relative abundances and periods, the mean half-lives being the same.

408

A. D’Angelo and J. L. Rowlands

To obtain the 8 group relative abundances for a particular fission rate spectrum Piksaikin et al (2002b) recommend the assumption of a linear dependence in energy relating the thermal and fast spectrum relative abundances.

6. THE ENERGY SPECTRA OF DELAYED NEUTRONS Since the work of Brady and England (I 989), further measurements have been made and these have been analysed by Campbell and Spriggs (2000, 2002) to produce energy spectra in the Hansen and Roach 16 energy group structure, for each isotope, in each of the 8 time groups. Table 14. Mean energies of the 8 group spectra (in keV) for the major actinide isotopes. (Data taken from LA-UR-99-4000)

We note that the differences between the mean energies for different groups are quite significant but the differences between the mean energies for different isotopes are small. It is considered that uncertainties in the energy spectra are no longer a significant factor in the calculation of /!&values. In their calculations Okajima et al (2002) used two different sets of spectra, the ENDF/B-VI spectra and the spectra in JENDL-3.2 (based on the summation calculations of Saphier, 1977). The differences were less than 1%.

7. CONCLUSIONS AND RECOMMENDATIONS The energy dependence of total yields is believed to be small, the difference between thermal reactor and fast reactor spectrum averaged values being at most a few percent. Fission product precursor summation calculations give much larger differences and the reason for this needs to be understood. The uncertainty about the possible variations through resonances also prevents a clear conclusion being reached about the relationship between thermal and fast spectrum yields. More work is needed to define the energy dependence of total yields. However, very accurate relative measurements (*l%) will be required for the major actinide isotopes. For the secondary isotopes the uncertainties are larger and more measurements having a lower precision would be useful. For the more exotic systems which are being studied at the present time, with contributions from intermediate energies being significant in some designs, more information could be required about the energy dependence at Mev energies. For the reactor systems for which &measurements have been made, and used as the basis for the adjustment studies summarised here, the sensitivity to these higher energies is too small for useful high energy information to be obtained.

Accurate relative measurements of the energy dependence of total yields, and of the fractional yields used to represent time dependence, would enable the systematics of the interrelationships to be explored in more detail. The JEF-2.2 and JENDL-3.2 total yield data give satisfactory results for the systems studied, there being no strong indication of a need to change them. It is considered that an accuracy of about +3% (1 s.d.) will

Conclusions

409

be obtained in fl&calculations made using these data (provided that the relative fission rate and fission rate distribution calculations are not introducing a significant error). There is very little gain in accuracy from the proposed adjustments. The & values calculated using ENDF/B-VI yields for the SNEAK and ZPR MOX melled cores are particularly low, although me values calculated for the benchmark series of cores are within about + 3% of the measured values. The low values calculated for the MOX fuelled cores are considered to be a consequence of the lower yield for 238Uin ENDFB-VI. There is a tendency for the measurements made in the benchmark series of cores to yield lower values of /$f than the measurements in the SNEAK and ZPR cores. The adjustment study made by Sakurai and Okajima, based on the benchmark series alone, has resulted in smaller yield values than the study by Fort et al which has included the SNEAK and ZPR measurements. However, we note that the uncertainties estimated for the SNEAK and ZPR measurements in the study by Fort et al are comparatively low when compared with those of the benchmark series, which are based on several independent measurements made in each core. For this reason the adoption of an average of the adjusted values based on the two studies is suggested. It is considered that using these averaged values an accuracy of * 3% (1 s.d.) will be achieved in /&r calculations for conventional thermal reactors and + 2% to f 3% for fast reactors fuelled with the major actinide isotopes (to be combined with any additional sources of uncertainty due to relative fission rate and fission rate distribution calculations and calculations of the relative importances of delayed neutrons, although the uncertainties arising from the use of ERALIB-1, JENDL-3.2 and ENDF/B-VI crosssection sets appear to be negligibly small). Summary of recommended U-235 thermal 0.0162

total yield values.

1U-235 fast 10.0163

1U-238 fast 10.0465

) Pu-239 thermal 10.00650

1 Pu-239 fast 10.00651

Based on these spectrum averaged values energy dependent values have been derived, suitable for inclusion in nuclear data library files. The data are given in the Appendix. The use of the 8 group representation of time dependence proposed by Spriggs, Campbell and Piksaikin, with the half-lives of the three predominant long-lived precursors being explicitly treated, is recommended as having a better physical basis than the traditional 6 group representation of Keepin. The relative yields and energy spectra derived by them are also recommended. Effects which have been considered in the past but which have not been discussed here include the possibility of chemical binding effects influencing delayed neutron emission and the role of (y,f) and (y,n) reactions associated with the delayed gamma emission. ACKNOWLEDGEMENTS The authors would like to thank the members of the NEA WPEC Subgroup on Delayed Neutron Data, and in particular Eric Fort, Robert Jacqmin, Shigeaki Okajima, Vladimir Piksaikin and Gregory Spriggs, for their valuable contributions and comments.

410

A. D’Angelo and J. L. Rowlands REFERENCES

Blachot J., Brady M.C., Filip A., Mills R.W. and Weaver D.R. (1990) Status of Delayed Neutron Data - 1990. Report NEACRP-L-323. NEANDC-299 “U”. OECDNEA. Borzakov S.B., Panteleev T.S., Pavlov S.S., Ruskov I., Zamiatnin Yu.S. (2002). Paper published in the present volume of Prog. Nucl. EnerQ. Brady M.C. and England T.R. (1989) Delayed Neutron Data and Group Parameters for 43 Fissioning Systems. Ntrcl. Sci. and Eng. 103, 129. Campbell J.M. and Spriggs G.D. (1999a), Delayed Neutron Spectral Data for Hansen-Roach Energy Group Structure. Los Alamos Technical Report LANL 99-2988. Campbell J.M. and Spriggs G.D. (1999b), g-Group Delayed Neutron Spectral Data for Hansen and Roach Energy Group Structure. Los Alamos Technical Report LANL 99-4000 (1999) and in the present volume of Prog. Nucl. Energy. Charlton W., Parish T., Raman S., Shinohara N. and Andoh M. (1997), Measurements of Delayed Neutron Decay Constants and Fission Yields from 23?J, 237Np, 24’Am, and 243Am. Proc. ht. Conf: on Nucl. Data for Sci. and TechnoL, Trieste (May, 1997). Cox S.A. and Whiting D.E.E. (1970), ANL-7610 p45 Cox S.A. (1974), Delayed neutron data - review and evaluation. ANLRVDM-5. D’ Angelo A. (1990), A Total Delayed Neutron Yields Adjustment Using ZPR and SNEAK Effective-Beta Integral Measurements. Proc. ht. Conf on the Physics of Reactors - Physor90, April,1990, Marseille, France, Vol. 1, Session III, pp. 84-94. D’Angelo A. (2002), Overview of the Delayed Neutron Data Activities and Results Monitored by the NEAWPEC Subgroup 6. Paper in the present volume of Pro:. Nucl. Energy. England T.R. and Rider B.F. (1994) Evaluation and Compilation of Fission Product Yields. Los Alamos National Laboratory Report, LA-UR-94-3 106 (Oct. 1994). Fischer E. (1977), Integral Measurements of the Effective Delayed Neutron Fractions in the Fast Critical Assembly SNEAK. Nucl. Sqi. and Eng. 62, 105-l 16. Fort E. and Long P. JEF/DGC-282 (1989) and Fort E., Filip A. and Long P. JEF/DOC-286 (1989). Fort E., Zammit-Averlant V., Salvatores M., Filip A. and Lebrat J-F. (2002). Recommended values of the Delayed Neutron Yield for U-235, U-238 and Pu-239. Paper in the present volume of Prog. Nucl. Energy. Isaev S.G., Piksaikin V.M., Kazakov L.E. and Roshchenko V.A. (2002) Delayed Neutrons as a Probe of Nuclear Charge Distribution in the Fission of Heavy Nuclei by Neutrons. Paper in the present volume of Prog. Nucl. Enercr KanekoY., Akino F. and Yamane Y. (1988) J. Nucl. Sci. Technol. 25 (9) pp 673-681. Sept. (1988). Keepin G.R. (1965), Physics of Nuclear Kinetics. Addison-Wesley Press. Krick MS. and Evans A.E. (1972) Nucl. Sci. and Eng, 47 3 11. Lammer M. (2000), Compilation and Evaluation of Fission Product Yield Nuclear Data. Final Report of an IAEA Coordinated Research Project. IAEA-TECDGC-1168, IAEA Vienna. Lendel A. et al. (1986), Determining delayed neutron yields by semi-empirical formulas. Atomnaya Energiya, 61, ~215-216 (1986). Litaize 0. and Santamarina A. (2001), Experimental Validation of the Effective Delayed Neutron Fraction in the MISTRALI-UOX and MISTRAL2-MOX Homogeneous Cores. JEFDGC-872 (May 2001). Mills R. W. (1999) Delayed Neutron Emission. Course notes for the 1999 Frederic Joliot - Otto Hahn School (Spring session) on ‘Neutron Data Measurements and Evaluation”, Geel, Belgium. Nakajima K., (1999), Measurements of the effective delayed neutron fraction for the TCA cores. Proc. Specialkts Meeting on Delayed Neutron Nuclear Data, JAERI, Tokai, Japan, pp 37-42, JAERI-conf 99-007, INDC(JPN)184/U , January (1999). Ohsawa T. and Oyama T. (1999), Possible Fluctuations in Delayed Neutron Yields in the Resonance Region of U235. Proc. Specialists’ Meeting on Delayed Neutron Nuclear Data, JAERI, Tokay, Japan, pp 43-48, JAERI-conf 99-007. lNDC(JPN)- 184/U and in the present volume of Prog. Nucl. Energy. Okajima S., Sakurai T., Lebrat J-F., Martini M. and Zammit-Averlant V. (2002), Summary on International Benchmark Experiments for Effective Delayed Neutron Fraction (peff). Paper in the present volume of Prog. Nucl. Energy. Piksaikin V.M.. Balakshev Ju.F., Isaev S.G., Kazakov L.E., Korolev G.G., Kuminov B.D., Semenova N.N., Sergachev AI., Tarasko M.Z. (1997), Measurements of Periods, Relative Abundances and Absolute Total Yields

41 I

Conclusions

of Delayed Neutrons from Fast Neutron Induced Fission of 235Uand *“Np. Proc. Int. Co& on Nucl. Datafbr Sci. and Technol., May, 1997, Trieste (Italy). Piksaikin V.M., Isaev S.G. (1998), Correlation Properties of Delayed Neutrons f?om Fast Neutron Induced Fission. Published by the IAEA Nuclear Data Section, Report INDC(CCP)-415, October 1998. Piksaikin V.M., Isaev S.G. and Goverdovski A.A. (2002a), Characteristics of Delayed Neutrons: Systematics and Correlation properties. Paper in the present issue of Prog. Nucl. Energy. Piksaikin V.M., Kazakov L.E., Isaev S.G., Tarasko M.Z., Roschenko V.A., Tertytchnyi R.G., Spriggs G.D. and Campbell J.M. (2002b), Energy dependence of relative abundances and periods of delayed neutrons from neutron induced fission of 235U, *‘*II, 239Pu in 6- and 8-group model presentation. Paper in the present volume of Prog. Nucl. Energy. Piksaikin V.M., Isaev S.G., Kazakov L.E., Korolev G.G., Roshchenko V.A., Goverdovski A.A., Tertytchnyi R.G. (2002~) Experimental studies of the absolute total delayed neutron yields thorn neutron induced fission of 238U in the energy range l-5 MeV. Paper in the present volume of Prog. Nucl. Energy. Sakurai T. and Okajima S. (2002), Adjustment of total delayed neutron yields of U-235, U-238 and Pu-239 in JENDL-3.2 using benchmark experiments on effective delayed neutron fraction. J. Nucl. Sci. Technol. (Jan. 2002). Saleh H.H., Parish T.A., Raman S. and Shinohara N. (1997), Measurements of Delayed Neutron Decay Constants and Fission Yields l?om *“U, 237Np,24’Am, and 243Am.Nucl. Sci. and Eng. 125,5 1. Spriggs G.D. and Campbell J. (1998). A Summary of Measured Delayed Neutron Group Parameters. Los Alamos Technical Report LA-UR-98-918 and in the present volume of Prog. Nucl. Energv. Spriggs G.D., Campbell J. and Piksaikin V.M. (1998), An R-Group Delayed Neutron Model Based on a Consistent Set of Half-Lives. Los Alamos Technical Report LA-UR-98-1619 and in the present volume of Prog. Nucl. Enere. Tuttle R.J. (1975), Delayed Neutron Data for Reactor Physics Analysis. Nucl. Sci. and Eng. 56, pp. 37. Tuttle R.J. (1979), Delayed Neutron Yields in Nuclear Fission. Proc. Consultants Meeting on Delayed Neutron Properties, Vienna, March 26-30, 1979; INDC(NDS)-107/G+Special, p.29, IAEA Vienna. Waldo R.W., Kamm R.A., and Meyer R.A. (1981), Delayed neutron yields: time dependent measurements and predictive model. Physical Review C, 23, n3, 1113-l 127 (1981). Wilson W.B. and England T.R. (2002). Paper in the present issue of Prog. Nucl. Energy. Zammit-Averlant V. (1998), Validation Integrale des Estimations du Parametre Beta Effectif pour les Reacteurs MOX et Incenerateurs. These pour obtenir le grade de Docteur, UniversitC d’AIX-Marseille.

APPENDIX.

RECOMMENDED

ENERGY

DEPENDENT

TOTAL YIELD VALUES

On the basis of the recommended spectrum averaged values energy dependent data have been derived, suitable for inclusion in the nuclear data libraries. Interpolation in the tabular values of (E, vd) is linear in energy. There are many ways that a corresponding set of energy dependent data could be chosen and it must be recognised that the following sets of values are not unique ways of representing the data. In the case of 238U the JENDL-3.2 (=JEF-2.2) data have been chosen as the starting point values because these provided the better agreement with the integral measurements. A small adjustment has been ma ;e to the values in the threshold range, a reduction of 0.7% to the values at lOE-5 eV, 3.5 MeV and 7 MeV. The resulting values are as follows (energy in eV; yield): 1.000000-5 2.000000+7

1 4.780000-2 1 1.880000-2

13.500000+6 1

14.780000-2

17.000000+6

13.570000-2

In the case of 235U and ‘39Pu the approach has been to assume a variation linear in energy below 1 MeV defined by values at lOE-5 eV, 200 keV (a point representative of the fast spectrum average value) and 1 MeV. Since the JEF-2.2 evaluations of Fort et al are the most recent these have been adopted for the data above the 1 MeV point. However, a simplification of the data is considered justified because of the uncertainties in the values. The number of significant figures has been reduced to 3 and the number of energy points has also been reduced.

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The proposed data for 23sU are as follows. Based on the thermal value (lOE-5 eV) of 0.0162, the fast spectrum value (200 keV) of 0.0163, a value of 0.0164 at 1 MeV and the JEF-2.2 data at 3.9 MeV and above (simplified) we have: -1.000000-5 3.900000+6 7.000000+6 2.000000+7

1.620000-2 1.670000-2 1.100000-2 7.100000-3

2.000000+5 5.700000+6 1.000000+7

1.630000-2 1.320000-2 1.100000-2

1.000000+6 6.000000+6 1.200000+7

1.640000-2 1.240000-2 8.900000-3

The value at 1 MeV has been chosen to give an energy dependence between thermal and 1 MeV which is more consistent with the Krick and Evens data, the variation being 1.2% between thermal and 1 MeV and 0.6% per MeV between 1 and 3.9 MeV (the Krick and Evans variation being 0.6% +I- 1.0% per MeV). The variation between thermal and 200 keV is the much larger value of 3% per MeV but this is affected by the number of significant figures used to represent the values. The proposed data for 239Pu are as follows. Based on the thermal value (lOE-5 eV) of 0.00650, the fast spectrum value (200 keV) of 0.0065 1, a value at 1 MeV of 0.0066 1 and again with the JEF-2.2 data at 2.4 MeV and above (simplified) we have: 1.oooooo-5 2.400000+6 6.500000+6 1.800000+7

6.500000-3 6.690000-3 3.900000-3 3.000000-3

2.000000+5 4.000000+6 1.000000+7 2.000000+7

16.5 10000-3 6.550000-3 3.780000-3 2.800000-3

1.000000+6 5.500000+6 1.200000+7

6.6 10000-3 5.140000-3 3.000000-3

The value at 1 MeV has been chosen to give a variation between 200 keV and 1 MeV more consistent with the Krick and Evans data (which gives a variation of 2% f 0.5% per MeV). With the value 0.00661 at 1 Mev the energy variation is 1.9% per MeV from 200 keV to 1 MeV and 0.9% per MeV between 1 and 2.4 MeV, the variation being 1.2% per MeV between thermal and 2.4 MeV.