An interpretational technique of sandwich activation measurements

NUCLEAR INSTRUMENTS AND METHODS

119 (1974) 599-604; C

NORTH-HOLLAND PUBLISH? :

AN INTERPRETATIONAL` TECHNIQUE OF SANDWICH ACTIVATION ME.4ISUREMENT L. BOZZI, F. CAPORELLA, M. COSIMI

and

M. MARTINI

Centro di Studi Nucleari della Casaccia, Rome, Italy

Received 18 January 1974 The sandwich foil technique can be used for spectrum measurements in facilities with slowing-down neutrons. Measurements were made in the equilibrium spectrum of a large iron block after the detector calibration in a well known

E -1 spectrum . The interpretation technique makes use of an appropria, calculation with an "ad hoc" program . A good agreement w, found between the experimental and the calculated spect-t.

1. lfntroduction The low accuracy of cross-section sets and of the calculation methods in shielding problems oftendo not allow a good evaluation of neutronspectra in reflecting and shielding zones inside nuclear reactors . Experimental techniques can then be appliedto investigate differential neutron distributions and to facilitate comparison of calculations and measurements . Several techniques can be utilized for the different energy ranges : threshold detectors and 'Li sandwich spectrometers cover the energy range above 1 MeV 1 " 2) ; proton-recoil spectrometers, when accurately used, give good results over the energy range extending approximately from I keV to I MeV 3 ) ; sandwich activation techniques can give interesting results for in-pile measurements in slowing-down spectra below a few keV`'') . A simple interpretational method was developed for this last technique: the ACTIV code which calculates thedetector's self-shielding cross sections averaged in a neutron spectrum which, optionally, can be constantor E -1 inside each finite energy group relative to the resonances considered. The purposeof this note is to show the results of the application of such a technique to a s=owing-down spectrum inside a large iron block.

is included between the energies E; and E, + 1 in the energetic range Eat . Assuming that the princi resonance (i.e . the resonance which gives the highest activation in the flux under investigation) is included between the energies El and EZ, then the integral eq. (1) can be divided into several parts, as follows: E

E: +J

+

E

= fE

Je

-P(E)a(E)F(E, it) dE +

4,(E)a(E)F(E, d)dP, + ~

i=2,/ Ea~

+L

~oa ER,

1P(E)a(E)F(E, d)dE +

4t(E)o(E)F(E, ti)dE.

( ?

We consider now a three-foil sandwich, each fn 4 having thickness d; we call F,(E, d) and F; (E, d) ti-,-self-shielding factors for the outer and inner spa, respectively . If d is chosen in such a way that 1, d< 1, for energies outside the resonance ranges and B,d? 1 inside the resonance ranges, where E, is the t ¬ataamacroscopic cross sectionof thedetectortheditrcroncc of activation between the outer and the inner foyi i given by:

2. SaMwich technique Theactivation A of a single foil of thickness d in an isotropic neutron flux -P(E) is given by : A=

-P(E)a(E)F(E, d)dE

Ae -

E,

O(E)a(E) [F.(E,d)-F;(E,d)]dE

4,(E)a(E)F(E, d)dE,

F(E, d) being the self-shielding factor and a(E) the activation cross section. Let us assume that the detector cross section as n resonanes, each of widthF, andthat the ith resonance

If we select those detectors for which 1- 4 E,.,, we can suppose theneutronflux to be constant inside each resonance range; under this assumption we can rewrite eq. (3):

599

L. BOZZI et al . A,-A i =

O(Eies)

a(E)[Fe(E, d)-Fi(E, d)]dE +

If we use eq. (5) for the reference spectrum and we consider the ratio between the quantities in eq. (6), we obtain :

d)] dE, (4) a(E)[Fe(E,d)-F,(E, + 4(Eses) i=2 J Eru Cref where O(Ere,) is the flux at the energy of the ith resonance or, if the neutron flux is a rapidly varying When the detector hasmore than one resonance, eq . (7) function of energy, 4i(E .) will represent the mean becomes : value of the flux inside the ith resonance range. A If the detector cross section has only one resonance, 1 C 1 C ~ i 0ref(Eres) +41,.(,E",.) res) X the second term of eq. (4) is identically zero and it is ~(Eres) =. Crof Cref i=2 possible to calculate directly the flux value at the resonance energy: ~ a(E)[Fe(E,d)-Fi (E,d)]dE ,I En, A~-Ai X E VEre ) _ cr(E) [F.(E, d) -Fi(E, d)]dE a(E) [Fe (E, d)-Fi (E, d)] dE In a following part of this paper we will analyze the methods for calculating the integral in eq. (5). When it is not possible or convenient to make absolute measurements of the activation, it is necessary to use a well-known reference spectrum, which allows relative measurements. Let us introduce two new quantities: c = (A .-^Ai)!E, and 1 ,ef `- ref 1

f

~~ j a(E)[F.(E,d)-Fi(E,d)]dE x E,e, E=

J~r

a(E)[F.(E,

d) -Fi(E, 4dE.

Since the flux at the secondary resonance energies in the second part of eq . (8) is unknown, it is necessary to proceed to theevaluation of this flux by meansof an where a is the efficiency of the counting chain, c and iterative procedure based on an approximate guess. arethe differences of counting rates . Assuming an E-1 spectrum inside the group relative crer

260 Detector tick

Fig. 1. Self-shielding factors forAu,In, W, Mn,andCu detectors in E-1 9uß

SANDWICH ACTIVATION MEASUREMENTS

to the ith resonance eq. (8) can be written as c

c

1

(~rer) - - orafores) + - F., 0(u 0(üi,".)) X . Crcf i°2 .

Cref

x

ER, EZ

_

a(E)LF, (E, d)-Fi(E, (I)]E -' dE s

O(Urios) X

i=z

x

a(E) [F.(E, d)-Fi (E, d)] E - t dE

Ew, ('E_

a(E) [F.(E, d)-Fi (E, d)] E - 'dE a(E) LF.(E, d) - Fi(E, d)] E- ' dE

3. Self-shielded cross-section calculations To evaluate theself-shielding factor ofeq . (8) we have developedthe ACTIVcode by extending to sandwiches of an arbitrary number of foils surrounded by neutron absorbing filters the model used by Pearlstein and Weinstock') for a single detector. A detailed description of the formulation used and the flowchart of the code is given in ref. 9. Calculations have been performed with an expansion of the nuclide cross sections with the Breit-Wigner model modified to account for potential scattering. Theenergy mesh waschosen to isolate thecontribution of every resonance. The effect of scattering in the filter and in the detectors has been included to a first approximation . Primary and secondary activation values have been calculated. Primary activations are those caused by neutrons that have not collided previously in either the sandwich or thefilter . Secondary activations are those caused by neutrons that have scattered only once previously, either. i n the sandwich or in the filter. The sandwich foils andthe filter were assumed to be infinite slab and theflux has been considered to be isotropic. Scattering was assumed to be elastic and isotropic in the laboratory system. The neutronenergy after collision was assumed to be distributed with the same probability between the energy before thecollision andthevalueE' =E(A - 1)Z/ (A+1)2, A being. the atomic mass of the scattering nucleus. To test theprogram we have made some evaluations of the integral self-shielding factors as a function of detector thickness . Calculated results are shown in

fig . 1 where they are compared with the corre experimental values reported in the literature, nance parameters are those recommended by rc . The agreement is very good for all detectors large activation vs scattering cross section ~remarkable differences are shown for materials high scattering cross section. The calculated shielding is overestimated, as our scattering it neglects the contributions to the activation by 1~1 :~ neutrons which have been scattered more than oinside the detector. Therefore self-shielding facte for Cu and Mn have uncertainties of up to 20®fa . 4. Description of the measuring technique

Indium, gold, tungsten, lanthanum, copper, manganese and sodium were found to be suitable for sandwich measurements. A number of foils, usually three, of a given material are placed together and irradiated as a single foil surrounded by a ring necessary to position the detectors and to prevent edge effects. The foils are 10 mm in diameter ; the ring foil is 20 mm in diameter and is three times as thick as the single detector . All sandwiches are irradiated in a small cadmium box, 1 mm thick, to prevent a thermal flux effect in the sandwiches during the E'' Roux calibration. The thickness of the foils, listed in table 1, is chosen by means of the adimensional quantity S

A~Ai -A,

Tant¢ 1 Sandwich detectors . Nuclide

Material

Thickness (mm)

t1sln 197Au 1s5W -391 . s$Mn 63Ctf

50% alloy In-Pb Metal Metal Metal 88%-12% alloy Mn-Ni Metal NaCl pellets

0.05 0.03 0.1 0.2 0.09 0.05 0 .75

23Na

Energyp..,i ..:ip resora= (eM; 4.1n 18.(; 72 .E 337 .0 571 .0 2850.0

where A. and Ai are the activities of the outer and inner foils of the sandwich according to the two following competing criteria :

Fig . 2. d slope as a function of detector thickness in an E-1 flux . TABLE 2 1) the S value is as large as possible ; 2) the contribution to the activation difference (3) - -Resonance integrals . from the main resonance is maximum in comparison with the same contribution due to the other resonances . Maximum and Elem nt /°° calculated by suggested ACTIV code resultsl 4) min mum value The S values are calculated by the ACTIV code and are shown in fig. 2 . Comparison between experimental and calculated 3 1515 1505 143215) "'Au values is not good for Mn and Cu because the scat158416) tering cross section is very high with ;respect to the s'Mn 1 .9 11 .1 10.717 ) activation one. This difference is obviously due to the 15.616) calculation procedure, because the errors in experi~Cu s a :1 3 .9887) mental data relative to the E` flux with high intensity s.6 ) are of the order of 2 6/6 maximum . On the other hand -in 2787 2372 19) resonance integrals at infinite dilution, calculated . by 3650 the ACTV Idriteslcid coe, agee wh ruts ontanen ih) te 494 276 22) literature (see table 2) ; therefore Cu and Mn S differ186 w ences do not depend on nuclear parameters, but are due to thé inadequate model for scattering . The consequence of the scattering model is that the t) self-shielding factors are overestimated for copper and 5 . Irradiation facilitlesl manganese; therefore we have found it convenient to Sandwich foil measurements were made in an iron utilize as broad group cross sections for such elements block contained in a hermetically closed stainless-steel and for the thickness used in the measurements those tank and placed in a light-water pool at the end of the cross-section values relative to the thickness for which heavy-water thermal column of a- TRIGA reactor calculated b values strictly agree with the experimental (fig. 3) . An enriched uranium fission plate supplies a ones. This procedure is supported by a comparison source of fast neutrons penetrating into the iron block. " between calculated and experimental` self-shielding To calibrate detector counting efficiencies an factor; for a single foil . identical set of foils was irradiated in the centre of the

SANDWICH ACTIVATION MEASUREMENTS

Fig. 3. Iron column and detector channels. -DTF 4 10°

"

SANDWICH

0W "M.

It)' Fig. 4. Flux slope in theiron equilibrium spectrum. RANA reactor at Casaccia, which is known to have an E-i epithermal neutron flux . Foil activities were measured by gamma counting with Nal detectors. Measurements in the iron were made in the middle

zone ofthe blockwhereaneutron equilibrium spectrum hasbeen established. Theneutron energetic distribution, typical of a slowing-down spectrum is such that the major contribution to the activity difference measured for each material was due to its lowest energy resonance. Therefore, the foil response is similar in the

unknown and in the reference neutron spectrum 4nd the sandwich technique can be successfully used. The measured differences vary between about 6% for manganese to about 55% for indium. An acceptable accuracy (2-15%) was obtained in the experimental determination of the difference of activities by using considerable care (in irradiation

and counting times) with the detectors with thesmaller difference of activities.

L. BOZZI ot al.

6. Experimental results and discussion The results of the measurements in' the iron block are shown in fig. 4and arecompared with acalculated 26-group spectrum obtained by the transport code DTF-IV '2) using the ABBN cross-section set13). Experimental and calculated flux points are normalized at the lanthanum energy, because theoretical results show that in the reference and the iron spectra the contribution of the principal resonance at the activity difference is about 100% for the lanthanum sandwich. Therefore the determination of the point flux at the lanthanum resonance energy can be obtained by eq . (7) with a remarkable precision. Several of the calculated higher-resonance points are included in fig. 4, even if the uncertainties in such points are very large due to the small percentage of measured activity contributed by the resonances. Experimental points' were calculated' from eq. (8) by the nuclear data output from the ACTIVcode, and by a flux guess obtained with the approximation that each measured activity difference was only depending on the principal resonance .An iterative process' was followed to account for the secondary-resonance contribution and we found the final flux slope within about i % with thesecond iteration already, due to the small activity differences (ranging from 5-10%) of the otherresonances in comparison with the principalone. The errors in the experimental points are, above all, due to statistical errors on the measured cunerences and, in minor percentage, to theflux guess and to the caieulated self-shielding factors., Therefore the error depends onthe S value andit ranges from 5%to 20 %. As it appears in fig. 4 the manganese :point deviates from the calculated flux farmore than by the foreseen errors ; this is justified by a 0.8 % manganese content in the iron used which causes aremarkable depression of the neutron flux at the Mn resonance energy in the middle of the block. The calculations, on thecontrary, do not show this sharp depression due to the broad group structureused.

References 1) W. L . Zijp, Review of activation methods for the determination of fast-neutron spectra, RCN 37 (Reactor Centruns Nederland, 1965). 2 H. Bluhm and D . Stegemann, Nucl. Instr. and Meth . 70 (1964) 2 . 3 ) E. F. Bennet, Nucl. Sci . Engng. 27 (1967) 16. 4) G. Ehret, Atompraxis 1 (1961) 393 . 5) A. Weitzberg, Proc . Conf. on Fass critical experbttents and their analysis, ANL 7320 (Argonne, 1966) p. 535 . 9) T . J. Connolly and F. de Kruijf, An analysis of twenty-four isotopes for use in multiple-foil measurements of neutron spectra below 10 keV; S. S . Schmidt, Recommended resolved and statistical resonance parameters for twenty-four isotopes, KFK-718 (1968). 1) M . Müller, Messung von Neutronenspektren in Energiebereich von 1 eV bis 10 kcV mit Hilfe der Sandwichtechnik, KFK-1233 (1970) . s) S . Pearlstein and E. V. Weinstock, Nucl . Set. Engng. 29 (1967) 28. B) L. Bozzi, F. Carorella and M. Cosimi, Il codice AGTIV, RTJFI (73) 35. to) BNL 325, 2nd Edition Suppl. no. 2 (1966) . 11) L. Bozzi and M. Martini, ESIS Newsletters (to be published). 12) K. D. Lathrop, DTF IV, a Fortran-4 program for solving the multigroup transport equation with anisotropic scattering, LA-3373 (1955) . 11) L. P, Abajan et al., Atomizdat, Moscow (1964). 14) W. L., Zijp, Review of activation methods for the determination of intermediate spectra, RCN-40 (Reactor Centrum Nederland, Oct . 1965) . 1s) K . Jirlow, J . Nuc1 . Energy Pt. A 11 (1960) 101 . 16) R . Vidai,- Mesure des intégrals de résonance d'absorption . CEA-R 2560 (1964). 17) A . Gibello, Nucl. Sci . Engng. 40 (1970) 51 . 1s) W. L. Zijp, Results of the W.G.R.D. inquir y into the utilization of activation detectors, RCN-71-025 (Reactor Centrum Nederland). 19) 3. P. Harris, L. Mmlha= and G. Thomas, Phys . Rev. 79 (195°)11. 20) N. P. Baumann, Resonance integrals and self-shielding factors for detector fop, DP-817 (1963). 21) R. B. Tattersall, H . Rose, 3. K. Panenden and D. Jowiu, J. . Bct . Energy Pt: A 1z Turco) 32. ' M A. M . MI Tureo and A. Rata, Pros. EAEs ) Symp. on~' Fast and Epithermal neutron spectra reactor (HERE/R/5400, 1964) pt 3, p. 221.