On the evaluation of 23Na neutron-induced reactions and validations

ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 612 (2010) 374–387

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

On the evaluation of

23

Na neutron-induced reactions and validations

D. Rochman a,, A.J. Koning a, D.F. da Cruz a, P. Archier b, J. Tommasi b a b

Nuclear Research and Consultancy Group NRG, Westerduinweg 3, P.O. Box 25, 1755 ZG Petten, The Netherlands ´ nergie Atomique, DEN Cadarache, F-13108 Saint-Paul-Lez-Durance, France Commissariat A l’E

a r t i c l e in f o

a b s t r a c t

Article history: Received 28 August 2009 Received in revised form 21 October 2009 Accepted 22 October 2009 Available online 29 October 2009

New recommendations for neutron-induced reactions on 23Na are presented for incident energies from thermal to 200 MeV including resonance parameters up to 1 MeV, and covariance files in the resonance and fast neutron regions. Calculations are based on the nuclear reaction code TALYS and covariances in the fast neutron range are obtained with a Monte Carlo approach. Discrepancies between experimental data and evaluations are presented, indicating needs for new measurements. Validations with integral benchmarks and a simplified model of the Kalimer-600 Sodium Fast Reactor are presented with a special emphasis on the void coefficient, including its uncertainty assessment. Finally, conclusions on the state of knowledge of neutron induced reactions on sodium are presented with recommendations for new measurements. & 2009 Elsevier B.V. All rights reserved.

Keywords: Neutron reactions Modeling Covariances Validation Void coefficient Sodium fast reactor

1. Introduction This paper aims to present the current status of knowledge on evaluations of neutron-induced reactions of 23Na, with as a final goal to obtain a good description of both differential measurements (cross-sections) and integral benchmarks (for Sodium Fast Reactors). Because sodium has a very high boiling temperature, is non-corrosive to structural materials used in the reactor, has a very low capture cross-section and thermal conductivity, its usage as a coolant contribute to low life-cycle costs. As an example of the need for a new evaluation, in some recent GEN-IV studies, (most notably in Refs. [1,2]), the sensitivity of the inelastic neutron scattering for 23Na in the few hundreds of keV energy regime was addressed. The main neutron libraries around the world contain evaluations for the 23Na neutron-induced reactions. Even though sodium has a large impact on applications, parts of the evaluations in these libraries are more than 20 years old, see Table 1. The thermal and resonance regions have not been changed in any of the three major libraries since 1981, mainly because of the low relevance of these energy regions for fast reactors. Since then, new measurements of the capture, (n,p) and (n,a) cross-sections [8–10] and of resonance parameters from 2.8 to 784 keV for 23 Na were realized [11].

 Corresponding author.

E-mail addresses: [email protected] (D. Rochman), [email protected] (A.J. Koning), [email protected] (D.F. da Cruz), [email protected] (P. Archier), jean.tommasi@ cea.fr (J. Tommasi). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.10.147

In the fast neutron range, many new measurements were done since the last European evaluations of 23Na in 1992:

 (n,2n): Filatenkov et al. [12], Xiangzhong et al. [13], Soewarso   

no et al. [14], Uwamino et al. [15], Hanlin et al. [16], (n,a): Gueltekin et al. [17], Fessler et al. [18], (n,el): Kopecky et al. [19], (n,inl): Kopecky et al. [19], Maerten et al. [20], and (n,p): Gueltekin et al. [17], Fessler et al. [18], Satoh et al. [21].

As presented later, many discrepancies remain between evaluations themselves and between evaluations and differential measurements. Possibly one of the most important examples is that for the inelastic cross-section, where the JEFF-3.1 evaluation does not follow differential measurements, certainly to obtain a good agreement with integral measurements. As this evaluation was performed decades ago, it is nowadays difficult to find the origin of and reasons for these discrepancies. A second example, less pertinent for fast systems, but more important for the general use of the evaluations are the discrepancies in the resonance range, once again between evaluations themselves and between evaluations and measurements. The position of the resonances do not agree and neither do their widths (see Table 3). In order to find in which case the actual knowledge is adequate, a new study of 23Na neutron-induced nuclear reactions is presented in the following. In the resonance region, the proposed resonance study results from an analysis based on previous measurements. In the fast neutron region, the new evaluation is based on a theoretical analysis with the nuclear

ARTICLE IN PRESS D. Rochman et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 374–387

2. Cross-sections 2.1. Thermal region In the thermal neutron region, the capture and elastic crosssections of JEFF-3.1 and JENDL-3.3 are derived from resonance parameters given in Ref. [4] from 1981. In the case of ENDF/BVII.0, the thermal cross-sections originate from 1976 and are in agreement with measurements from Ryves [24] (see Table 2). The capture and elastic cross-sections presented in this recommendation are adopted from the Atlas of Neutron Resonances compilation [25]. Nevertheless, uncertainties have been increased so that there is an overlap with the thermal crosssections from JEFF-3.1 and JENDL-3.3, see Fig. 1. 2.2. Resolved resonance region The resonance parameters extracted in this work are given in the Reich–Moore formalism. They are based on parameters given in the Atlas of Neutron Resonances [25], Moxon et al. [11] and on the pointwise total cross-sections from the EXFOR database. The inelastic cross-section, which opens at 440 keV is not taken into Table 1 Origin and date of the different Na neutron-induced reaction evaluations. 23

Na

JEFF-3.1 [3] ENDF/B-VII.0 [5] JENDL-3.3 [7]

Resonance region

Fast neutron region

Mughabghab [4] Larson [6] Mughabghab [4]

JEF-2.2 (1992) ENDF/B-V (1977) New (2000)

Table 2 Thermal elastic and capture cross-sections for

(n,g) (n,el)

23

Na (in barns).

Present work

JEFF-3.1

JENDL-3.3

ENDF/B-VII.0

Atlas

0:518 7 5:4% 3:04 7 3:4%

0.531 3.09

0:531 7 7:4% 3:09 7 3:3%

0.528 3.39

0:517 7 0:8% 3:038 7 0:2%

600 Cross section (mb)

23Na(n ,γ) th

550 500 450 400 C Po ol Ba me man rth ran 4 ol ce 6 om 5 G ew 1 G rosh 53 rim e e v5 Co land 5 ck 5 i 5 Jo ng w 57 itt Ro 59 se M Wo 59 ea lf d 6 K ow 0 oe s hl 61 e Ya Ry r 6 m ves 3 am 7 G uro 0 K leas 70 am o EN in n D ish 75 F/ i B JE -V 82 N II. D 0 L3. 3 JE FF -3 .1 Th is wo rk

model code TALYS [22], version 1.0. On the basis of a large suite of implemented nuclear reaction models, this code is able to produce a complete set of cross-sections, yields, energy spectra and angular distributions. In the evaluation process, the nuclear model parameters of TALYS are adjusted to reproduce the existing experimental data, while we also directly include experimental data if we judge these to be of better quality than our model calculations. The present study is completed by covariance files, obtained in the resonance range from experimental uncertainties, and in the fast neutron range by means of Monte Carlo. A similar approach has recently been applied to the isotopes of Pb and Bi and details of the Monte Carlo analysis can be found in Ref. [23]. To complete our study, a series of validation benchmarks are presented: criticality-safety benchmarks, MASURCA experiments (plutonium burning cores), JANUS-8 (Neutron Transport Through Sodium and Mild Steel). Additionally, the impact of the 23Na nuclear data uncertainties are propagated to the uncertainties of the sodium void coefficient of a Kalimer-like sodium reactor. Finally, in the light of the benchmark results, recommendations for new measurements are addressed.

375

Fig. 1. Measured and recommended 23Na ðnth ; gÞ cross-sections. The gray band represents a linear fit to the experimental data.

account in this analysis. It is then assumed that there are no interference terms between the inelastic and the elastic crosssections. Resonance parameters were obtained for 40 resonances up to 1 MeV and are presented in Table 3. In the majority of cases, the radiative width Gg cannot be derived from experiments and is then assumed to be equal to an average of the measured ones for the same angular momentum l value. Uncertainties on the resonance parameters are obtained from the above cited references ([11,25] and from the EXFOR database). If no uncertainties are reported in these references, and for assumed radiative widths, a value of 50% is assigned as a 1s standard deviation. The resonance region extends up to 520 keV in the JEFF-3.1 and JENDL-3.3 evaluations and up to 541 keV in the ENDF/B-VII.0 evaluation. A particular effort in this work was to increase the resonance region up to 1 MeV so that the total, elastic and capture cross-section structures are described by resonance parameters and not by pointwise cross-sections. This gives a larger flexibility to obtain cross-sections at different temperatures and to perform uncertainty propagation (see later). In Fig. 2, the two main problems of the JEFF-3.1 evaluation are presented. The top and middle parts of Fig. 2 show a shift in resonance energy E0 to the low energies for the total cross-section when compared to the pointwise data from Larson et al. [6]. Resonance parameters in the JEFF-3.1 evaluation were partly adopted from Ref. [4] (as JENDL-3.3). The middle and bottom parts of Fig. 2 present another type of discrepancy with experimental data. In this energy region (and for higher energy), the JEFF-3.1 evaluation gives a too high total cross-section compared to many different measurements. Similarly, the elastic cross-section in JEFF-3.1 presents the same discrepancy with experimental data. In the present evaluation, even if not performed with an resonance analyzing tool such as SAMMY or REFIT, the obtained evaluated total and elastic cross-sections are in good agreement with experimental data. Concerning the capture cross-section, the experimental crosssections in the resonance range are scarce. For resonance information such as radiative widths, the values reported in Ref. [25] were adopted in this work. Results from 650 to 900 keV are presented in Fig. 3, together with the evaluations from JEFF3.1, JENDL-3.3 and ENDF/B-VII.0. For the other evaluations, the resonance region ends in the 500 keV range and the capture cross-sections are represented by linear approximations (see Fig. 3). In the case of the present work, we have decided to include resonance information, based on average radiative widths for the majority of resonances. According to the presented discrepancies, it seems important to make a new analysis of the raw data in the resonance region with a tool as SAMMY or REFIT (if the data exist), or to perform new measurements, taking into account the inelastic channel.

ARTICLE IN PRESS 376

D. Rochman et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 374–387

Table 3 Resonance parameters up to 1 MeV for Wigner formalism). Origin

This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 ENDF/B-VII.0 This work JEFF-3.1 This work This work This work This work This work This work This work

23

Na recommended in this work (in Reich Moore formalism), compared to values from JEFF-3.1, ENDF/B-VII.0 (in multi-level Breit

E0 (keV)

J

 176(0)

2

7.617(11) 7.617 7.617(10) 53.173(50) 53.04 53.22(4) 117.42(11)

l

Gn

Gg

(eV)

(eV)

0

3975(2200)

1.7(8)

3 1 2 2 2 2 1

2 1 1 1 1 1 1

0.0074(37) 0.0296 0.0058(0) 1080(35) 1152 1112(16) 25.8(8)

2.1(15) 1.00 0.6(1) 0.99(10) 1.0 0.78(27) 4.24(60)

117.43(2) 143.11(14) 143.10 143.13(8) 201.10(20) 200.20 201.15(9) 236.71(24)

1 0 3 0 1 1 1 1

1 2 1 1 1 1 1 2

26.8(32) 17.6(2.4) 5.48 16.5(100) 4490(350) 5470 4925(76) 94(11)

4.2(14) 5.8(4) 0.89 7.1(30) 4.0(1.3) 4.0 2.94(36) 1.6(3)

236.71(4) 242.81(24) 243.00 242.97(33) 298.39(30) 298.65 298.32(37) 305.25(30)

2 0 0 1 2 2 2 0

2 1 1 0 0 0 0 2

65.2(70) 426(36) 1790 328(18) 2090(50) 2000 2039(27) 16.0(23)

1.59(42) 4.14(210) 4.61 1.50(24) 1.14(15) 1.14 1.020(90) 2.0(4)

305.20(20) 430.53(43) 431.30 430.90(44) 494.04(50)

0 0 0 1 0

2 1 1 2 2

68.3(350) 6200(1000) 7600 4000(374) 535(52)

9.7(49) 11.0(15) 11 5.29(158) 1.6(4)

535.16(53) 537.50

1 1

0 0

36000(15000) 35311

10.7(20) 10.6

597.67(60) 598.0 599.70(60) 683.53(68) 714.43(71) 767.70(76) 790.50(79) 917.50(92) 983.00(98)

1 1 1 0 3 2 1 1 1

1 1 2 2 1 2 2 2 1

20200(3800) 25900 204(220) 580(290) 42000(2550) 1250(500) 38000(10000) 19100(14000) 6020(2000)

0.800(16) 0.8 2.1(14) 2.1(14) 4.1(21) 2.1(15) 2.1(15) 2.1(15) 4.1(21)

E0 (keV)

J

2.835(4) 2.850 2.81(4) 35.355(2) 35.38 35.39(12) 113.47(11) 113.80

1 1 1 2 3 1 1 2

131.85(13) 131.19

l

Gn

Gg

(eV)

(eV)

0 0 0 1 1 1 2 1

377(7) 411 376(15) 1.48(16) 0.549 1.60(8) 0.43(182) 0.144

0.339(14) 0.33 0.353(2) 0.82(9) 0.788 1.9(3) 2.1(15) 0.216

3 2

2 1

0.64(20) 1.07

2.1(15) 1.60

190.10(19)

3

2

18.2(90)

1.1(1)

190.6(1) 213.60(21) 212.60 214.30(41) 239.26(24) 237.50 239.05(7) 243.05(24)

0 0 0 0 2 2 2 1

2 1 1 1 1 1 1 0

18.2(90) 16460(1000) 16000 14280(240) 5455(100) 5500 5349(53) 345(17)

9.3(47) 4.9(8) 4.9 4.64(96) 1.40(24) 1.40 1.20(10) 1.60(44)

299.38(30) 299.20 299.41(52) 393.58(39) 393.80 392.32(36) 448.05(43) 445.50 448.82(18) 508.52(51)

3 1 1 1 1 1 2 2 2 0

1 1 1 1 1 1 1 2 2 2

88(3) 300 130(15) 24100(1000) 25500 22760(247) 5770(1000) 9000 7026(167) 440(220)

1.2(2) 2.6 2.56(77) 12.0(27) 1.2 9.87(155) 4.2(15) 0.8 3.52(65) 0.59(14)

564.11(56)

0

2

240(220)

2.1(14)

627.31(63) 695.79(69) 748.17(75) 774.00(77) 905.60(90) 967.00(97)

0 3 0 2 2 2

2 2 2 1 2 2

2260(1300) 78100(29000) 700(260) 21500(10500) 23100(20000) 851(440)

2.1(14) 2.1(14) 2.1(15) 4.1(21) 2.1(15) 2.1(15)

Values in brackets are the uncertainties on the last digits (‘‘18.2(90)’’ means 18:2 7 9:0).

2.3. Fast neutron region 2.3.1. Nuclear modeling All nuclear model based results come from TALYS [22]. The evaluations described in this paper are based on a theoretical analysis that utilizes the optical model, compound nucleus statistical theory, direct reactions and pre-equilibrium processes, in combination with databases and models for nuclear structure. As the evaluation methods with TALYS have extensively been described in several other publications we will only give a short description of the various models and parameters that are used. Only the dispersive optical model will be outlined in somewhat more detail. For a more extensive description of the calculation order of the implemented reaction mechanisms and the nuclear models we refer to Refs. [26–29].

2.3.1.1. Optical model. The starting point for our nuclear model calculations are the KD03 optical model potentials (OMP) of Ref. [30] which are used in the ECIS-module [31] of TALYS. However, 23 Na falls just outside the scope of [30]. Therefore, we made a specific dispersive OMP for 23Na, which provides the optimal reproduction of all experimentally determined reaction channels. The entire OMP formalism given in Section 2 of Ref. [30] applies, and we will not repeat it here. There is, however, an important extension which we will describe below. All symbols not explained are defined in Ref. [30]. The theory of the nuclear optical model can be reformulated in terms of dispersion relations that connect the real and imaginary parts of the optical potential. These dispersion relations are a natural result of the causality principle that a scattered wave cannot be emitted before the arrival of the incident wave. The dispersion component DV stems

ARTICLE IN PRESS D. Rochman et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 374–387

Cross section (b)

12

8 6

where the surface form factor gðrÞ is given by its first derivative

4

gðr; Ri ; ai Þ ¼  4ai

220

230 240 250 Incident Energy (keV)

12 Cross section (b)

DVðr; EÞ ¼ DV V ðr; EÞ þ DV D ðr; EÞ ¼ DVV ðEÞf ðr; RV ; aV Þþ DVD ðEÞgðr; RD ; aD Þ ð3Þ

2 210

260

270

Exp. JEFF-3.1 ENDF/B-VII.0 This work

23Na(n,tot)

10 8

ð4Þ

the volume dispersion term is given by Z P 1 WV ðE0 Þ 0 dE DVV ðEÞ ¼ p 1 E0  E

ð5Þ

and the surface dispersion term is given by Z P 1 WD ðE0 Þ 0 dE : DVD ðEÞ ¼ p 1 E0  E

ð6Þ

Hence, the real volume well depth of Eq. (7) of [30] becomes

4

VV ðEÞ ¼ VHF ðEÞ þ DVV ðEÞ

2

and the real surface well depth is

298

10 9 8 7 6 5 4 3

300 302 Incident Energy (keV)

304

306

VD ðEÞ ¼ DVD ðEÞ:

WðEF  EÞ ¼ WðEF þEÞ

700

750 800 Incident Energy (keV)

850

900

Fig. 2. 23Na(n,tot) from 210 to 900 keV. In the top and bottom panels, uncertainties are presented by a colored band. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

10.0 23Na(n,

γ)

Exp. JEFF-3.1 JENDL-3.3 ENDF/B-VII.0 This work

1.0

0.1

650

700

750 800 Incident Energy (keV)

850

900

Fig. 3. 23Na(n,g) cross-section from 650 to 900 keV from this work (with uncertainties) compared with the JEFF-3.1, JENDL-3.3 and ENDF/B-VII.0 evaluations.

directly from the absorptive part of the potential, Z P 1 Wðr; E0 Þ 0 dE DVðr; EÞ ¼ p 1 E0  E

ð1Þ

where P denotes the principal value. The total real central potential can be written as the sum of a Hartree-Fock term V HF ðr; EÞ and the total dispersion potential DVðr; EÞ Vðr; EÞ ¼ V HF ðr; EÞ þ DVðr; EÞ

ð7Þ

ð8Þ

Note that we have dropped the r-dependence in Eqs. (7) and (8). This is possible with our choice of common geometry parameters for the real and imaginary parts of the potentials in Ref. [30]. In general, Eqs. (5) and (6) cannot be solved analytically. However, under the assumption that the imaginary potential is symmetric with respect to EF ,

Exp. JEFF-3.1 ENDF/B-VII.0 This work

23Na(n,tot)

650

Cross section (mb)

d f ðr; Ri ; ai Þ dr i

6

296

Cross section (b)

Since Wðr; EÞ has a volume and a surface component, the dispersive addition is

Exp. JEFF-3.1 ENDF/B-VII.0 This work

23Na(n,tot)

10

377

ð2Þ

ð9Þ

where W denotes either the volume or surface term, we can rewrite the dispersion relation as Z 1 2 WðE0 Þ DVðEÞ ¼ ðE  EF ÞP dE0 ð10Þ 2 2 0 p EF ðE  EF Þ  ðE  EF Þ from which it easily follows that DVðEÞ is skew-symmetric around EF ,

DVðE þ EF Þ ¼  DVðE  EF Þ

ð11Þ

and hence DVðEF Þ ¼ 0. This can then be used to rewrite Eq. (1) as   Z P 1 1 1 dE0  0 DVðEÞ ¼ DVðEÞ  DVðEF Þ ¼ WðE0 Þ 0 p 1 E  E E  EF Z 1 E  EF WðE0 Þ dE0 ¼ ð12Þ 0  EÞðE0  E Þ p ðE F 1 This integral can be solved analytically for both WD and WV [32], and the solutions are hardwired in the ECIS code. In sum, the basic observables are described with the same number of OMP parameters as in Ref. [30]. However, through the dispersion relations we automatically get an extra contribution to VV (from WV ) and VD (from WD ). In practice this means for the parameterizations of Ref. [30] that the v1 parameter is several MeV lower than for a non-dispersive potential and that some of the other parameters (usually rV and aV ) are slightly changed. The parameters used for our dispersive 23Na potential are given in Table 4. For protons, we use our standard global OMP [30], however, we multiply the radius of the real volume potential by a factor 0.96 to better fit the (n,p) data. For deuterons, tritons, helions and alpha particles, we use a simplification of the folding approach of Watanabe [33], see also Ref. [34]. After this, we multiply the radius and diffuseness of the real volume potential for alpha particles each by a factor of 0.98, to better fit the (n,a) data. 2.3.1.2. Compound nucleus reactions. We use Moldauer’s width fluctuation model [35] for low-energy compound nucleus reactions since that model was shown to be the best [36] for practical

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calculations. In our implementation, the model yields the compound cross-section for all discrete levels and the continuum as well as the elastic and inelastic angular distribution for all levels. The important ingredients for the compound nucleus model are transmission coefficients and level densities. The particle transmission coefficients emerge from the optical model described above. Similarly, gamma-ray transmission coefficients enter the compound nucleus model for the calculation of the capture cross-section. The normalization for the gammaray transmission coefficients TX‘ [26–29] is Gnorm ¼ 4, which produces the best overall agreement with the experimental capture cross-section. For the level density r that is required in the compound nucleus formula we take a combination [37] of the constant temperature model at low energies and the Fermi gas model at high energies. In the Fermi gas expression, we use the level density parameter a which is energy-dependent and takes into account the damping of shell effects at high excitation energy [38]. For the target nuclides considered in this paper, the level density parameters were adjusted, and they are given in Table 5.

2.3.1.3. Direct reactions. For direct inelastic scattering off the odd nucleus 23Na we use the weak-coupling model, which assumes that a valence particle or hole interacts only weakly with a collective core excitation. We performed Distorted Wave Born Approximation (DWBA) calculations with 22Ne as the core, with deformation parameters b2 ¼ 0:562 and b3 ¼ 0:331. The DWBA calculations also provide the direct inelastic scattering angular distributions, or equivalently the Legendre coefficients, which are added to their compound counterparts to give the total angular distribution per discrete state.

2.3.1.4. Pre-equilibrium and multiple emission. At incident energies above about 10 MeV, a significant part of the reaction flux is emitted in the pre-equilibrium stage, i.e. it takes place after the first stage of the reaction but long before statistical equilibrium of the compound nucleus is attained. The default pre-equilibrium model of TALYS is the two-component exciton model which has Table 4 Dispersive OMP parameters for neutrons incident on

23

Na.

Par.

Value

Par.

Value

Par.

Value

Par.

Value

Par.

Value

rV v4 d1 vso1

1.180 7:E  9 15.5 6.0

aV w1 d2 vso2

0.636 8.0 0.0214 0.0035

v1 w2 d3 wso1

52.5 90.0 12.5  3.1

v2 rD rSO wso2

0.0084 1.268 1.000 160.

v3 aD aSO Ef

2:6E  5 0.540 0.580  9.69

The parameters are explained in Ref. [30].

Table 5 Nuclear model parameters for level densities and gamma-ray transmission coefficients. Parameter

Value

Parameter

Value

Parameter

Value

a(23Na)

3.09247 26.450 17.531 0.60

a(20F) EE1 (CN) EM1 (CN)

4.06099 22.946 19.214 0.70

a(23Ne) GE1 (CN) GM1 (CN) gp (24Na)

3.70947 10.325 4.400 0.70

sE1 (CN) sM1 (CN) gp (23Na) gn (24Na)

gn ð23 Na)

been tested against basically all available experimental nucleon spectra for A 4 24 [39]. The partial level density parameters used in the model are gp ¼ Z=15 and gn ¼ N=15. The only exceptions to these default values are given in Table 5. The model also contains the adjustable transition matrix element M 2 for each possible transition between neutron–proton exciton configurations, see Ref. [39]. For 23Na, this value was multiplied by 1.2 to give the best overall agreement with the data. For pre-equilibrium angular distributions and reactions involving photons, deuterons, tritons, 3He and alpha particles, see Refs. [26–29]. At incident energies above approximately 7–10 MeV (the neutron separation energy), the residual nuclides formed after the first binary reaction are left with enough excitation energy to enable further decay by particle emission. This is called multiple emission. We distinguish between two mechanisms: multiple Hauser–Feshbach (compound) decay and multiple pre-equilibrium decay. For incident energies up to several tens of MeV, Hauser– Feshbach decay is sufficient to treat multiple emission. For these energies, it can be assumed that pre-equilibrium processes only take place in the binary reaction and that secondary and further particles are emitted by compound emission. After the binary reaction, the residual nucleus may be left in an excited discrete state or an excited state within a bin which is characterized by excitation energy, spin and parity. Hence, the only differences between binary and multiple compound emission are that width fluctuations and angular distributions do not enter the model and that the initial compound nucleus energy is replaced by an excitation energy bin of the mother nucleus. With this scheme, TALYS follows all reaction chains until all emission channels are closed, while the spectra of all emitted particles that are produced along the chain are recorded in the appropriate arrays. If the residual nucleus has a high excitation energy, resulting from a binary reaction with a high incident energy, this nucleus is far from equilibrated and it should be described by more degrees of freedom than just excitation energy, spin and parity. In general, we will track of the particle-hole configurations that are excited throughout the reaction chain and thereby calculate multiple preequilibrium emission up to any order within the exciton model. The multiple pre-equilibrium emission is described by Ref. [39]. Calculations are performed up to 200 MeV.

0.80

All parameters are explained in the text. The parameters a and gn ; gp are given in MeV1 , EE1 , and GE1 in MeV and sE1 in mb.

2.3.2. 23Na(n,tot) and 23Na(n,el) Above 1 MeV, the total cross-section is not described with the resonance approximation but with the previously described optical model. Nevertheless, resonance structures are observed up to 8–10 MeV, as presented in Fig. 4. As these structures cannot be reproduced by a smooth cross-section obtained from any optical model, the evaluated total cross-section is then equal to the pointwise experimental data from Refs. [6,40–43], as in the case of JENDL-3.3. Above 10 MeV, the smooth cross-section from the optical model is kept as is in the present evaluation. It can be seen in Fig. 4 that the agreement between experimental data and the evaluation is very good from 10 to 200 MeV. The elastic cross-section is reconstructed from the difference between the total and the reaction cross-sections from 1 to 200 MeV, see Fig. 4. Where experimental data exist (up to 2.2 MeV), the agreement with the evaluated cross-section is good. From 2.2 to 10 MeV, the present evaluation is similar to JENDL3.3. Above 10 MeV, the present elastic cross-section is slightly lower than the one from JENDL-3.3, but other evaluations stop at 20 MeV. It can be noted than the JEFF-3.1 elastic cross-section is systematically higher than experimental data and than other

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evaluations, due to a lower total inelastic cross-section. It is indicated in the JEFF-3.1 evaluation that ‘‘Above 2 MeV, the JEF2 data were scaled by 0.69 for what concerns the inelastic crosssection and by 1.32 for what concerns the elastic cross-section. These corrective factors were determined in order to match with Kopecky’s data at lower energy. They are also consistent with the validation indication’’. The validation work which is referred to in this description is partially present in Ref. [44]: ‘‘The adjustment does not indicate any significant correction (to the MASURCA benchmark). However, there are good reasons to consider as correct the experimental data obtained at Oak Ridge and which are 20–30% higher than JEF2 values above 700 keV’’. The only experimental data present in the EXFOR database from Oak Ridge National Laboratory on 23Na above 500 keV are those of Kinney and McConnell [45], presented in the top panel of Fig. 4. According to these data, JEFF-3.1 is systematically higher than Ref. [45], which is in contradiction of the previous statement extracted from the JEFF-3.1 evaluation description [44].

2.3.3. 23Na(n,inl) The inelastic channel opens at 440 keV, well below the limit of 1 MeV that divides the resonance description and pointwise crosssections. The total inelastic cross-section and the partial inelastic cross-section to the first excited level were precisely measured at Geel [19,20] and Oak Ridge [46]. For partial inelastic crosssections up to the 6th level, the measurement at the Lowell University [47] is also of high resolution. Most of the evaluations include the experimental resonance structure up to a certain energy, with some deviations depending on post-adjustment due to results of benchmarks. For JENDL-3.3 and JEFF-3.1, the evaluations are closely related to the Geel measurements from

Ref. [20], whereas the ENDF/B-VII.0 is similar to the data from Ref. [46], see Fig. 5. Regarding experiments, both measurements from Geel [19,20] give the same partial inelastic cross-section to the first excited state. In the present recommendation, we have decided the following:

 Partial inelastic to the 1st excited level: up to 2.1 MeV: accept

 

5 23Na(n,el)



Exp. JEFF-3.1 JENDL-3.3 This work

3

1 0 1

2

4 6 Incident Energy (MeV)

8

10

100

Exp. JEFF-3.1 JENDL-3.3 This work

4.0

0.75 0.50

0.00 Exp. JEFF-3.1 JENDL-3.3 This work

Exp. JEFF-3.1 JENDL-3.3 This work

1.00 Cross section (b)

23Na(n,tot)

3.0 2.0

23Na(n,inl ) tot

0.25

5.0

Cross section (b)

the measurements of Refs. [19,20]. In this energy range, this work is similar to the JEFF-3.1 cross-section (see Fig. 5) and closely follow the experimental cross-section. The JENDL-3.3 cross-section is systematically higher by 50 to 150 mb compared to Refs. [19,20] and as explained in the JENDL-3.3 file, data from Ref. [20] were multiplied by 1.25 to agree with results of the JASPER IHX-IB benchmark [48]. From 2.1 to 4.2 MeV, there is a significant discrepancy between libraries and experimental data. The JEFF-3.1 evaluation is based on the JEF-2 evaluation, multiplied by 0.69 to match Ref. [19] below 2 MeV. The resulting cross-section is significantly lower than any measurement in this energy range. In the present evaluation, data from Ref. [47] are believed to be too high compared to other measurements (especially compared to Refs. [19,49–51]), see Figs. 5 and 6. Data from Ref. [47] are then scaled down by 20% to be in agreement with previous references, see Fig. 6. The obtained adjusted data were fitted using a Be´zier function. Results of the fit is used in the present evaluation up to 4.2 MeV, which is on average consistent with the JENDL-3.3 evaluation. Above 4.2 MeV, the original TALYS calculation is conserved. Partial inelastic to the 2nd excited level: accept Refs. [47,46] measurements up to 8 MeV, use TALYS calculation above. This evaluation is higher than JEFF-3.1 above 2 MeV. Partial inelastic to the 3rd excited level up to the 6th: accept Ref. [47] measurement up to 4 MeV. Use TALYS calculation above. For partial inelastic cross-sections to higher levels, the TALYS calculations are kept.

1.00

2 Cross section (b)

Cross section (b)

4

379

23Na(n,inl ) 51

0.75 0.50 0.25

1.0

0.00 0.0

0.4 1

Fig. 4.

2 23

Na(n,el) and

4 6 Incident Energy (MeV) 23

8

10

Na(n,tot) cross sections from 1 to 200 MeV.

100

0.6

0.8 1 1.2 Incident Energy (MeV)

1.5

2

Fig. 5. 23Na(n,inltot ) and 23Na(n,inl51 ) (inelastic cross section to the first excited level) from threshold to 2.2 MeV.

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23Na(n,inl51)

Exp. JEFF-3.1 JENDL-3.3 This work

0.75

100 23Na(n,n52) 2

100 0.50

0.25

0.00 2

3

4

5 6 Incident Energy (MeV)

7

8

Fig. 6. 23Na(n,inltot ) and 23Na(n,inl51 ) (inelastic cross section to the first excited level) from 1.8 to 9 MeV.

The total inelastic cross-section is then obtained by the summation of all partial cross-sections and the inelastic cross-section to the continuum. Results for the total inelastic cross-section and for the partial inelastic cross section to the first excited level are presented in Figs. 5 and 6. As mentioned previously, the total inelastic cross-sections from JEFF-3.1 and this recommendation are lower than the experimental data from [46] up to 2 MeV. This is due to an inconsistency between Ref. [46] and Refs. [19,20]. In the present work, as Refs. [19,20] are preferred compared to Ref. [46], the evaluation is in agreement with the measured partial inelastic cross-section but not with the measured total inelastic cross-section. In the case of JENDL-3.3, the opposite choice was made, so that the JENDL-3.3 total inelastic cross-section is in agreement with measurements from Ref. [46] and the partial inelastic cross-section is discrepant with Refs. [19,20] (Figs. 7 and 8).

Na(n,2n) 2.3.4. In the case of the (n,2n) cross-section on 23Na, there are two distinct sets of experimental data (see Fig. 9), with a higher group consisting of measurements performed by Zhi-Zheng et al. [52] and Liskien et al. [53]. All previous evaluations except ENDF/BVII.0 follow the lower group (which are also most recent and most extensive in terms of independent measurements and in terms of broader energy range). The older decay data used in Ref. [53] are no longer judged as correct (for the 22Na half-life and its decay scheme), which implies a decrease of the reported cross-section by 10–15%. Another cross section is reported by Liskien et al. in Ref. [53] on 46Ti(n,p), using the same experimental installation. Similarly, the (n,p) cross-section is 20 to 30% too high compared to other experimental data and evaluations. In the case of Ref. [52], very little information is known as the data where not presented in a referered journal. In the case of the present evaluation, we have also decided to consider only the lower set of experimental data.

Exp. This work JEFF-3.1 JENDL-3.3

100 80 60 40 20

23Na(n,n53)

0

4 6 8 Incident Energy (MeV)

Exp. This work JEFF-3.1 JENDL-3.3 23Na(n,n ) 54

80 60 40 20

2

4 6 8 Incident Energy (MeV) 23

Na

120 23Na(n,n ) 55

100 80 60 40 20

Exp. This work JEFF-3.1 JENDL-3.3

0

0 3 4 5 6 7 8 9 Incident Energy (MeV)

3 4 5 6 7 8 9 Incident Energy (MeV)

Fig. 8. 23Na ðn; inl54 Þ (inelastic cross-section to the fourth excited level) and ðn; inl55 Þ (inelastic cross section to the fifth excited level).

23

Na

250 This work JENDL-3.3 ENDF/B-VII.0 JEFF-3.1 Filatenkov 99 Xiangzhong 95 Soewarsono 92 Uwamino 92 Hanlin 92 Others Ikeda 88

200 150 100

23Na(n,2n)

50 0 12

Fig. 9. Evaluated

23

120

Fig. 7. 23Na ðn; inl52 Þ (inelastic cross-section to the second excited level) and ðn; inl53 Þ (inelastic cross section to the third excited level).

Cross section (mb)

Cross section (b)

1.00

200

0

Perey 71 JEFF-3.1 JENDL-3.3 This work

0.25

Exp. This work JEFF-3.1 JENDL-3.3

Cross section (mb)

0.50

Cross section (mb)

Cross section (b)

0.75

300

Cross section (mb)

23Na(n,inltot)

1.00

Cross section (mb)

380

14 23

16 Incident Energy (MeV)

18

20

Na(n,2n) cross-sections compared with experimental data.

2.3.5. 23Na(n,a) and 23Na(n,p) The (n,a) cross-section was measured with high accuracy up to 11 MeV at the LANSCE facility [54]. Fine resonance structures can be observed out of the statistical uncertainties. This measurement is fully reproduced in our evaluation. Above, recent measurements from 13 to 20 MeV [17,55] are used in this work to guide our TALYS calculation, see Fig. 10. The (n,p) cross-section was also measured with high accuracy up to 11 MeV at the LANSCE facility [54]. This measurement is, as for the (n,a) case, reproduced in our evaluation. Above 11 MeV, recent measurements from 13 to 20 MeV [17,55] are used in this work to guide our TALYS calculation.

3. Covariance data In general, the covariance analysis performed in this work is similar to the methodology used for the Pb and Bi evaluations [23]. The energy range is separated in two parts: the thermal

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A covariance evaluation was realized based on the methodology presented in Ref. [23], using the resonance parameters and uncertainties from Table 3. The capture kernel A, if known, is obtained from Ref. [25]. To accommodate for thermal cross-section uncertainties, artificial uncertainties were given to the neutron and radiative widths of the bound level of 23Na. The obtained cross-section uncertainties in the resonance range are presented in Figs. 2 and 3. As many of the radiative widths were not measured, large capture cross-section uncertainties are obtained. Nevertheless, the uncertainty on the capture integral is 4%, which can be explained by the fact that the first positive resonance (at 2.835 keV) contributes 96% to the capture integral. As the radiative width for this resonance is experimentally known at 4%, the same uncertainty is found for the capture integral. Studies on uncertainties were also performed for the US and Japanese libraries for 23Na. For comparison, uncertainties for the capture cross-section up to 1 MeV for these two libraries and the present evaluation are presented in Fig. 11. For the 23Na(n,tot) reaction, the ENDF/B-VII.0 library provides covariances based on calculations which take into account the first and second positive energy resonances. It is mentioned in the description of the ENDF/B-VII.0 file that ‘‘The uncertainties in the resonance parameters are most useful in self-shielding work’’. Our current approach, compared to the ENDF/B-VII.0 evaluation, presents the advantage to consider the whole resonance range and to provide parameter uncertainties and correlation which can be used for all sorts of applications. The JENDL-3.3 evaluation presents a two-step uncertainty curve, which does not reflect the resonance structures of the cross-section. One can notice that there are no resonance parameter covariances in the JENDL-3.3 evaluation, but instead a pointwise cross-section covariance description is presented from thermal energy to 20 MeV. For the 23Na(n,g) reaction, resonance structures can be observed in the ENDF/B-VII.0 evaluation starting at 600 eV up to 600 keV and uncertainties are generally higher than in our evaluation. In the case of the JENDL-3.3 evaluation, the covariance

Exp. JENDL-3.3 ENDF/B-VII.0 JEFF-3.1 This work

Cross section (mb)

75

The covariance analysis is performed by means of a Monte Carlo procedure and is detailed in Ref. [23]. By randomly varying all TALYS nuclear model parameters within limited ranges, random nuclear data (cross-sections, single and double differential data etc.) are obtained. Covariances are then extracted from these random files. In the following, only cross-section uncertainties will be presented.

100 10−2 10−3 10−4

25

JENDL-3.3 ENDF/B-VII.0 This work

40

23Na(n,γ)

30 20 10 0 10−2

10−1

100

101 102 103 Incident Energy (eV)

Fig. 11. Top: capture cross-section for and resonance range for 23Na(n,g).

250

50

(n,γ)

10−1

10−5

Cross section (mb)

23Na(n,p)

100

3.2. Uncertainties analysis in the fast neutron region

Cross section (b)

3.1. Covariance analysis in the resonance region

information is averaged over large energy groups, with uncertainties which are higher until the first positive resonance and of comparable order of magnitude above it. Nevertheless, the step behavior from sub-thermal to C 10 keV is artificial, as it does not reflect that mainly one resonance (at 2.835 keV) dictates the cross-section (and uncertainty) shape in this region. In our work, the cross section uncertainties below the 2.835 keV resonance directly derives from the Gn and Gg uncertainties of this resonance. The shape of the cross-section uncertainties due to a particular resonance has been detailed in Ref. [23].

Uncertainty (%)

resonance region and the fast neutron region. In the thermal resonance range, total, elastic and capture cross-sections are treated in terms of the resonance formalism and their associated covariances are presented for resonance parameters (MF-32 in the ENDF-6 format). In the fast neutron range, covariances are expressed in terms of pointwise cross-sections (MF-33 in the ENDF-6 format).

381

200

Exp. JEFF-3.1 JENDL-3.3 ENDF/B-VII.0 This work

23

23Na(n,α)

150 100

0 10 15 Incident Energy (MeV)

Fig. 10. Evaluated

23

Na(n,p) and

23

20

5

105

106

Na. Bottom: uncertainty in the thermal

50

5

104

10 15 Incident Energy (MeV)

Na(n,a) cross-sections compared with experimental data.

20

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(n,tot)

JENDL-3.3 This work

Uncertainty (%)

4

2 23Na(n,tot)

1

Na

0.50 23Na(n,γ)

Cross section (mb)

0.45 Exp. This work JEFF-3.1 JENDL-3.3

0.40 0.35 0.30 0.25 0.20 0.15 0.10 1

Fig. 14.

5 4 3 2 1 10

2

5 Incident Energy (MeV)

10

20

23

Na(n,g) cross-section and uncertainties in the fast energy range.

(n,el)

JENDL-3.3 This work

8

3

23

Similar to Refs. [23,29], we show the impact of the evaluations on criticality benchmarks, as compiled in the National Energy Agency International Criticality Safety Benchmark Evaluation

Cross section (b)

5 4 3 2 1 5

4. Criticality-safety benchmarks including

Uncertainty (%)

Crosssection (b)

In the fast neutron region, the uncertainties of the total crosssection are directly obtained from the optical model. Uncertainties are presented in Fig. 12. The usual shape is obtained with high uncertainties at low energies and a decreasing trend as the neutron energy is increasing. Uncertainties on the total crosssection for the JENDL-3.3 library are rather constant, and probably scaled by experimental data. In the case of the elastic cross-section, the uncertainties are obtained in this work as the difference between the total crosssection and the reaction cross-section. The total inelastic cross-section uncertainty is obtained from the quadratic sum of all the partial cross-section uncertainties. The partial cross-section uncertainties are in agreement with the quoted uncertainties in Refs. [20,19], see Fig. 13. Above 3 MeV, the obtained uncertainties are much smaller than in JENDL-3.3, where two partial inelastic cross-sections are considered: to the first excited level and to the continuum. In the case of the (n,2n) cross-section, the uncertainties presented in this work cover the spread of experimental data, with the exception of Refs. [52,53] (which are significantly above the other cross-sections). Even though the capture cross-section is of little importance in the fast neutron range (less than half a mb), covariances are provided in this work, which covers the spread of experimental data, see Fig. 14.

6 4 2 23Na(n,el)

0

0 3 5 10 Incident Energy (MeV)

1000 800 600 400 200 0

23

Na(n,tot) and

3 5 10 Incident Energy (MeV)

20

23

Na(n,el) cross sections and uncertainties in the fast neutron range.

(n,inl)

Exp. uncertainties JENDL-3.3 This work

15

1

Uncertainty (%)

Uncertainty (%)

Cross section (mb)

Fig. 12.

20

Cross section (mb)

1

10 5 23Na(n,inl)

(n,2n) 110 60 10 23Na(n,2n)

30 25

Exp. uncertainties JENDL-3.3 This work

20 15 10 5 0

0 0.5

1

3 5 Incident Energy (MeV)

10

20

12

14 16 18 Incident Energy (MeV)

20

Fig. 13. Left: 23Na(n,inl) cross-section and uncertainties. In the case of JENDL-3.3, the uncertainties are obtained from the inelastic cross-section to the first excited level and to the continuum. Right: 23Na(n,2n) cross-section and uncertainties.

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Project criticality benchmark series [56]. We consider four benchmark series for thermal systems and three for fast systems:

      

leu-sol-therm-18 (LST-18), 6 cases, leu-met-therm-18 (HMT-18), 2 cases, heu-sol-therm-2 (HST-2), 13 cases, pu-sol-therm-8 (PST-8), 29 cases, pu-met-mixed-1 (PMM-1), 6 cases, heu-mix-mixed-5 (HMM-5), 6 cases, and mix-comp-fast-1 (MCF-1), 1 case.

These benchmarks were also calculated for the JEFF-3.1, ENDF/BVII.0 and JENDL-3.3 libraries. Results are presented in Fig. 15. In this figure, the uncertainties are statistical ones. In order to evaluate the impact of sodium on this experiment, calculations are presented with different sodium evaluations, while other isotopes are taken from the JEFF-3.1 library. As could be anticipated, 23Na does not have a large impact on keff benchmarks. From Fig. 15, no clear indication that an evaluation performs better than another can be obtained. A similar result is obtained when propagating the 23Na nuclear data uncertainty to the keff values, following the method described in Ref. [64]. In the case of a Sodium Fast Reactor, Monju type, the uncertainty on the calculated keff is about 120 pcm and the uncertainty on the calculated beff is o5 pcm. It is clear that the validation of the 23Na nuclear data cannot be obtained by means of criticality-safety benchmarks because of their low sensitivity to sodium.

5. Janus-8 and MASURCA benchmark experiments

C/E for keff

1.0125 1.0075

5.1. Janus-8 shielding benchmark 5.1.1. Description The National Energy Agency compiled in SINBAD [57] (Shielding Integral Benchmark Archive Database) an experimental report for the Janus Phase 8 Integral Experiment [58]. This experiment was designed to provide experimental data on the penetration of neutrons through a 2.8 m-thick sodium region. The fast neutron detection was carried out with activation foils composed of Rhodium and Sulfur. The modeling of the Janus-8 benchmark was implemented in the TRIPOLI-4.5 Monte Carlo code [59] at the CEA Cadarache. As previously, calculations are presented with different sodium evaluations, while other isotopes are taken from the JEFF-3.1 library. 5.1.2. C/E comparisons The results for the 103Rh(n,inl)103mRh and 32S(n,p) 32P reactions are presented in Fig. 16 for different evaluations. For 103Rh, the same trends are obtained for JEFF-3.1, JENDL-3.3 and the present 23Na evaluation. The ENDF/B-VII.0 sodium evaluation gives a higher C/E due to a compensation between cross-sections levels and angular distributions. For 32S, the JEFF-3.1 sodium evaluation provides the best C/E agreement. The important discrepancies compared to the other evaluations are mainly due to the lower JEFF-3.1 total crosssection between 3 and 20 MeV. Sensitivity calculations also show an important effect for the elastic scattering angular distributions of secondary neutrons. Usually, angular distributions and cross-sections have the same weight in propagation benchmarks like the Janus-8 Experiment. It suggests that double differential measurements for the elastic process are of critical interest. 5.2. MASURCA experiments 5.2.1. Description Since 1976, an extensive series of experimental programs have been performed on the MASURCA critical assembly at Cadarache.

hmt-18-

A more relevant type of analysis consists of calculating benchmarks with large amounts of sodium as in the Janus-8 and MASURCA experiments. The effects of the different sodium evaluations are presented on reaction rates, keff s and void coefficients.

383

JEFF-3.1 JENDL-3.3 ENDF/B-VII.0 This work

1.0025 0.9975

1.0225 1.0175 1.0125 1.0075 1.0025 0.9975 0.9925 0.9875

hmm-5-

lst-18-

hst-2-

1 2 3 4 5 6 tail ple 1 2 3 4 5 1 3 de sim Benchmark Cases

5

7

9

11

13

mcf-1

C/E for keff

0.9925

pmm-1-

JEFF-3.1 JENDL-3.3 ENDF/B-VII.0 This work

1 2 3 4 5 6 1 2

4

pst-86

Fig. 15. Calculated keff for 23Na related criticality benchmarks with the corresponds to the benchmark uncertainties.

8 23

10 12 14 16 18 20 Benchmark Cases

22 24 26 28

30

Na evaluations. The error bars represent statistical uncertainties. The shadow around 1.00

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103Rh

(n,n’) 103mRh

C/E

1 0.9 0.8

JEFF−3.1 JENDL−3.3 ENDF/B−VII.0 This work

0.7 20

40

60

80

100 120 Distance (cm) 32S

140

160

180

200

(n,p) 32P

1.2

C/E

1 0.8 0.6 0.4 0.2

JEFF−3.1 JENDL−3.3 ENDF/B−VII.0 This work 50

100

150 200 Distance (cm)

250

300

Fig. 16. Calculation of Experiment ratio (C/E) for Janus-8 Benchmark. Experimental relative uncertainties for the 103Rh(n,inl) reaction are not shown entirely on this figure but are 4 57% at 195 cm.

Among other things, numerous multiplication factors and sodium void reactivity effects (SVR) have been measured and analyzed at the CEA using the ERANOS-2.1 code [60]. The list of experiments presented in the following are: PRE-RACINE [61], RACINE [62] and CIRANO ZONA2A [63]. The first two programs proposed cores with about 21% Pu/(Pu þ U) enrichment central zone and are referred as ZONA1. The last program is a plutonium burning core with a Pu/(Pu þ U) enrichment zone of about 27% and is called ZONA2. A paper especially dedicated to SVR in MASURCA cores will soon been published by Tommasi et al. and will give thorough details about the description of the cores. With these three programs, 8 keff and 46 sodium void coefficients are presented to estimate the impact of the different 23 Na evaluations.

5.2.2. Difference between Calculation and Experiment (C-E) The results of the calculations are given in Tables 6 and 7. For the SVR, the (C-E) are ranked for ZONA1 fuel from small ð o 100 pcmÞ to large SVR ð Z100 pcmÞ. In the case of ZONA2 fuel, there are only small SVR. These results are converted from pcm to b using beff in the following formula: SVR ¼

kvoid  kref 1 107 kvoid  kref beff

ð13Þ

where the number of delayed neutron beff is given in pcm. Table 6 shows that 23Na nuclear data have an impact of about 400 pcm on the keff in the MASURCA experiments. The present evaluation is in between the two extremes from JEFF-3.1 and ENDF/B-VII.0, and (C-E)s for SVR are better than for JENDL-3.3 and ENDF/B-VII.0. It nevertheless exceeds the average experimental uncertainties. The sodium evaluation from JEFF-3.1 provides the best (C-E) agreements in the case of SVR. However, one can notice that above 2 MeV, the JEFF-3.1 elastic and inelastic cross-sections in this evaluation are not consistent with existing measurements.

Table 6 Average (C-E) in pcm on keff in MASURCA cores using the different evaluations of 23 Na.

C-E for keff

This work

JEFF-3.1

JENDL-3.3

ENDF/B-VII.0

57

248

14

 135

Table 7 Average (C-E) in b for sodium void reactivity effects (SVR) in MASURCA cores using the different evaluations of 23Na. (C-E) in b

Small SVR in ZONA1 fuel

Large SVR in ZONA1 fuel

SVR in ZONA2 fuel

Uncer. (in b) This work JEFF-3.1 ENDF/B-VII.0 JENDL-3.3

0.80 0.99 0.50 1.36 1.39

1.35 6.06 2.20 8.57 8.18

0.83 2.39 0.52 3.28 4.22

5.2.3. Sensitivity coefficients A sensitivity calculation for the SVR on a Sodium Fast Reactor (representative of a typical Generation-IV Sodium Fast Reactor studied at the CEA) has been performed with the ERANOS code. Results are presented on Fig. 17. Note that the SVR are highly sensitive to (n,el) and (n,inl) reactions from 100 keV to 4 MeV whereas the sensitivity to (n,gÞ cross-section remains secondary. Those profiles show that the energy region around 1 MeV is of critical importance and that new measurements in this range would be of high interest for the evaluation community.

6. Void coefficient for the Kalimer-600 sodium fast reactor In order to assess the impact of the 23Na nuclear data uncertainties on the void coefficient of a Sodium Fast Reactor,

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0.08

20

23Na(n,n)

Number of counts/bins

0.1

23Na(n,n’) 23Na(n,γ)

Sensitivity (%/%)

0.06 0.04 0.02 0

Kalimer void coeffcient (23Na) SVR= 8.02510 ± 0.55092 $

15

Reduced Chi-square=0.215

10 5 0

7.8

−0.02 −0.04

7.9 8.0 Void coeffcient value ($)

8.1

8.2

Fig. 18. Calculated sodium void coefficient (SVR) for the Kalimer-600 design, varying the 23Na nuclear data file.

100

101

Fig. 17. Sensitivity profile on Sodium Void Reactivity Effect to 23Na elastic, inelastic and radiative-capture cross-sections for a typical CEA Sodium Fast Reactor.

we have selected the Korean design for the Kalimer-600 Nacooled fast reactor design as presented in Ref. [65]. A simplified full core model of the Kalimer-600 was implemented in MCNP [66]. Details of the modeling can be found in the above references. The main difference between our model and the original Kalimer600 design is the use of one single fuel zone, instead of the originally proposed three-fuel-zone core. An equilibrium reactor core with 4-batches was considered, and the core inventory is taken at beginning of equilibrium cycle. The fuel type considered is a metal alloy U-TRU-10%Zr, with isotopic vector as provided by KAERI. The sodium void reactivity (SVR) in units of dollars ($) can be obtained from Eq. (13) divided by 100. The effective delayed neutron fraction beff (in units of pcm) and the keff values are obtained from the MCNP calculations, following the calculation method presented in Ref. [67]. kref corresponds to the core flooded with Na coolant, and kvoid to the same core voided of Na coolant. In both cases the Na coolant present in the axial and radial reflectors is supposed to remain unchanged. In order to propagate 23Na nuclear data uncertainties, the evaluations presented above are formatted to a transport ENDF file and then processed with the NJOY code to be used in the MCNP model. Following the methodology presented in Refs. [64,68], random transport ENDF files are created by varying model parameters. Each of the transport file is then used in a separate MCNP calculation and each time a different sodium void coefficient is obtained. The distribution of the SVR is presented in Fig. 18 for more than 800 MCNP calculations. Convergence for the different parameters of the SVR distribution is of importance in Monte Carlo calculations. Three parameters as a function of the sampling numbers are presented in Fig. 19 (mean, variance and skewness). The total width of the distribution has two components, one from the statistics used in each MCNP calculation (in the order of 3%), the second one from the spread of 23Na nuclear data. After convergence of the three quantities presented in Fig. 19, the final SVR is equal to 8.02510 ð 73%statistical 76%nuclear data Þ.

7. Conclusion The knowledge of the neutron induced reaction on 23Na was reviewed in this work. A new evaluation is presented with its

8.5 Updated SVR ($)

10−2 10−1 Energy (MeV)

Updated uncertainty ($)

10−3

Updated skewness

−0.06 10−4

385

Sodium Fast Reactor (Kalimer-600) 8.3 8.1 7.9



0.6 0.5 0.4

<σ>

0.3 0.0 -0.1 -0.2 -0.3



-0.4 0

200

400 600 Sample number

800

Fig. 19. Convergence towards the final sodium void coefficient (SVR) value, the associated width and the skewness of the SVR contribution for the Kalimer-600 reactor. The top panel represents the updated average SVR value, whereas /sS in the middle panel denotes the width (or uncertainty) due to the 23Na nuclear data. The bottom panel presents the updated skewness of the distribution.

validation results on criticality and sodium void reactivity benchmarks compared to other evaluated libraries. A summary of the analysis is presented in Table 8. As shown by the uncertainty propagation study, 23Na has a minor impact on keff benchmarks, but is relevant in the case of sodium void reactivity benchmarks. In the case of the Kalimer600 Sodium Fast Reactor, the knowledge of the 23Na data can be translated to about 6% uncertainty on the void coefficient. Following the conclusions of Ref. [2] where the target accuracy for void coefficient for fast reactors is 7% (taking into account Na and other fuel components), the actual knowledge of 23Na for void coefficient simulations is unsatisfactory. A more comprehensive study reveals that, the JEFF-3.1 evaluated 23Na performs better for the sodium void reactivity benchmarks. In order to achieve this result, this evaluation does not agree with differential cross section measurements such as the elastic and inelastic cross-sections. Alternatively, the present evaluation agrees better with differential measurements, includes the latest experimental data, provides covariances, but does not

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Table 8 Summary of the study for uncertainties and validations.

keff (SFR) Void coefficient (Kalimer)

23

Uncertainty due Na nuclear data

Impact on benchmarks

100–400 pcm C 6%

None Significant

Best performing library

Problems

Crit. Saf. keff JANUS keff

None JENDL-3.3 & This work

Not performing well

MASURCA

JEFF-3.1

in MASURCA benchmarks Not in agreement with differential measurements

Recommendations Resonance range Resonance range Fast neutron range Fast neutron range Fast neutron range

New transmission measurements New (n,inl) measurements Above 1 MeV: new (n,tot) measurements Above 1 MeV: new (n,el) measurements New partial (n,inl) measurements

perform well on the sodium void reactivity benchmarks. Additionally, the target accuracy for the inelastic cross section from threshold to 1.3 MeV is 4 to 10%, for a Sodium Fast Reactor [2], and the present covariance analysis gives an uncertainty higher than 10% for this cross-section. There is therefore a need for more accurate experimental data. In conclusion of this work, no definite recommendation can be expressed for the different evaluations as long as discrepancies for experimental data are not solved. We recommend to perform new measurements in the resonance range (transmission measurements), new elastic and/or total cross-section measurements in the fast neutron range, and finally, with a higher priority, new high resolution inelastic measurements from threshold to a few MeV. References [1] G. Palmiotti, M. Salvatores, G. Aliberti, Validation of simulation codes for future systems: motivations, approach, and the role of nuclear data, in: Proceedings of the Fourth Workshop on Neutron Measurements, Evaluations and Applications, Prague, Czech Republic, October 16–18, 2007. [2] M. Salvatores, et al., Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations, Nuclear Energy Agency, NEA/WPEC-26, 2008. [3] A.J. Koning, et al., The JEFF evaluated nuclear data project, in: Proceedings of the International Conference on Nuclear Data for Science and TechnologyND2007, Nice, France, May 22–27, 2007. [4] S.F. Mughabghab, M. Divadeenam, N.E. Holden, Neutron Cross Sections, Neutron Resonance Parameters and Thermal Cross Sections, vol. I, Academic Press, New York, 1981. [5] M.B. Chadwick, P. Oblozˇinsky´, M. Herman, et al., Nucl. Data Sheets 107 (2006) 2931. [6] D.C. Larson, J.A. Harvey, N.W. Hill, Measurement of the neutron total cross section of sodium from 32 keV to 37 MeV, Oak Ridge National Laboratory Report ORNL-TM-5614, 1976. [7] K. Shibata, J. Nucl. Sci. Technol. 39 (2002) 1065. [8] R. Firestone, Private communication, 2003. [9] S. Roth, F. Grass, F. De Corte, L. Moens, K. Buchtela, J. Radioanal. Nucl. Chem. 169 (1993) 159. [10] F. De Corte, A. Simonits, A. De Wispelaere, J. Hoste, J. Radioanal. Nucl. Chem. 133 (1989) 43. [11] M.C. Moxon, D.S. Bond, J.B. Brisland, The measurement of the total crosssection of sodium and carbon, in: Proceedings of International Conference on the Physics of Reactors, vol. 1, Marseille, France, 1990, p. 32. [12] A.A. Filatenkov, S.V. Chuvaev, V.N. Aksenov, V.A. Yakovlev, A.V. Malyshenkov, S.K. Vasil’ev, M. Avrigeanu, V. Avrigeanu, D.L. Smith, Y. Ikeda, A. Wallner, W. Kutschera, A. Priller, P. Steier, H. Vonach, G. Mertens, W. Rochow, Systematic measurement of activation cross sections at neutron energies from 13.4 to 14.9 MeV, Khlopin Radiev Institute, Leningrad Reports, no. 252, 1999. [13] K. Xiangzhong, W. Yongchang, Y. Jingkang, Y. Junqian, Commun. Nucl. Data Prog. 14 (1995) 5.

[14] T.S. Soewarsono, Y. Uwamino, T. Nakamura, Neutron activation cross section measurement from 7Li(p,n) in the proton energy region of 20 MeV to 40 MeV, JAERI-M Report, no. 92–027, 1992, p. 354. [15] Y. Uwamino, H. Sugita, Y. Kondo, T. Nakamura, Nucl. Sci. Eng. 111 (1992) 391. [16] L. Hanlin, Z. Wenrong, Y. Weixiang, Chin. J. Nucl. Phys. 14 (1992) 83. [17] E. Gueltekin, V. Bostan, M.N. Erduran, M. Subasi, Ann. Nucl. Energy 29 (2002) 2019. [18] A. Fessler, Y. Ikeda, J.W. Meadowa, A.J.M. Plompen, D.L. Smith, Nucl. Sci. Eng. 134 (2000) 171. [19] S. Kopecky, R. Shelley, H. Maerten, J. Wartena, H. Weigmann, High resolution inelastic scattering cross sections, in: 27Al and 23Na in the Proceedings of the Conference on Nuclear Data for Science and Technology, vol. 1, Trieste, Italy, 1997, p. 523. [20] H. Maerten, J. Wartena, H. Weigmann, Simultaneous high-resolution measurement of differential elastic and inelastic neutron cross sections on selected light nuclei, Private communication to EXFOR, 1994. [21] Y. Satoh, T. Matsumoto, Y. Kasugai, H. Yamamoto, T. Iida, A. Takahashi, K. Kawade, Measurement of formation cross section producing short-lived nuclei by 14 MeV neutrons—Na, Si, Te, Ba, Ce, Sm, W, Os, JAERI Reports, no. 95, 008, 1994, p. 189. [22] A.J. Koning, S. Hilaire, M.C. Duijvestijn, TALYS-1.0, in: Proceedings of the International Conference on Nuclear Data for Science and Technology—ND2007, May 22–27, 2007, Nice, France. [23] D. Rochman, A.J. Koning, Nucl. Instr. and Meth. A 589 (2008) 85. [24] T.B. Ryves, D.R. Perkins, J. Nucl. Eng. 24 (1970) 419. [25] S.F. Mughabghab, Atlas of Neutron Resonances, fifth ed., Elsevier Publisher, Amsterdam, 2006. [26] A.J. Koning, M.C. Duijvestijn, Nucl. Instr. and Meth. B 248 (2006) 197. [27] M.C. Duijvestijn, A.J. Koning, Ann. Nucl. Energy 33 (2006) 1196. [28] A.J. Koning, M.C. Duijvestijn, J. Nucl. Sci. Technol. 44 (2007) 823. [29] A.J. Koning, M.C. Duijvestijn, S.C. van der Marck, R. Klein Meulekamp, A. Hogenbirk, Nucl. Sci. Eng. 156 (2007) 357. [30] A.J. Koning, J.P. Delaroche, Nucl. Phys. A 713 (2003) 231. [31] J. Raynal, Notes on ECIS94, CEA Saclay Report no. CEA-N-2772, 1994. [32] J. Raynal, ECIS-96, Specialists’ Meeting on the nucleon nucleus optical model up to 200 MeV, Bruye res-le-Chˆatel, November 13–15, 1996, p. 111. [33] S. Watanabe, Nucl. Phys. 8 (1958) 484. [34] D.G. Madland, in: Proceedings of a Specialists’ Meeting on Preequilibrium Reactions, Semmering, Austria, OECD, Paris, February 10–12, 1988, p. 103. [35] P.A. Moldauer, Nucl. Phys. A 344 (1980) 185. [36] S. Hilaire, Ch. Lagrange, A.J. Koning, Ann. Phys. 306 (2003) 209. [37] A. Gilbert, A.G.W. Cameron, Can. J. Phys. 43 (1965) 1446. [38] A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Sov. J. Nucl. Phys. 21 (1975) 255. [39] A.J. Koning, M.C. Duijvestijn, Nucl. Phys. A 744 (2004) 15. [40] D.G. Foster Jr., D.W. Glasgow, Phys. Rev. C 3 (1971) 576. [41] J.C. Clement, R. Fairchild, C.G. Goulding, P. Stoler, P.F. Yergin, Total MeV cross sections of Na and C from 0.5 to 40 MeV, Rensselaer Polytechnic Institute Report RPI-328-200, 24, 1970. [42] S. Cierjacks, P. Forti, D. Kopsch, L. Kropp, J. Nebe, H. Unseld, High resolution total neutron cross section for Na, Cl, K, V, Mn and Co between 0.5 and 30 MeV, Kernforschungszentrum Karlsruhe Report KFK-1000, Suppl. 2, 1969. [43] A. Langsford, P.H. Bowen, G.C. Cox, F.W.K. Firk, D.B. Mcconnellb, M. Saltmarsh, High resolution neutron time of flight measurements on Na and C from 0.2 to 140 MeV, in: The Proceedings of the Nuclear Structure Conference, Antwerpen, Belgium, 1965, p. 529. [44] E. Fort, W. Assal, A. Avery, P. Blaise, J.C. Bosq, S. Cathlau, C. Dean, J.P. Fink, G. Rimpault, J. Rowlands, P. Smith, M. Salvatores, R. Soule, V. Zammit, JEF-2.2 Validation: Part 1—General Purpose File, JEFDOC-759, 1999, NEA Data Bank. [45] W.E. Kinney, J.W. McConnell, High resolution neutron scattering experiments at ORELA, in: Proceedings of the International Conference on Interaction of Neutron with Nuclei, vol. 2, Lowell, 1976, p. 1319. [46] F.G. Perey, W.E. Kinney, R.L. Macklin, High resolution inelastic cross section measurements for Na, Si, and Fe, in: Proceedings of the Third Conference on Neutron Cross-Sections and Technology, vol. 1, Knoxville, USA, 1971, p. 191. [47] D.R. Donati, S.C. Mathur, E. Sheldon, B.K. Barnes, L.E. Beghian, P. Harihar, G.H.R. Kegel, W.A. Schier, Phys. Rev. C 16 (1977) 939. [48] N. Yamano, C. Konno, K. Ueki, Validation of JENDL-3.2 sodium data with shielding benchmarks, in: G. Reffo, A. Ventura, C. Grandi (Eds.), Proceedings of the Conference on Nuclear Data for Science and Technology, Bologna, 1997, p. 1189. [49] J.H. Towle, W.B. Gilboy, Nucl. Phys. 32 (1962) 610. [50] E.N. Shipley, G.E. Owen, L. Madansky, Phys. Rev. 115 (1959) 122. [51] Th. Schweitzer, D. Seeliger, S. Unholzer, Kernenergie 20 (1977) 174. [52] X. Zhi-Zheng, P. Li-Min, W. Zhi-Hua, Nucl. Sci. Techn. (Shanghai) 2 (1991) 153. [53] H. Liskien, A. Paulsen, Nucl. Phys. 63 (1965) 393. [54] H. Weigmann, G.F. Auchampaugh, P.W. Lisowski, M.S. Moore, G.L. Morgan, Neutron induced charged particle reactions on 23Na, in: The Proceedings of the International Conference on Nuclear Data for Science and Technology, Antwerp, Belgium, 1982, p. 184. [55] A. Fessler, Y. Ikeda, J.W. Meadows, A.J.M. Plompen, D.L. Smith, Nucl. Sci. Eng. 134 (2001) 171. [56] International Handbook of evaluated Criticality Safety Benchmark Experiments, NEA/NSC/DOC(95)03/I, in: J. Blair Briggs (Ed.), Organisation for Economic Co-operation and Development, Nuclear Energy Agency, 2004. [57] OECD Nuclear Energy Agency Data Bank SINBAD, Website: /http://www.nea. fr/html/science/shielding/sinbad/sinbadis.htmS.

ARTICLE IN PRESS D. Rochman et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 374–387

[58] A. Avery, JANUS Phase 8 Benchmark Experiment-Data for Inclusion in the SINBAD Database, NEA 1517/42 SINBAD REACTOR, Winfrith, 1998. [59] J.P. Both, H. Derriennic, B. Morillon, J.C. Nimal, A survey of TRIPOLI-4, in: Proceedings of Eighth International Conference on Radiation Shielding (ICRS8), Arlington, Texas, USA, 24–28 April 1994, pp. 373–380. [60] J.M. Ruggieri, J. Tommasi, J.F. Lebrat, C. Suteau, D. Plisson-Rieunier, C. De Saint Jean, G. Rimpault, J.C. Sublet, ERANOS 2.1: International Code System for GEN IV Fast Reactor Analysis, in: Proceedings of International Congress on Advances in Nuclear Power Plants ICAPP 06, Reno, USA, 2006, p. 2432. [61] Y.H. Bouget, et al., Nucl. Technol. 44 (1979) 61. [62] G. Humbert, et al., Nucl. Sci. Eng. 87 (1984) 233. [63] P.J. Finck, J.C. Cabrillat, M. Martini, R. Soule, G. Rimpault, R. Jacqmin, The CIRANO experimental programme in support of advanced fast reactor

[64] [65]

[66]

[67] [68]

387

physics, in: Proceedings of PHYSOR 1996 Conference, vol. 2, Mito, Japan, 1996, p. 66. A.J. Koning, D. Rochman, Ann. Nucl. Energy 35 (2008) 2024. S.G. Hong, S.J. Kim, H. Song, Y.I. Kim, Neutronic design of KALIMER-600 core with moderator rods, in: Proceedings of the 2004 International Congress on Advances in Nuclear Power Plants (ICAPP’04), Pittsburgh, PA, 13–17 June 2004 ANS, La Grange Park, p. 646. D.F. da Cruz, Neutronic studies on the KALIMER-600 Na-cooled fast reactor design, NRG-22176/09.93884, Nuclear Research and Consultancy Group NRG, Petten, The Netherlands, 2009. R.K. Meulekamp, S.C. van der Marck, Nucl. Sci. and Eng. 152 (2006) 142. D. Rochman, A.J. Koning, S.C. van der Marck, Annals of Nuclear Energy 36 (2009) 810.