United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency

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1 Available at: IC//57 Uited Natios Educatioal, Scietific ad Cultural Orgaizatio ad Iteratioal Atomic Eergy Agecy THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SCREENING EFFECT IN (p) REACTIONS ON HEAVY ELEMENT TARGETS Pb, 92 U, 74 W, 79 Au Nguye Mog Giao 1 Hug Vuog Uiversity, 342Bis Nguye Trog Tuye Street, Ta Bih District, Hochimih City, Vietam ad The Abdus Salam Iteratioal Cetre for Theoretical Physics, Trieste, Italy, Le Thi Thah Truc Hug Vuog Uiversity, 342Bis Nguye Trog Tuye Street, Ta Bih District, Hochimih City, Vietam ad Nguye Thi Ai Thu Trasport College, 189 Kih Duog Vuog Street, District 6, Hochimih City, Vietam. MIRAMARE TRIESTE July 1 Seior Associate of ICTP.

2 Abstract We preset a simple model to calculate multiplicities of the eutros emitted i the 6 iteractio of a proto beam eergy from.5 GeV to 1.5 GeV o some targets such as Pb 197 Au , 79, 92 U usig the database of the JENDL-HE library. The results are compared with others Model ad the available experimetal data [3,6,8,9]. The agreemet is satisfactory. 1

3 INTRODUCTION Oe of the mai problems of uclear power owadays is radioactive waste maagemet. Some of the produced radioactive isotopes have a very log lifetime, potetially represetig log term radiatio hazards. Effective trasmutatio of these isotopes ito the short lived or stable oes eeds cotiuous eutro fluxes with itesity i the 16 /cm 2 rage [3]. Such itesity is approximately times larger tha itesities typically available i a large scale reactor. I curretly proposed Accelerator Drive Systems (ADS), the accelerator bombards heavy target with high itesity (about ma) ad eergy aroud 1GeV proto beam to produce the above metioed high itesity of eutros. The eutros ca be further multiplied i a sub-critical reactor which surrouds the spallatio target ad i which log lived uclear waste is trasmuted. Although the (p, ) reactio mechaism has bee kow for may years, the actual uderstadig is ot sufficiet whe oe has to face the desig of the realistic target-blaket systems. Hece, ew accurate studies of eutro productio i proto iduced reactios, as well as of eutro s propagatio through differet materials, are eeded. I the past, few experimet results were available for thi target [15], i which the icidet proto beam is of equal eergy ad the target is cosidered homogeeous. Problems such as screeig effect, the loss of projectile eergy ad the umber of residual protos o target have ot bee metioed yet, but for massive target additioal studies of eutro spectra ad cross-sectio are eeded. I this work, spallatio eutros were geerated by bombardig about 5 cm log cylidrical target with the icidet eergy 1 GeV. Neutro multiplicities geerated by a 6 icidet proto beam o 82 Pb target of legth 5 cm ad the umber of residual protos o target was calculated. The obtaied results have bee discussed ad compared with the experimetal data take from literatures [8]. The mai idea of this paper is the target is divided ito layers to calculate the proto eergy loss ad eutro yields from (p, ) reactio o each sub-layer of target. This is the differece betwee our work ad other work [9], [13], [16]. CALCULATION MODEL All calculatios previously cosidered that the target is homogeeous ad the icidet proto eergy does ot chage durig iteractio with target uclei which is called the homogeeous Model. For the cocept, we used the JENDL-HE uclear library to calculate the eutro multiplicity from spallatio reactio o the targets 82 Pb, 79 Au, 92 U. Calculatio results from homogeeous model o the lead target with thickess from cm to cm show i table 1 ad figure 1 below: 2

4 Table 1: The eutro multiplicity o targets Pb-6 Thickess (cm) Neutro multiplicity (/p) Homogeeous LAHET [6] model Figure 1: Neutro multiplicity o lead target i homogeeous ad LAHET code model The calculatios have bee compared with the calculated data from LAHET- Iteratioal code [6]. From the obtaied results, we ca coclude that the homogeeous model used i this study does ot give results i good agreemet with the calculated data from iteratioal data. To improve, we offer a ew calculatio model. As we kow, whe protos eter a medium, they lose eergy for iteractio with target uclei. This loss ca be calculated from the Bethe Bloch formula. Assumig the target is divided ito layers, proto eergy comes to the target be E. Neutros produced i the first layer are due to the iteractio of proto with target. Whe passig the first layer, proto eergy reduced to E 1 - it is the icidet eergy at the secod layer of target, where: de E = E 1 dx 3

5 At that time, the umber of eutros produced i the secod layer was N. The iteractio process will cotiue, lastly, the umber of eutros geerated is: I this problem, we assume that the target thickess is 5 cm ad divided ito 5 layers, of 1 cm thickess each. Thus the umber of eutros geerated is: With this model, we also used the JENDL library to calculate the eutro multiplicity 6 o the target Pb 82. Calculatio results from the ew model o the lead target with thickess from cm to 5 cm is show i table 2, figures 2 ad 3. 1 Table 2: The eutro multiplicity o targets Pb-4 Thickess (cm) 5 Neutro multiplicity (/p) New model LAHET [6] d =1cm d =1cm d =1cm d =1cm E p = E de de E1 = E 1 de2 E2 = E1 E3 = E2 dx dx dx E E dei = Ei dx Figure 2: The evisaged model of spallatio eutro target 4

6 Figure 3: Spallatio eutro yield o lead target i homogeeous model ad LAHET code model It is evidet from the figure that the calculated values for Pb are i relatively good agreemet with iteratioal code values. (The ew model results relatively coicide with the LAHET code data usig both the Bertii ad the ISABEL model ad with experimet data.) We also calculate the umber of residual proto after particle beam (Ep = 1 GeV) goes through x cm target thickess. Table 4 below illustrates this. Table 4: Number of residual proto after particle beam goes through x cm target thickess Target thickess (cm) 5 Number of residual proto (%) Au We used the ew model to calculate the spallatio eutro yield o some targets W, 79, 92 U. The figures below illustrate eutro multiplicities geerated by a icidet proto beam at differet eergies o targets 82 Pb, 79 Au, 92 U, W, 28 Ni, 23V. 5

7 Neutro multiplicity (/p) Proto eergy (MeV) Figure 4: Neutro multiplicit o Pb-6,W-184, U-238,Ni-6, V-51, Au-197 targets at 15MeV I figure 4, we show the values of eutro multiplicities obtaied with icidet eergy 15 MeV. 6 We made a compariso of eutro multiplicities o differet targets, such as, 82 Pb, Au ad U i case the same thickess (see figures 5 ad 6 below) Pb6 U238 Au197 x= cm 16 /p Ep (GeV) Figure 5: The eutro multiplicity o targets Pb-6, U-238, Au- 197 at cm thickess 6

8 Pb 6 U 238 Au 197 x= cm /p E (GeV) Figure 6: The eutro multiplicity o targets Pb-6, U-238 at cm thickess We ca see that whe target thickess icreases, the eutro multiplicity icreases. This proves that eutro multiplicity depeds o target thickess. Now, we cosider the eutro multiplicity o targets Pb-6, U-238, Au-197 i case they have the same thickess. Figures 7, 8, 9 ad illustrate these Pb 6 U 238 x=35 cm 8 6 /p E (GeV) Figure 7: The eutro multiplicity o targets Pb-6, U-238 at 35 cm thickess 7

9 cm cm 35 cm Pb 6 /p E (GeV) Figure 8: The eutro multiplicity o target Pb-6 at differet thickesses cm, cm, 35 cm 8 x= cm x= cm x=35 cm U /p E (GeV) Figure 9: The eutro multiplicity o target U-238 at differet thickesses cm, cm, 35 cm 5 Au x= cm x= cm x=35 cm /p E(GeV) Figure : The eutro multiplicity o target Au-197 at differet thickesses cm, cm, 35 cm 8

10 We have followig remarks: The eutro multiplicity icreases whe the icidet proto eergy icreases. Whe the thickess of targets icreases, the eutro multiplicity icreases with icreasig of the icomig proto eergy. From that poit, we ca draw that eutro efficiecy depeds o target material. At the proto eergy (E p ) with the same target thickess, the value /p icreases liearly The we cosider the eutro multiplicity o targets i the case of the same icidet proto eergy i figures 11 ad 12 5 E=1. Gev E=1.5 Gev E=2. Gev E=3. Gev Pb 6 /p x (cm) Figure 11: Spallatio eutro yield o Pb-6 target at E p = 1GeV, 1.5GeV, 2GeV, 3 GeV 8 E=1. GeV E=1.5 GeV E=2. GeV E=3. GeV U /p x(cm) Figure 12: Spallatio eutro yield o U-238 target at E p = 1GeV, 1.5GeV, 2GeV, 3 GeV 9

11 From the above figures, we ca see that the eutro multiplicity icreases with the icidet particle eergy. I short, the spallatio eutro yield depeds strogly o the target compositio ad geometry, ad o the eergy of the impigig proto. Figures 13 ad 14 show a compariso of spallatio eutro yield betwee the calculatio results with the measured data of Doctoral Thesis of Marcus Eriksso- Departmet of Nuclear ad Reactor Physics, the Royal Istitute of Techology- Stockholm 5. The calculated results are good agreemet data. Compariso with other works (a) Result from Doctoral Thesis of Marcus Eriksso [8] (b) Result from this work Figure 13: Spallatio eutro yield as fuctio of icidet proto eergy o lead target Figure 14: Compariso betwee result of Marcus Eriksso ad this work result

12 CONCLUSION This paper gives the exteded iitial results of the target study usig the database of JENDL- HE library for simulatio of particle iteractios with differet materials with the aim to choose ad desig a optimal target i respect to spallatio eutro yield. The result of our simulatio supplies a larger umber of produced eutros; this may be attributed to the fact that i the simulatio all eutros are couted, already i the experimet the detectors do ot measure all eutros. Ackowledgmets This work was doe withi the framework of the Associateship Scheme of the Abdus Salam Iteratioal Cetre for Theoretical Physics, Trieste, Italy. Refereces [1] [2] [3] [4] [5] [6] [7] [8] [9] [] S. Aefalos et al., Developmet of CRISP package for Spallatio Studies ad its utilizatio i ADS (Accelerator Drive System), Nuclear Sciece ad Egieerig, 5 (Accepted for Publicatio) A. Letoureau et al., Neutro productio i bombardmets of thi ad thick W, Hg, Pd target by.4,.8, 1.2, 1.8, ad 2.5 GeV protos. Nucl. Ist. ad Meth. B17 () C.D. Bowma et al., Nucl. Istr. ad Meth. A3 (1992) 336 D. Dazhao, Z. Zhixiag, F. Sheg ad S. Qigbiao, et al., Proceedigs, Symposium o Coceptio research of the clear uclear eergy system drive by accelerator, Beijig, Atomic Eergy Publishig House, Beijig () (i Chiese) ENDF-6 Formats Maual Data Formats ad Procedures for the Evaluated Nuclear Data File ENDF/B-VI ad ENDF/B-VII-The Member of the Cross Sectio Evaluated Workig Group- Natioal Nuclear Data Ceter Brookhave Natioal Labotory- NY José R. Maiorio, Sara T. Mogelli, Adimir dos Satos, Sergio Aefalos, Airto Deppma ad Thiago Carluccio, A review of models ad codes for eutro source (spallatio) calculatio for ADS applicatio, Iteratioal Nuclear Coferece- INAC 5 X.C. Mao et al., High-eergy Physics ad Nuclear Physics, 23(4) (1999) 2 (i Chiese) Marcus Eriksso, Accelerator-Drive Systems: Safety ad Kietics, Doctoral Thesis - Departmet of Nuclear ad Reactor Physics- Royal Istitute of Techology- Stockholm 5- P.C.R. Rossi ad J.R. Maiorio, The utilizatio of MCNPX 2.5 for ADS target calculatio, Iteratioal Nuclear Atlatic Coferece- INAC 7 C. Rubbia et al., CERN/AT/95-45(ET)/(1995) 11

13 [11] [12] [13] [14] [15] [16] E. Richard et al., LA-NR-14 (1989) F. Sheg et al., Ph.D. Thesis, Chia Istitute of Atomic Eergy, Eur. Phys. J. A4 (1999) (i Chiese) S. Meard, J.P. Schapira, D. Vautheri ad P. Boche, Iteractio of a high eergy proto beam with a thick target: a model descriptio, Nucl. Phys. (1997) V. Baylac-Domegetroy, Ivestigatio related to the geeratio of reactio products i the target of Accelerator Drive Systems for uclear waste icieratio, FZKA publicatio, December 3 Yu.V. Trebukhovsky et al., ITEP-3, 3; Yad. Fiz.67, 87 (4) Z. Zhao, Z. Luo, Y. Xu ad D. Dig, Study o ADS Pb (Pb/Bi) spallatio target, Chia Istitute of Atomic Eergy Beijig, Chia 12