Measurement of e Westcott Conventionality Thermal Neutron Flux and Suchlike at Irradiation Facilities of e KUR Hiroshi CHATANI Research Reactor Institute, Kyoto University Kumatori-cho, Sennan-gun, Osaka 59-494, Japan E-mail: chatani@rri.kyoto-u.ac.jp The ermal neutron flux and e epiermal index, i.e., e streng of e epiermal de/e component relative to e neutron density including bo ermal and epiermal neutrons, at e hydraulic conveyer (Hyd), pneumatic tube No. 2 (Pn-2) and slant exposure tube (Slant), i.e., principal exposure facilities of e Kyoto University Reactor (KUR), are measured by e multiple foil activation meod using e Au(n, )Au-198 and Co(n, )Co-6(g+m) reactions. Alough neutron flux varies wi core configuration et al., e.g., number of fuel elements, e available values at Hyd are at e ermal neutron flux is (1.7.3) 1 14 cm 2 sec 1, e epiermal index is.373.9 and e fast neutron flux is (3.8.2) 1 13 cm 2 sec 1. Moreover, ermal and fast t neutron flux distributions are low at e top and high at e bottom of an Al irradiation capsule of Hyd. The gradient is 14 % / 8 cm in height. The distributions in e horizontal direction are flat wi a 2.2 cm diam. 1. Introduction There are some experimental holes and irradiation facilities in e KUR for practicing various experiments. The irradiation facilities are used for e production of radioisotopes (RI), radioactive analysis, material testing, cross-section measurement and so for. Therefore, determination of e neutron flux is of great importance for evaluating or predicting e activity or neutron fluence, i.e., flux time. Furermore, recently, studies on nuclear transmutation management have been actively carried out. Concerning e experiments using reactors, measurement of e (n, ) cross sections is required. In particular, when e (n, ) reaction cross sections, normally listed values, are measured, it is necessary to determine e 22 m sec 1 neutron flux. Accordingly, e Westcott conventionality ermal neutron flux [1], epiermal index and so for are studied at Hyd: at e center of e KUR core, Pn-2: in e graphite reflectors and Slant: outside e reflectors; configurations of e facilities are illustrated in Figs. 1 and 2. Furermore, neutron flux distributions of ermal+epiermal (sum of ermal and epiermal) and fast in e irradiation capsules are measured. These distributions are useful for discussing e ununiformity of activation or setting up monitor foils for e measurement of e cross-sections. 2. Westcott conventionality ermal neutron flux using multiple foil activation meod According to e convention proposed by Westcott et al.[1], e effective cross section σˆ in e well-moderated ermal neutron reactors is expressed as
( ) σ ˆ = σ g + rs, (1) where is a 22 m sec 1 cross section, g and s are functions of e temperature T and are measures of e departure of e cross-section law from e 1/v form in e ermal and epiermal regions, respectively. The former factor is e Westcott g-factor, which is tabulated by Westcott [2]; r is e epiermal index. If e cross section obeys a 1/v law, g = 1 and s =. Furermore, s is defined as s 1 4 T = I σ π T, (2) where T is e room temperature 293.6 K, and I is a reduced resonance integral which is obtained by subtracting e 1/v-term from an excess resonance integral I, which is given by I = I. 45σ, if cadmium cutoff energy E Cd is.5 ev. Therefore, e reaction rate will have e form [3] ( gg r T T s ) R = nv σ + G epi. (3) Here, n is e neutron density including bo ermal and epiermal neutrons, and v is 22 m sec 1. G and G epi are e corrections of self-shielding for ermal and epiermal neutrons, respectively, and ese are described in e following. G is calculated using [4] 1 2E3( τ ) G =, ( = Σ a t) 2τ τ, (4) where E 3 is e exponential integral, a is e macroscopic absorption cross-section for 22 m sec 1 neutrons, and t is e ickness of e detector. Moreover, Beckurts and Wirtz [5] propose a simple approximation for G epi as 1 G epi =, (5) 1+ 2µ δ a where a is e mass absorption coefficient at e peak of a resonance and is e surface mass loading. s is e invariant quantity of s and is expressed as divide Eq. (3) by gg, T s = s = I T σ π 1 4 [6]. Furermore, to σ gg s G R = nv nv r T T + gg epi. (6) Equation (6) is a linear equation accompanied by an intercept nv (Westcott ermal neutron flux) and an inclination nv r T T (epiermal neutron flux). Exactly e same equation having a common intercept and inclination will be formed for e Au(n, )Au-198 and Co(n, )Co-6(g+m) reactions, if Au and Co are irradiated at e same time and at e same position [3].
Table 1 Nuclear data and parameters used Reaction (barns) [7] I (barns) [7] g (at 4 ) G G epi Au(n, )Au-198 98.65.9 155 28 1.64 [2].999.992 Co(n, )Co-6(g+m) 37.18.6 74 2 1.999.997 3. Experimental The activation detectors used were.1143%au-al alloy foils,.314%au-al alloy wires and.483%co-al alloy foils. Therefore, G G 1, since ese detectors can be approximated to infinite dilution. In e case of Hyd, several tens mg of Au-Al and Co-Al were hermetically enclosed in a 5-mm-diameter quart tube, set in an Al capsule, and en irradiated at 5 kw for 1 min. Induced activities were measured using calibrated high-purity Ge detectors (HPGe). Moreover, fast neutron fluxes were measured using e Ti(n,p)Sc-47 or at of -48 reactions. Arrangements of e detectors in e capsules for all e cases have been shown elsewhere [8, 9]. 4. Results and discussion Appearances of Eq. (6) for ese ree facilities are shown in Fig. 3. Results of e ermal neutron fluxes and so for are tabulated in Table 2. The epiermal index varies from.11 to.47 depending on e facilities. It is clarified at by making e most of e distinctive qualities of each facility, measurement of e (n, ) effective cross sections for various epiermal indexes is possible. Therefore, e effective cross section at r T T =, i.e., at e Maxwellian component only, on e extension line connecting two effective cross-sections measured at different facilities, will be available [1]. Relative distributions of e ermal+epiermal and e fast neutron fluxes in e irradiation capsules are shown in Figs. 4, 5 and 6. In ese figures, ermal+epiermal distribution simply means e relative reaction rate of e Au(n, ); erefore, in e cases of Hyd, Pn-2 and Slant, respectively, approximately 6, 7 and 17 % of e reaction rates are caused by epiermal neutrons. Difference of e ermal neutron fluxes of Hyd 1 st exp. and Hyd 2 nd exp. in Fig. 3 is considerably dependent on e number of e fuel elements, which were 24 and 21, respectively. Graphite ermal column Lead Slant R A Hyd B SSS Si Lon g Hyd Si A 93% enriched fuel elements 2% enriched silicide fuel element A, B, C, D, R: Control rods 9.7 cm C D Pn-3 Pn-2 SSS Graphite reflectors Material controlled irradiation facility Pn-1 Light water Lon g Long-term irradiation plug D2O ermal column Fig.1 Horizontal core configuration
CO 2 gas Polyey Slant Hyd Light water Pn Aluminum lene jar (5 ml) KUR Core capsule 12 cm 9.7 cm 5.7 cm 5.7 cm Polyeylene capsule Light water Fig. 2 Vertical configuration of e irradiation facilities Table 2 Westcott ermal neutron flux and so for at e irradiation facilities of e KUR Facility: Hyd (1 st exp.) Pn-2 Slant Detector position in a capsule: 1 cm above e bottom Near e center 2 cm above e bottom nv (cm 2 sec 1 ) ( 1.7.3) 1 14 ( 1.76.4) 1 13 (1.9.3) 1 13 nv r T T (cm 2 sec 1 ) ( 4..1) 1 12 ( 8.21.21) 1 11 (1.18.3) 1 11 r T.373.9.466.12.18.4 T Cd-ratio of Au (R Cd ) a) 2.53.6 2.22.6 6.3.3 Fast neutron flux (cm 2 sec 1 ) ( 3.8.2) 1 13 b) ( 3.4.1) 1 12 c) 12 b) (1.5.4 ) 1 a) Calculated using R Cd g + s r T = r T T T f s δ + g K 1 where K is Westcott s K -factor which is tabulated by Westcott et al. [1], f is transmission of e 4.9 ev neutrons rough a Cd ickness δ. δ b) Determined using e averaged cross section σ = 17.7 mb of e Ti(n,p) 47 Sc reaction for e fission neutron spectrum of 235 U. c) Determined using e averaged cross section σ =.32 mb of e Ti(n,p) 48 Sc reaction.
Fig. 4 Neutron flux distributions in an Al capsule of Hyd. Left: horizontal direction: along e inner wall of e capsule; Right: along e vertical axis Fig. 5 Neutron flux distributions in a polyeylene capsule of Pn-2. Left: horizontal direction: along e inner wall of e capsule; Right: along e vertical axis Fig. 6 Neutron flux distributions in a polyeylene jar of Slant. Left: horizontal direction: along e inner wall of e jar; Right: along e vertical axis
-2-1 ( ) cm R σ gg sec Fig. 3 Appearances of Eq. 4 for Hyd (1 st and 2 nd experiments), Pn-2 and Slant Intercept: ermal neutron flux Inclination: epiermal neutron flux 5. References s G gg epi [1] C. H. Westcott, W. H. Walker and T. K. Alexander, Effective cross sections and cadmium ratios for e neutron spectra of ermal reactors, Proc. 2 nd Int. Conf. Peaceful Use of Atomic Energy, Geneva, New York, 16, 7-76 (1958). [2] C. H. Westcott, Effective cross section values for well-moderated ermal reactor spectra, AECL-111 (196). [3] H. Matsuoka and T. Sekine, Reactor-neutron monitoring wi multiple activation detectors, JAERI-M 9552 (1981) (in Japanese). [4] G. C. Hanna, The neutron flux perturbation due to an absorbing foil; a comparison of eories and experiments, Nucl. Sci. Engineering, 15, 325-337 (1963). [5] K. H. Beckurts and K. Wirtz, Neutron Physics Springer-Verlag, Berlin, 268 (1964). [6] W. H. Walker, C. H. Westcott and T. K. Alexander, Measurement of radiative capture resonance integrals in a ermal reactor spectrum, and e ermal cross section of Pu-24, Can. J. Phys., 38, 57-77 (196) [7] S. F. Mughabghab, M. Divadeenam and N. E. Holden, Neutron Cross Sections (Vol.1), Neutron Resonance Parameters and Thermal Cross Sections, Academic Press, New York (1981). [8] H. Chatani, Measurement of e neutron flux distributions, epiermal index, Westcott ermal neutron flux in e irradiation capsules of Hydraulic conveyer (Hyd) and Pneumatic tubes (Pn) facilities of e KUR, KURRI-TR-432 (April, 21) (in Japanese). [9] H. Chatani, Measurement of e neutron flux of irradiation facilities of e KUR ( ), Slant exposure tube, 36 Scientific Lecture Meeting, KURRI (Jan., 22) (in Japanese). http://www-j.rri.kyoto-u.ac.jp/kouen/kouen36/36houbun/p13. pdf (in Japanese). [1] T. Sekine and H. Baba, A study of reactor-neutron-induced reactions: Double neutron capture process and e systematics of e (n,2n) reaction, JAERI 1266 (1979).