Analysis of nuclide production in the MEGAPIE target

ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 605 (2009) 224–232

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

Analysis of nuclide production in the MEGAPIE target A.Yu. Konobeyev a,, U. Fischer a, L. Zanini b a b

¨ r Neutronenphysik und Reaktortechnik, Forschungszentrum Karlsruhe GmbH, 76021 Karlsruhe, Germany Institut fu Spallation Neutron Source Division ASQ, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland

a r t i c l e in f o

a b s t r a c t

Article history: Received 9 June 2008 Received in revised form 23 March 2009 Accepted 23 March 2009 Available online 5 April 2009

MEGAPIE, the first liquid metal target irradiated by a proton beam at the MW power level, was successfully operated in 2006. A continuous beam of 575 MeV protons with a current up to 1.35 mA irradiated the liquid lead–bismuth target placed in the SINQ target location at PSI (Switzerland) for a period of 4 months. The activation of the lead–bismuth irradiated in MEGAPIE has been investigated. Experimental crosssections and evaluated data available for neutron- and proton-induced reaction cross-sections at incident energies from 105 eV to 600 MeV, and results of nuclear model calculations have been used to obtain nuclear reaction rates. Calculated nuclide and gas production rates are compared with calculations using the MCNPX and FLUKA Monte Carlo codes. The total activation of the LBE agrees well with the other codes. Discrepancies with FLUKA and MCNPX are mainly in two mass regions, where experimental data are scarce: the region 30oAo50, and the region 140oAo170. The results obtained can be used for the further study of the safe operation of liquid heavy metal targets of Accelerator-Driven Systems and spallation neutron sources and for the definition of the priorities in the development of evaluated nuclear data libraries at intermediate nucleon energies. & 2009 Elsevier B.V. All rights reserved.

Keywords: Accelerator-Driven System MEGAPIE High-energy particle interaction Activation Nuclide production Lead–bismuth target

1. Introduction Accelerator-Driven Systems (ADSs) are one of the proposed options for the incineration of minor actinides [1]. In the roadmap towards the demonstration of the ADS concept [2], an important element is the spallation target, which is the interface between the two principal components of an ADS, the high-power accelerator and the subcritical core. In this framework, the MEGAwatt PIlot Experiment (MEGAPIE) project [3] was started in 2000 to design, build and operate a liquid metal spallation target of 1 MW beam power. The creation and the accumulation of stable and radioactive nuclides in the target material during the irradiation of the target are a very important issue for many reasons: safety concerns related to gas production, licensing, study of accident cases, target handling and disposal after irradiation. From a scientific point of view, postirradiation experiments can lead to information on the nuclide inventory allowing benchmarking the calculation tools. Monte Carlo codes are an essential tool for this kind of investigation, and were used extensively during the design phase of MEGAPIE, as well as during the experimental measurement program [4]. The MEGAPIE target was operated in the SINQ facility at PSI. In the MEGAPIE target a loop of about 82 l of lead–bismuth eutectic (LBE) circulates enclosed by a steel structure. The target is about 5 m long and the LBE loop circulates by means of a

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E-mail address: [email protected] (A.Yu. Konobeyev). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.03.218

main electromagnetic pump, while a bypass pump is used for a secondary loop to cool the window. The target was inserted in the SINQ block replacing the previous solid targets [5], and was operated during 4 months in 2006. The target was irradiated by a proton beam of 575 MeV energy and a peak current of 1.375 mA, with a power on target of nearly 0.8 MW. In the MEGAPIE project two codes were used extensively, FLUKA and MCNPX. In this paper we present an alternative calculation tool that was used in the MEGAPIE post-test analysis phase, consisting in the code system SNT. In this way we aim at demonstrating the validity of this tool in the framework of liquid metal target development. The goal of this work is to study the nuclide production in the lead–bismuth target. Experimental nuclear reaction cross-sections [6] and evaluated data [8–11] available for neutron- and proton-induced reactions at incident energies from 105 eV to 600 MeV and results of nuclear model calculations were used to obtain nuclear reaction rates. To assess the validity of SNT, calculated nuclide composition and gas production rates are compared with calculations performed for MEGAPIE using FLUKA [12] and MCNPX [13]. The SNT code system allows studying in an easy way the origin of nuclides produced under irradiation. The contribution of various ranges of particle energy distributions in the nuclide production was examined. The goal of this investigation is to obtain information on the activity and nuclide concentration in the MEGAPIE target, on the contribution of various groups of nuclides to the activity of the target, on the influence of different ranges of particle energy distributions on the nuclide production,

ARTICLE IN PRESS A.Yu. Konobeyev et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 224–232

and on values of gas production rates. The information obtained can be important for the forming and the correction of the priority list for the evaluation of cross-sections of radionuclide yields in the lead–bismuth targets irradiated with protons at intermediate energies. Section 2 describes briefly the method of the nuclide composition calculation and discusses the input data. Section 3 describes the production of radionuclides in the lead–bismuth target.

225 r

Where Ni is the concentration of ith nuclide at the time t; lik is the rate of the nuclear reaction resulting to the transformation of kth d nuclide into ith nuclide, lik is the corresponding radioactive decay r rate, li is the transmutation (disappearance) rate of ith nuclide d due to nuclear reactions and li is the radioactive decay rate of the nuclide. r r The nuclear reaction rates lik and li are given by

lrik ¼

XZ

sðjÞ ðEÞjðjÞ ðEÞ dE ik

(2)

sðjÞ ðEÞjðjÞ ðEÞ dE abs; i

(3)

j

2. Brief description of the method of nuclide composition calculation in irradiated materials

lri ¼

XZ j

2.1. The dynamics of nuclide transformations The change in the concentration of nuclides in irradiated materials is defined by the following equations: dN i X r d r d ¼ ðlik þ lik ÞNk ðtÞ  ðli þ li ÞNi ðtÞ dt kai

(1)

where j(j)(E) is the energy distribution of particles of j-type, which is assumed a constant at the considered irradiation is the cross-section for the production time (Section 3); sðjÞ ik of ith nuclide due to interactions of kth nuclide with particles ðjÞ is the ‘‘absorption’’ cross-section equal to the of jth type; sabs; i difference between the total reaction cross-section and inelastic

104

Cross-section (mb)

natPb(p,p')x

103

natPb(p,d)x

103 102

102

101 Bertrand (71): Bi-209 Guertin (05): Pb-208 Wu (79): Bi-209 Segel (82): Pb-208 Herbach (06): Pb-nat Evaluated data

Guertin (05): Pb-208 Wu (79): Bi-209 Segel (82): Pb-208 Herbach (06): Pb-nat (corr) Evaluated data

101

100 101

102

103

101

102

103

103

Cross-section (mb)

Guertin (05): Pb-208 Segel (82): Pb-208 Barashenkov compilation (72) Herbach (06) Evaluated data

102

103

Leya (05) natPb(p,He)x Guertin (05): Pb-208 Segel (82): Pb-208 Dubost (67) Goebel (64) Enke (99) (corr) Herbach (06) systematics (07)

102

101 101 100 natPb(p,t)x

Evaluated data 100

10-1 101

102

103

Proton energy (MeV)

101

102

103

Proton energy (MeV)

Fig. 1. Evaluated proton, deuteron, triton and helium isotope production cross-section for natural lead irradiated with protons. Experimental data are from Refs. [6,25–27,29,30].

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A.Yu. Konobeyev et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 224–232

104

Cross-section (mb)

209

209

Bi (p,p')x

103

Bi (p,d)x

103 102

102

101

Bertrand (71): Bi-209 Guertin (05): Pb-208 Wu (79): Bi-209 Segel (82): Pb-208 Herbach (06): Pb-nat Evaluated data

Guertin (05): Pb-208 Wu (79): Bi-209 Segel (82): Pb-208 Herbach (06): Pb-nat (corr) Evaluated data

101

100 101

Cross-section (mb)

103

102

103

Bertrand (71) Wu (79) Dubost (67) Barashenkov compilation (72) Mekhedov (70) Herbach (06) Evaluated data

102

101

102 Bertrand (71) Wu (79) Dubost (67) Goebel (64) systematics (07)

103

103 209Bi

(p,He)x

102

101 101 209

Bi(p,t)x

100 Evaluated data

10-1

100 101

102

103

Proton energy (MeV) Fig. 2. Evaluated proton, deuteron, triton and helium isotope production cross-section for

102

101

103

Proton energy (MeV) 209

Bi irradiated with protons. Experimental data are from Refs. [6,25–27,29,30].

Particle energy distribution (cm-2 s-1 MeV-1)

1020 1019 1018 1017 1016

neutrons

1015 1014 1013 1012 1011 1010 109 108

protons

107 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 Proton energy (MeV) Fig. 3. Average energy distributions of neutrons and protons in the lead–bismuth eutectic.

ARTICLE IN PRESS A.Yu. Konobeyev et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 224–232

scattering cross-section for jth particles interacting with ith nuclide. The numerical solution of Eqs. (1)–(3) has been obtained using the SNT code [14–22]. The code was specially designed for modelling the transmutation and activation of materials irradiated with low-, intermediate- and high-energy particles. Input data for the code include the irradiation history, particles spectra and nuclear reaction cross-sections. Cross-sections can be presented using different formats, ENDF/B, EAF and others. Table 1 Average neutron and proton fluxes in lead-bismuth (particles/cm2/s). Energy range

Neutrons

Protons

13

Eo20 MeV 20oEo150 MeV E4150 MeV

2.05  10 (96.48%) 5.91 1011 (2.77%) 1.59  1011 (0.75%)

1.10  1010 (0.97%) 1.29  1011 (11.44%) 9.88  1011 (87.58%)

Total

2.13  1013 (100%)

1.13  1012 (100%)

227

The code run includes the check and treatment of input data, the numerical solution of the system of differential equations describing the nuclide kinetics, and the treatment and printing of results. More details on the code and its use can be found in Refs. [14–22].

2.2. Nuclear data used for nuclide composition calculations The calculation of nuclear reaction rates has been performed using evaluated data from Refs. [7–11]. Data include evaluations performed by different authors considering all presently available experimental cross-sections for lead and bismuth isotopes irradiated with neutrons and protons at energies from 105 eV up to 600 MeV. Data include also the detailed information about nuclear reaction cross-sections for nuclei produced in the irradiation of isotopes of lead and bismuth. Names of data sets, energy ranges and numbers of target nuclei used in the calculation of nuclide composition are shown below.

Fig. 4. Activity of lead–bismuth calculated in the present work and in Refs. [4,39,41].

Table 2 Data illustrating the contribution of various nuclides to the total activity of irradiated lead-bismuth. Five maximal relative contributions (R) are shown at different times after the irradiation. Time of cooling (days) 0 1 min 60 min 1d 2d 10 d 30 d 60 d 180 d 1 yr 2 yr 10 yr 20 yr 100 yr 200 yr 1000 yr 2000 yr 10000 yr 20000 yr 100000 yr 200000 yr 1000000 yr a

Total activity (Bq) a

1.23+16 1.20+16 8.83+15 4.03+15 3.06+15 1.20+15 5.32+14 3.08+14 1.35+14 6.52+13 2.79+13 1.01+13 6.63+12 1.03+12 2.87+11 4.94+10 1.44+10 4.44+09 3.93+09 1.84+09 9.56+08 1.72+08

The record x.x+yy means x.x10yy.

Nuclide, R (%)

Nuclide, R (%)

Nuclide, R (%)

Pb 203 Pb 203 Pb 203 Bi 206 Bi 206 Bi 205 Bi 205 Po 210 Au 195 Au 195 H3 Bi 207 Bi 207 Bi 207 Hg 194 Hg 194 Hg 194 Pb 202 Pb 202 Bi 208 Bi 208 Bi 208

Bi 206 Bi 206 Bi 206 Pb 203 Tl 201 Bi 206 Po 210 Au 195 Po 210 Po 210 Au 195 H3 H3 Pt 193 Au 194 Au 194 Au 194 Tl 202 Tl 202 Pb 202 Pb 202 Pb 205

Tl 201 Tl 201 Tl 201 Tl 201 Pb 203 Po 210 Au 195 Bi 205 Os 185 H3 Bi 207 Tl 204 Pt 193 Hg 194 Bi 207 Pb 202 Pb 202 Bi 208 Bi 208 Tl 202 Tl 202 Bi 210 m

4.23 4.33 5.86 10.5 12.5 18.0 18.7 21.7 30.2 31.4 20.8 41.4 51.0 57.2 26.6 44.3 32.0 37.5 37.1 40.8 65.2 80.4

3.79 3.87 5.26 10.1 10.0 14.4 14.6 20.7 27.2 22.3 18.9 36.4 31.7 19.4 26.6 44.3 32.0 37.5 37.1 27.8 14.5 9.16

3.50 3.57 4.87 9.36 10.0 6.99 13.4 10.1 5.62 9.38 17.9 7.67 9.16 8.64 23.2 3.79 12.8 20.1 22.2 27.8 14.5 3.19

Nuclide, R (%)

Nuclide, R (%)

Tl 200 Tl 200 Tl 200 Bi 205 Bi 205 Au 195 Ir 189 Os 185 H3 Bi 207 Tl 204 Pt 193 Tl 204 Au 194 Pt 193 Tl 202 Tl 202 Nb 94 Nb 94 Pb 205 Pb 205 Tl 206

Pb 201 Pb 201 Pb 201 Tl 200 Tl 200 Ir 189 Bi 206 Re 183 Bi 207 Tl 204 Po 210 Po 208 Hg 194 H3 Po 209 Bi 208 Bi 208 Nb 93 m Tc 99 Tc 99 Tc 99 Nb 93 m

3.05 3.12 4.24 7.61 9.65 6.38 5.36 5.97 4.66 7.84 11.5 6.87 1.99 8.64 17.5 3.79 12.8 1.56 1.25 0.89 1.71 3.19

2.84 2.90 3.75 7.28 6.50 6.26 4.91 4.57 3.83 5.89 8.37 1.87 1.52 2.27 2.80 1.84 6.30 0.79 0.49 0.80 1.12 0.93

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Reactions with neutrons

Radioactive decay properties of nuclei were taken from JEFF3.1.1 [7].

1.0

3.1. The total activity of irradiated lead–bismuth The calculated activity of irradiated lead–bismuth is shown in Fig. 4 for the time after the irradiation from several seconds up to

1.0

0.4

0.2

Relative contribution

H-3 Au-195 Po-210

0.2

9

10

10

8

6

10

5

10

7

4

10

10

3

10

10

2

10

1

10

0

10

-1

Fig. 6. Relative contribution of groups of nuclides with different atomic numbers in the total activity of irradiated lead–bismuth.

1.0

Bi-207

0.4

10

-2

Cooling time (day)

neutrons: E < 20 MeV neutrons: E < 150 all neutrons all n + protons E < 150 MeV all neutrons and protons

Pb-202 +Tl-202

0.6

10

-3

0.0

Bi-208 Relative contribution

0.6

Pb-205

Hg-194 +Au-194 0.8

Z < 30 Z < 40 Z < 50 Z < 70 Z < 80 Z < 85

0.8

10

Yields of heavy clusters in nucleon interactions with lead and bismuth isotopes were estimated with the help of the ‘‘nuclear forces break down’’ model [24]. Parameters of the model have been specified in Ref. [20]. Cross-sections were obtained for 69 residual nuclei from 7Be to 28Na produced in the irradiation of lead and bismuth isotopes with neutrons and protons of intermediate energy. New evaluation of proton, deuteron, triton, 3He and alphaparticle production cross-section for lead and bismuth has been performed in the present work. The evaluation has been done using available experimental data from EXFOR [6] and Refs. [25–30], cross-section obtained by systematics [31], and results of model calculations. At energies below 200 MeV neutron data were taken from JEFF-3.1. The experimental proton production cross-section from Ref. [26] has been corrected to include data for the whole energy range of emitted protons. Calculations have been carried out using the nuclear models implemented in the TALYS code [32], the ALICE/ASH code [33], the DISCA-C code [34] and the CASCADE code [35–37]. All models mentioned above include the simulation of the non-equilibrium emission of clusters from excited nuclei. Examples of evaluated data are given in Figs. 1 and 2. The tritium production cross-section for different target nuclei except lead and bismuth has been evaluated at incident nucleon energies above 150 MeV using the semi-empirical approach from Ref. [38].

-4

PADF [10], proton energy Ep below 150 MeV, 2322 nuclei, PADF-600 [11], 150 MeVoEpo575 MeV, 23 nuclei (Pb, Bi and Po isotopes), YIELDX [20,23], 150 MeVoEpo575 MeV, 725 nuclei (except Pb, Bi and Po isotopes).

The nuclide composition has been calculated for the lead–bismuth eutectic irradiated in MEGAPIE. The energy of primary protons is 575 MeV and the average proton current is 0.947 mA for 123 d of irradiation. The total volume of lead–bismuth was of about 82 l. Results presented below correspond to the 123 d irradiation period. Averaged particle spectra in lead–bismuth eutectic calculated by MCNPX [13] are shown in Fig. 3. Values of average neutron and proton fluxes and contributions of different energy ranges are given in Table 1.

10

Reactions with protons

3. The nuclide production in the lead–bismuth target

10

JEFF-3.1A [7], neutron energy En below 20 MeV, 691 target nuclei, JEFF-3.1 (general purpose file) [7], 20oEno150 MeV, 31 nuclei, IEAF-2001 [8], 20oEno150 MeV, 641 nuclei, IEAF-2007 [9], 150oEno575 MeV, 669 nuclei.

Relative contribution

228

Bi-206

0.8 0.6 0.4 0.2

Pb-203 0.0 6

7

10

10

10

5

10

10

4

10

10 8 10

3

10

2

0

-1

-2

10 1 10

10

10

10

-3

10

8

-4

10

7

10

10 10

6

10

10 9

5

10

4

10

2

10 3 10

0

-1

-2

-3

-4

10 1 10

10

10

10

10

10

Cooling time (day)

9

Hg-194+Au-194

0.0

Cooling time (day) Fig. 5. Relative contribution of radionuclides in the total activity of the lead–bismuth after the irradiation. Radionuclides with the maximal contribution are shown.

Fig. 7. Contribution of radionuclides produced under the irradiation of neutrons and protons with different energies in the total activity of lead–bismuth.

ARTICLE IN PRESS A.Yu. Konobeyev et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 224–232

229

Table 3 Contribution in % of different parts of neutron and proton energy distributions to the nuclide production in irradiated lead-bismuth. Nuclidea

T1/2 (d)

Neutrons o20 MeV

Neutrons 20–150 MeV

Neutrons 4150 MeV

Protons o150 MeV

Protons 4150 MeV

Po 210 Po 209 Po 206 Bi 210 Bi 210 m Bi 208 Bi 207 Bi 206 Bi 205 Pb 205 Pb 203 Pb 202 Tl 204 Tl 202 Tl 201 Tl 200 Hg 203 Hg 197 Hg 195 m Hg 194 Au 199 Au 196 Au 195 Au 194 Pt 195 m Pt 193 Pt 193 m Pt 191 Pt 188 Ir 189 Ir 188 Os 185 Re 183 Re 182 W 181 W 178 Ta 179 Ta 177 Hf 175 Hf 172 Lu 173 Lu 172 Lu 171 Lu 170 Lu 169 Yb 169 Yb 166 Tm 167 Tm 165 Er 160 Ho 163 Dy 154 Tb 157 Tb 155 Tb 153 Gd 151 Gd 150 Gd 149 Gd 148 Gd 147 Gd 146 Eu 149 Eu 148 Eu 147 Eu 146 Eu 145 Sm 146 Sm 145 Pm 145 Pm 143 Nd 140 Co 56 C 14 Be 10 H3

1.384+02 3.726+04 8.800+00 5.012+00 1.096+09 1.344+08 1.160+04 6.243+00 1.531+01 5.588+09 2.162+00 1.936+07 1.384+03 1.224+01 3.041+00 1.088+00 4.660+01 2.692+00 1.733+00 1.622+05 3.139+00 6.183+00 1.861+02 1.584+00 4.100+00 1.826+04 4.340+00 2.802+00 1.020+01 1.320+01 1.729+00 9.380+01 7.000+01 2.667+00 1.210+02 2.160+01 5.880+02 2.350+00 7.000+01 6.830+02 4.880+02 6.700+00 8.250+00 2.012+00 1.419+00 3.202+01 2.362+00 9.246+00 1.252+00 1.191+00 1.669+06 1.096+09 3.616+04 5.320+00 2.340+00 1.240+02 6.648+08 9.280+00 2.725+04 1.586+00 4.827+01 9.310+01 5.450+01 2.400+01 4.590+00 5.930+00 3.652+10 3.400+02 6.465+03 2.660+02 3.370+00 7.731+01 2.082+06 5.844+08 4.500+03

99.96 0.004 o0.001 99.97 99.92 73.1 10.6 o0.001 o0.001 24.6 2.0 0.05 0.03 0.002 o0.001 o0.001 1.5 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 0 o0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.005

0.03 o0.001 o0.001 0.03 0.08 15.2 66.9 62.7 48.4 45.7 46.5 35.5 53.0 44.8 28.7 22.4 30.5 8.6 12.5 2.0 13.5 5.6 3.4 3.6 14.2 1.1 5.8 0.3 0.02 0.04 0.02 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 0 0 0 12.5

0 0 0 0 0 1.3 2.0 2.6 3.7 3.2 6.5 7.6 9.1 10.6 9.4 10.8 14.1 16.3 0 15.7 9.1 5.7 16.6 4.7 0 15.6 0.02 12.0 10.4 9.1 10.3 8.3 6.8 6.3 7.8 5.8 6.0 5.9 5.8 6.1 6.4 6.1 6.9 7.9 9.4 9.7 15.0 12.0 16.8 55.2 28.4 96.7 86.0 89.3 95.1 99.7 99.8 98.8 99.6 99.8 99.8 97.6 66.6 99.8 95.5 91.9 79.1 73.6 34.1 28.1 8.8 7.1 6.1 7.2 8.4

0.007 11.8 56.5 0 0 1.8 7.5 11.6 17.6 7.9 12.6 12.2 1.6 1.4 9.0 7.9 0.1 4.1 1.5 1.3 0.03 0.1 2.1 0.2 0.02 0.7 0.07 0.1 0.008 0.02 0.008 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 o0.001 0 0 0 2.8

o0.001 88.2 43.5 0 0 8.6 13.0 23.1 30.2 18.6 32.4 44.6 36.2 43.1 52.8 58.9 53.8 71.0 86.0 80.9 77.4 88.7 78.0 91.5 85.8 82.6 94.1 87.6 89.5 90.9 89.6 91.7 93.2 93.7 92.2 94.2 94.0 94.1 94.2 93.9 93.6 93.9 93.1 92.1 90.6 90.3 85.0 88.0 83.2 44.8 71.6 3.3 14.0 10.7 4.9 0.3 0.2 1.2 0.4 0.2 0.2 2.4 33.4 0.2 4.5 8.1 20.9 26.4 65.9 71.9 91.2 92.9 93.9 92.8 76.3

The concentration of each nuclide produced under the irradiation by particles from definite energy range is divided by the total amount of this nuclide forming during irradiation. Only nuclides with half-lives greater than 1 d and with the contribution of protons above 150 MeV less than 95% are shown. See the footnote to Table 2. a Contributions of different particle energy ranges can be approximately considered as additive values for all nuclides shown in the table.

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0.8

0.6

protons

0.4

0.2 Bi-208

4

5

6

7

8

9

10

10

10

10

10

10

3

10

10

2

10

1

10

0

10

-1

-2

10

10

10

-3

0.0 -4

Of particular interest is the knowledge of the activities of radionuclides at various cooling times. Table 2 shows the list of main radionuclides, for which the contribution to the total activity of lead–bismuth is maximal at different times after the irradiation. Fig. 5 shows radionuclides with the maximal contribution in the total activity at cooling times from several seconds up to 5  107 yr. Fig. 6 presents the relative contributions of group nuclides with different atomic numbers. It is seen that the activity of radionuclides with the atomic number from 70 to 84 dominates at all times after the irradiation.

Hg-194 +Au-194

10

3.2. The contribution of various nuclides to the long-lived activity of irradiated lead–bismuth

1.0

10

5  107 yr. For the comparison the values obtained in Refs. [4,39] using FLUKA 2006.3b [12] and INCL4/ABLA (MCNPX 2.5.0) [13] are shown. It is seen that the agreement between various calculations is rather good, with the exception of some discrepancy at about 5–10 yr of cooling. Part of the discrepancy is due to the tritium, which is dominating at these cooling times (Table 2) and is not properly calculated by the currently used INCL4/ABLA version in MCNPX 2.5.0.

Relative contribution

230

Cooling time (day) Fig. 8. Contribution of protons in the total activity of irradiated lead–bismuth.

3.3. The origin of nuclides produced under the irradiation

3.4. The comparison of nuclide yields calculated using various codes Nuclide yields calculated in the present work have been compared with results obtained in Ref. [4] using FLUKA 2006.3b [12] and INCL4/ABLA (MCNPX 2.5.0) [13]. Fig. 9 shows the yields of atoms in the LBE of MEGAPIE calculated with FLUKA and SNT codes. Figs. 10 and 11 present the statistics of the ratio of activity of radionuclides calculated by various codes and data libraries to the activity obtained in the present work (SNT). Data on Fig. 10 refer to all radionuclides presented in various sets of calculations after 1 yr of the cooling of irradiated lead–bismuth. Fig. 11 shows the statistics for radionuclides with activity higher than 109 Bq 1 yr after the end of the irradiation (75 nuclides). One can see that in the last case

Fig. 9. Comparison between calculated yields (atoms/proton) in the LBE of MEGAPIE, with FLUKA (version 2006.3b) and SNT codes.

0.6

FLUKA INCL4/ABLA (MCNPX)

0.5 Relative number

The contributions to the nuclide production of different parts of particle spectra were examined: the neutron energy range below 20 MeV, neutron energies between 20 and 150 MeV, neutrons with the energy above 150 MeV, protons with the energy below 150 MeV and proton energies above 150 MeV. Fig. 7 shows the contribution of radionuclides produced under the irradiation of lead–bismuth by neutrons and protons with different energies in the total activity. The irregularities reflect the change of the contribution of various groups of nuclides in the activity. Table 3 presents the contribution of different energy ranges of neutrons and protons in the production of radionuclides in lead–bismuth. The concentration of each nuclide formed under the irradiation by particles from the specific energy range was divided by the total amount of this nuclide produced during the irradiation and shown in Table 3 in percents. Only nuclides with half-lives greater than 1 d and nuclides with the contribution of protons above 150 MeV less than 95% in its production are shown. For this reason the main fission products are not included in the table, because their production in lead–bismuth is mainly by proton interactions with energies above 150 MeV. Fig. 8 shows the relative contribution of protons of all energies in the total activity of lead–bismuth after the irradiation.

0.4 0.3 0.2 0.1 0.0 10-5 10-4 10-3 10-2 10-1 100 101 102 Activity/Activity (SNT)

103

104

105

Fig. 10. Ratio of the activity of radionuclides calculated by FLUKA (thin line) and INCL4/ABLA (MCNPX) (thick line) to the activity of radionuclides obtained in the present work (SNT). See details in the text.

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Table 5 Cross-sections for the hydrogen and helium isotope production averaged using energy distributions of neutrons and protons in lead-bismuth (Fig. 3).

0.6 0.5 Relative number

231

Particle produced

Averaged cross-section (mb)

FLUKA INCL4/ABLA (MCNPX)

0.4

Proton Deuteron Triton 3 He+4He

0.3

Protons

Neutrons

2160 325 90.8 220

18.4 4.65 1.09 2.21

0.2 Table 6 Production rates of hydrogen and helium isotopes (atoms per incident protons) in lead-bismuth calculated in Refs. [4,39] and in the present work basing on evaluated data (Figs. 1 and 2).

0.1 0.0 10-5 10-4 10-3 10-2 10-1 100 101 102 Activity/Activity (SNT)

103

104

105

Fig. 11. Ratio of the activity of radionuclides calculated by FLUKA (thin line) and INCL4/ABLA (MCNPX) (thick line) to the activity of radionuclides obtained in the present work (SNT). Radionuclides with the activity higher than 109 Bq are selected. See details in the text.

Table 4 Comparison of activities (Bq) of radionuclides relevant to the safety analysis after 1 yr of cooling. Nuclide

FLUKA

INCL4/ABLA (MCNPX)

SNT

H3 Se 75 Kr 85 Rb 83 Y 88 Zr 95 Ru 106 Rh 101 Rh 102 Cd 109 Sn 113 Sn 119 m Lu 173 Hf 172 Hf 175 Ta 179 Re 183 Os 185 Pt 193 Au 195 Hg 194 Tl 204 Bi 207 Po 208 Po 210

7.72+12 4.79+10 1.17+11 8.82+10 2.46+11 1.32+11 6.17+11 7.67+10 2.14+11 1.30+11 3.12+10 3.01+11 1.85+11 1.28+11 6.21+10 6.82+11 3.59+11 1.12+12 6.57+11 1.90+13 9.33+10 2.70+12 4.26+12 2.18+12 2.19+13

– 4.56+10 1.19+11 8.93+10 1.95+11 1.35+11 4.67+11 8.50+10 1.56+11 1.54+11 4.07+10 2.39+09 2.07+11 1.14+11 7.56+10 1.05+12 5.71+11 1.99+12 6.57+11 1.76+13 7.12+10 4.38+12 5.05+12 9.43+11 2.07+13

6.12+12 1.15+11 1.59+11 3.22+11 6.11+11 1.14+11 4.57+11 1.73+11 1.92+11 4.47+11 1.33+11 2.08+11 3.48+11 2.39+11 1.20+11 1.40+12 6.88+11 1.93+12 7.89+11 2.05+13 1.04+11 3.84+12 5.11+12 1.59+12 1.45+13

See details in the text and the footnote to Table 2.

the agreement between various calculations is better. The analysis of difference in the calculated activity of radionuclides (Fig. 10) has shown that the main deviation between different results is observed for the yield of fission products with atomic masses far from fission peaks. Absolute yields for these mass ranges are rather small and experimental data for nucleon interactions with heavy nuclei are scarce. Table 4 illustrates the absolute values of activities of radionuclides calculated using various codes and data libraries. The data are shown for 25 radionuclides with the highest activity after 1 yr of cooling, chosen from the list of most relevant nuclides for safety analysis [4,40]. The difference of results is caused mainly by the use of various data sets and model calculations in the activation analysis. In the case of 210Po the difference can

Particle

Proton Deuteron Triton Helium isotopes

MCNPX 2.5.0 INCL4/ABLA

Bertini/Dresner

1.57 – – 0.173

1.83 0.089 0.048 0.203

FLUKA 2006.3b

SNT

1.15 0.22 0.073 0.114

1.2770.17 0.21070.020 0.05770.012 0.13370.025

result from the application of pre-defined 63 group (n, g) reaction cross-sections in MCNPX (CINDER90) calculations. The comparison of various codes relating to MEGAPIE is given also in Ref. [41]. 3.5. Production rates for hydrogen and helium isotopes Table 5 shows proton, deuteron, triton and helium production cross-sections averaged using energy distribution of neutrons and protons in lead–bismuth eutectic. Corresponding p+Pb and p+Bi cross-sections were discussed in Section 2.2. It is seen that the contribution of protons in hydrogen and helium production is more than 80%. The production rates obtained for hydrogen and helium isotopes are printed together with results of Bertini/Dresner, INC4/ABLA and FLUKA 2006.3b calculations [4,39] in Table 6. One should note that the ‘‘SNT’’ data were obtained using crosssections evaluated based on the results of measurements (Figs. 1 and 2). The error shown for ‘‘SNT’’ originates from the evaluation procedure (Section 2.2). The rates obtained by FLUKA and INCL4/ABLA show the best agreement with evaluated data compared with the default model of MCNPX code Bertini/Dresner.

4. Conclusion In the present work the nuclide composition of the irradiated MEGAPIE lead–bismuth target has been calculated. An important feature of the calculations is the use of all available experimental information on neutron- and proton-induced reaction crosssections for lead and bismuth isotopes at energies from 105 eV to 600 MeV. This information is incorporated in evaluated data files applied for the calculation. The analysis of the activity of irradiated lead–bismuth eutectic has been performed: the contribution of groups of nuclides produced in the spallation, fission and cluster emission, the contribution of separate radionuclides and main contributors to the activity of lead–bismuth have been determined at different times after the irradiation. The influence of various ranges of neutron and proton energy distributions on the nuclide production

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