Nuclear Data Needs for Fast Reactors
Go Chiba
Japan Atomic Energy Agency
e-mail:chiba.go@jaea.go.jp

In the present paper, we show that the neutronics parameter uncertainties expectedin current design studies of fast reactors are reasonable when both diﬀerential data andintegral data are taken into consideration. This conclusion is based on an assumptionthat cross section covariance is properly evaluated. We attempt to verify the cross section
covariance of JENDL-3.3 with the integral data, which were obtained at critical assemblies
at Los Alamos National Laboratory. As a result, we suggest that uncertainty of P1
coeﬃcient of elastic scattering cross sections of U-238 seems to be underestimated.

IIntroduction

Various researches on nuclear data for fast reactor applications have been carried out
until now. Currently, targets of nuclear data researches for fast reactor applications shift
to improvement of the nuclear data quality of minor actinides and ﬁssion products. In
the present paper, we will discuss necessities of nuclear data researches for fast reactor
applications except for those on minor actinides and ﬁssion products, and attempt toobtain its conclusion.

IINuclear data needs for fast reactors‘Nuclear data needs for fast reactors’ are motivations to improve the prediction accuracies for neutronics parameters of fast reactors. Table 1 shows uncertainties in neutronics
parameters with 1σ reliability, which are expected in the current design studies for fastreactors. These uncertainties are composed of uncertainties induced by nuclear data andnumerical simulations for neutron transport.
Before we discuss a necessity to reduce these uncertainties, we have to show that theseuncertainties are reasonable. This is the main target of the present paper. The necessity
to reduce uncertainties is a future topic.
Neutronics parameter uncertainties induced by nuclear data uncertainties can be estimated using covariance data given in nuclear data ﬁles and sensitivity coeﬃcients. Table
2 shows an example of this estimation for a 1,500MWe fast reactor(1). This result shows
Table 1: Neutronics parameter uncertainties expected in fast reactor design studies

Criticality
Sodium-voided reactivity
Doppler reactivity

2006 Symposium on Nuclear Data

Uncertainties (%)
0.4
7.5
7.5

SND2006-IV.01-1that the current nuclear data satisﬁes the expectation for prediction accuracies of thesodium-voided reactivity and the Doppler reactivity. However, uncertainty in criticality
is much larger than the expectation. Table 3 shows the component-wise uncertainties incriticality. It is desirable to improve nuclear data for such nuclide and reaction, if possible.
It has been shown above that we cannot satisfy the expectation of prediction accuracies
of neutronics parameters in the current design studies only with the diﬀerential data,
which are information on evaluated nuclear data ﬁles. Hence, we have utilized also theintegral data, which are, for example, multiplication factor or spectrum indices obtainedat critical assemblies or power reactors via the cross section adjustment technique basedon the Bayesian theory. Table 4 shows neutronics parameter uncertainties when using
both the diﬀerential and integral data. It is shown that the expectation in the design
studies is satisﬁed using these information.
We have shown above that the uncertainties expected in the current design studies
are reasonable. However, it should be noted that the above conclusion is based on thefollowing assumptions:• Uncertainties induced by numerical simulations for neutron transport are ‘properly’estimated.
• Covariance data for nuclear data are ‘properly’ estimated.
The current numerical simulations for neutron transport are based on the deterministic
Table 2: Nuclear data-induced neutronics parameter uncertainties
Uncertainties (%)
Criticality
1.0
Sodium-voided reactivity
6.0
Doppler reactivity
8.0

Table 3: Nuclide- and reaction-wise uncertainties in criticality

Pu-239, χ
Pu-239, (n,f)
U-238, (n,n’)
Fe, (n,n’)

Uncertainties (%)
0.40.50.3
0.5

Table 4: Nuclear data-induced neutronics parameter uncertainties with diﬀerential andintegral data

Criticality
Sodium-voided reactivity
Doppler reactivity

2006 Symposium on Nuclear Data

Uncertainties (%)
0.26
4.0
7.0

SND2006-IV.01-2

theory. Hence, it is not easy to quantify uncertainties induced by numerical simulations.
Especially, it is diﬃcult to quantify a correlation between the uncertainties for criticalassemblies and those for power reactors since the structure of unit lattice (fuel assembly)
is totally diﬀerent from each other. If it is possible to utilize the Monte-Carlo method forneutronics simulations, the uncertainties induced by numerical simulations may be easily
estimated.
Since evaluated nuclear data is ‘evaluated’ by a person, evaluated nuclear data dependon the person. The evaluated nuclear data is veriﬁed through its application into integral
data. This procedure can be also applied to covariance of nuclear data. In the next
chapter, we will show an example to verify the covariance data with integral measurement
data.

IIIVeriﬁcation of evaluated covariance data with integral measurement data

In this chapter, we will utilize experimental data obtained at fast critical assemblies
in Los Alamos National Laboratory. The features of these assemblies are shown in table
5.
Table 5: Features of critical assemblies
Name

Fuel

JEZEBELPu
JEZEBEL-240 Degraded Pu
GODIVAU
FLATTOP-Pu
Pu
FLATTOP-25
UURadius
Exp. error
reﬂector(cm)(∆k/kk 0 )No
6.38490.002
No6.65950.002
No8.74070.001
Yes
24.142 (Fuel:4.5332)
0.003
Yes
24.1242 (Fuel:6.1156)
0.003

Figure 1 shows C/E values of criticalities of these assemblies with the latest nuclear
data ﬁles. The error bars in this ﬁgure refer to 1σ uncertainties of measurement data.
These neutron transport calculations are carried out with the continuous-energy MonteCarlo code.
The nuclear data-induced uncertainties in these criticalities, Vk , can be estimated as~M~G~t
Vk = G(1)~ is sensitivities of nuclear data to kef f and M~ is covariance matrix of nuclear
where G~ with the discrete ordinates transport methoddata. In the present study, we calculate G
and use covariance data given in JENDL-3.3. The calculated uncertainties, i.e., standard
deviations and correlation matrix, are shown in table 6 and 7.
To verify deviations of these C/Es from 1.0 and uncertainties in C/Es, we calculate
χ2 value deﬁned as~ − 1.0)~ − 1.0)~ · V~ −1 (CE~ tχ2 = (CE(2)~ refers to a vector of C/E values, 1.0~ a vector whose elements are 1.0 and V~
where CEcovariance matrix deﬁned as
V~ = V~k + V~e + V~m(3)2006 Symposium on Nuclear Data

SND2006-IV.01-3

1.0061.004
1.002

C/E value

10.998
0.996
0.994
0.992

JENDL-3.3
JEFF-3.1
ENDF/B-VII
JENDL-3.2

0.99
JezebelJezebel-240 Flattop-Pu

GodivaFlattop-25

Figure 1: C/E values of criticalities of LANL small-sized fast critical assemblies
Table 6: Standard deviations in criticalities induced by nuclear data uncertainties
Core
JEZEBELJEZEBEL-240
FLATTOP-Pu
FLATTOP-25
GODIVA

Standard deviation
0.00540.00570.00640.00520.0041

C/E0.9970
1.0014
0.99170.99841.0032

Table 7: Correlation matrix in criticalities induced by nuclear data uncertainties
JEZ JEZ240 FLAT-Pu FLAT-25 GODIVA
JEZ
1.00
0.98
0.85
0.07
0.09
JEZ240
1.00
0.85
0.05
0.07
FLAT-Pu
1.00
0.31
0.08
FLAT-25
1.00
0.77
GODIVA
1.00

where V~e corresponds to uncertainties in experimental data and V~m statistical errors incalculated values. We obtain 6.8 of this χ2 value in the present case. A value, that χ2 isdivided by the degree of freedom (5 in this case), becomes about 1.4. This result suggeststhat nuclear data covariance, or uncertainty in experimental data or statistical errors inMonte-Carlo calculations are slightly underestimated.
In the results obtained with JENDL-3.3, C/E values for U-reﬂected assemblies (FLATTOP-

2006 Symposium on Nuclear Data

SND2006-IV.01-4

Pu and FLATTOP-25) are much smaller than those of bare assemblies (JEZEBEL andGODIVA). However, as shown in table 7, nuclear data-induced uncertainties of JEZEBELand FLATTOP-Pu (GODIVA and FLATTOP-25 also) have strong correlations to eachother. Hence, it is diﬃcult to describe this ‘reﬂector-bias’ with nuclear data uncertainty.
This bias is not observed in the ENDF-VII result at all. Through sensitivity analyses,
this diﬀerence is caused by a diﬀerence in the P1 coeﬃcients of elastic scattering crosssections of U-238. Figure 2 shows this coeﬃcient. Figure 3 shows diﬀerences of the P1
1
JENDL-3.3
JEFF-3.1
ENDF/B-VII

P1 coefficient

0.8

0.6

0.4

0.2

010000100000
1e+06
Neutron energy [eV]

1e+07

Figure 2: P1 coeﬃcients of elastic scattering cross sections of U-238
coeﬃcients of ENDF/B-VII and JEFF-3.1 to that of JENDL-3.3. JENDL-3.3 evaluates
this cross section larger about 10% systematically than the other data ﬁles.
0.1
ENDF-VII
JEFF-3.1
Relative difference

0.05
0-0.05
-0.1
-0.15
-0.2
100000

1e+06
Neutron energy [eV]

1e+07

Figure 3: Diﬀerence in P1 elastic scattering cross sections of U-238 to JENDL-3.3

2006 Symposium on Nuclear Data

SND2006-IV.01-5

Relative standard deviation

0.15

0.1

0.05

010000100000
1e+06
Neutron energy [eV]

1e+07

Figure 4: Standard deviation of P1 elastic scattering cross sections of U-238
Figure 4 shows standard deviations of this cross section based on JENDL-3.3. This
uncertainty is much smaller than the diﬀerence between diﬀerent nuclear data ﬁles.
With this comparison and the reﬂector-bias observed in the JENDL-3.3 results, it canbe said that the uncertainty for P1 coeﬃcients of elastic scattering cross sections of U-238
seem to be underestimated in JENDL-3.3 evaluations.

IVConclusion

We have shown that the neutronics parameter uncertainties expected in the current
design studies of fast reactors are reasonable when both diﬀerential and integral data
are taken into consideration. We also pointed out that this conclusion is based on anassumption that cross section covariance is properly evaluated. We have attempted toverify the evaluated cross section covariance with the integral data.

References[1] T.Hazama, et al., ‘Development of the uniﬁed cross-section set ADJ2000R for fast
reactor analysis,’ JNC TN9400 2002-064 (2002) [in Japanese].

2006 Symposium on Nuclear Data

SND2006-IV.01-6