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Nuclear Instruments and Methods in Physics Research B 264 (2007) 83–95

NIMBBeam Interactions

with Materials & Atoms

Determination of the radionuclide inventory in accelerator wasteusing calculation and radiochemical analysis

D. Schumann a, J. Neuhausen a, R. Weinreich a, F. Atchison a,*, P. Kubik b, H.-A. Synal b,G. Korschinek c, Th. Faestermann c, G. Rugel c

a Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerlandb Paul Scherrer Institut, c/o Institute of Particle Physics, ETH Zurich, CH-8093 Zurich, Switzerland

c Technische Universitat Munchen, D-85747 Garching, Germany

Received 15 May 2007Available online 10 August 2007

Abstract

We use a description of the work carried out to determine the radioactive inventory for a redundant beam-dump from the PSI accel-erator complex, as an illustration of techniques for the classification and characterisation of accelerator waste and how some difficultiescan be circumvented. The work has been carried out using a combination of calculation and sample analysis: The inventory calculationeffectively involves a large scale Monte-Carlo transport calculation of a medium-sized spallation facility and for the sample analysis,standard radiochemical analysis techniques have had to be extended to include AMS measurements so as to allow measurement of someof the long half-life, waste disposal relevant, nuclides.� 2007 Elsevier B.V. All rights reserved.

PACS: 28.41.Kw

Keywords: Radioactive wastes; Transport calculation; Radiochemical analysis; AMS

1. Introduction

The orderly disposal of radioactive waste, irrespective ofthe method to be used, requires knowledge of the nuclideinventory. This is required for the safety assessment ofany storage facility (for short or long term use) and forthe division, when allowed, between materials than canand can not be re-cycled; of course, the degree of detailin the inventory required, may vary somewhat dependingon the characteristics of the storage facility.

Medium to high energy accelerator facilities have severalcharacteristics that make the determination of nuclideinventories more difficult (or less accurate) than, forinstance, at a nuclear reactor. The major part of the activa-

0168-583X/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.nimb.2007.08.002

* Corresponding author. Tel.: +41 (0)56 310 3256; fax: +41 (0)56 3102199.

E-mail address: francis.atchison@psi.ch (F. Atchison).

tion stems, in both cases, from neutrons but in the case ofaccelerators (i) several less-well defined activating particlesources are involved, (ii) medium/high energy neutronsare present so that a significantly larger range of productnuclides for each activated material are produced and alsothe activation is spread over a larger volume of material,(iii) irradiated materials that at best have compositionsknown only to manufacturers specifications and (iv) infor-mally maintained records of designs, operation schedules,etc. A further consequence of the large spread of the acti-vation (in both real estate and nuclide terms) is that deter-mination of the activation by sample analysis alone wouldinvolve daunting quantities of analysis for radio-chemistsand also, because of the very significant contribution fromvery low-level waste, considerable increase in the sensitivi-ties of their analysis would be required: the dose cached bypersonnel retrieving samples would be a cause for majorconcern.

84 D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95

Despite the somewhat daunting list of difficulties, astudy of the problem here at PSI has led to a strategy,the PWWMBS (PSI West Waste Management Bookkeep-ing System) system [1], which can deliver complete invento-ries with acceptable accuracy (a factor of three to ten) forany component removed from our accelerator complex,be it operational waste or from the final decommissioning.The PSI accelerator complex has been in operation for over30 years and consists of two 72 MeV cyclotrons, one a con-ventional single-magnet machine, the other a sectorfocussed design with a 870 keV Cockcroft-Walton injector,a 590 MeV sector focussed cyclotron that presently deliversa proton current of 1.6 mA and a heterogeneous set of userareas using both 72 MeV and 590 MeV protons coveringan area of about 20,000 m2; more details may be foundon the PSI accelerator web site [2].

Regular maintenance yields a steady flow of operationalwaste and necessary upgrades to parts of the system occurat intervals of several years to give localised peaks. Deter-mination of the nuclide inventory for all this waste isrequired.

2. Inventory calculations

2.1. The PWWMBS system

The basis of the PWWMBS method is to use gammadose-rate measurements on each item of waste to normalisean appropriate representative inventory. The representativeinventory is calculated within the package using nuclideproduction rates produced by folding a representative irra-diation spectrum with cross-sections for the material com-position of the waste item and solving the Batemanequations for an appropriate irradiation time sequence.The cross-sections are obtained from an activation cross-section library [3].

The system incorporates a data base with representativespectra, material compositions and operations data. Theseare accessed through component and irradiation positiondefinitions, which means that it only requires the followinginformation about the waste item to be supplied, (i) itsinstallation date, (ii) its position in the complex, (iii) thedate of its removal, (iv) the date and (v) the value of themeasured gamma dose-rate, (vi) its material type and (vii)its weight. As we are dealing, in part, with existing wasteand the accelerator complex has been in operation for morethan thirty years, a set of suitably pessimistic but reason-able default values are provided to cover cases where itemsof information are missing.

In the case of normal waste, the irradiation is dominatedby a wide-band neutron spectrum extending from thermalenergies (circa. 20 meV) to close to the energy of the pro-tons from the accelerator (590 MeV or 72 MeV in ourcase). Being a secondary particle spectrum, the shape willbe dictated mainly by the characteristics of the primaryproton interaction region (which defines the primary neu-tron spectrum) and the slowing down properties of the bulk

material near the activated material; the higher energy partof the spectrum will tend to retain the shape of the primarysource. From a neutronic standpoint, the accelerator com-plex consists mainly of large volumes of concrete, heavy-concrete or iron shielding (or in case of iron, also magnetyokes) and other materials, magnet coils, pumps, etc. willmake small perturbations to a fully developed or equilib-rium spectrum for each of the bulk materials: the variousregions of the complex will be completely defined neutron-ically on the basis of the surrounding bulk material and theprimary neutron source(s) generating the spectrum.

The PSI facility, being a high-power installation, has tobe operated so that beam loss is restricted to a few regionsspecially designed to handle the beam power and also to bemaintainable. A systematic theoretical analysis of varia-tions of nuclide inventory with composition and form ofirradiating spectrum (a combination of selected primaryneutron spectrum within and around a given bulk material)showed that waste from anywhere in the whole complex(including the three accelerators) can be adequately treatedusing one of seven shapes of spectrum, and a representativematerial compositions selected from relatively few materialclasses (mild steel, stainless steel, aluminium alloy, etc.).

The choice of representative materials has been based onan analysis of usage throughout the facility. Their compo-sitions are derived from combining measured materialcompositions made here at PSI over the years and thosetaken from the literature and an assessment of the trace ele-ment compositions to better than the one weight part permillion level; because of the importance of their irradiationproducts, a reliable upper limit estimate for the amounts ofuranium, thorium, holmium, europium, silver, cobalt andlithium is particularly necessary. Presently, 16 main materi-als are defined; aluminium alloy, brass, mild steel, stainlesssteel, cast iron, Bundeseisen (a steel, ‘‘box ultra’’, used forshielding that came from a 10,000 t batch), copper, lead(soft and hard), concrete, heavy concrete, PVC, soft solder,marble, inconel and glass. More may need to be added asthe waste stream proceeds. An important ancillary pointfrom the study is that use of the full energy range of theirradiating neutron spectrum is important, as the neutronenergy leading to relevant nuclides varies with element; thisis not only relevant to the production of disposal-relevantnuclides but also because comparatively young inventoriesare needed for the gamma normalisation.

The final information required to carry out the inven-tory calculation is the irradiation sequence for the pieceof waste. The beam current at various monitoring pointsin the complex are stored at about 10 minute intervals onthe logging computer. The complex operates for about 9months of the year on a cycle of 20 days operation andone day for regular maintenance. Under normal circum-stances the gamma dose-rate measurement is made severalmonths after the end of irradiation so that values averagedover each operational year are sufficient; a suitable averageproton current, the proton charge delivered and the end ofthe yearly operational period: a suitable average is

D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95 85

obtained by biasing the average beam current towards val-ues at the end of the period.

The method is being validated using a programme ofsample taking and analysis [4], which at the present stageindicates agreement at better than a factor of 10; the workon this is not yet complete. Because of the validation, thePWWMBS calculation method can, to a certain extent,be viewed as a tool for extrapolating partly measuredinventories to other waste: the principles of the methodare readily adapted to other accelerator facilities.

The PWWMBS system includes the treatment of wastematerials from the region of the primary proton losspoints, but as general representations of the irradiationfield in such regions is not a reasonable approach, the sys-tem requires the nuclide production rates for each wasteitem to be supplied; these are derived from detailed trans-port calculation of their irradiation environment.

2.2. The beam-dump activation calculation

The Target-E system is a complex arrangement ofmeson target (Target-E itself), secondary beam-line com-

Fig. 1. Vertical and horizontal sections through the Target-E complex as icomponents to show useful features. The figure is a reconstruction of a drawappropriate. (Note: the pE3 beam line was pitched upwards at 30�.)

ponents, beam-dump and shielding. The version underconsideration here (see Fig. 1) started operation in 1975and ran until the end of 1989, when it was replaced by anew design to handle proton currents up to 2 mA. Overits operational lifetime it handled 6.18 A h (1.4 · 1023) of587 MeV protons. The proton current, averaged over eachyear’s operational period, increased from 8 to 180 lA. Forshort periods currents of up to 300 lA were used.

The primary goal of the calculation was to provideradioactive nuclide inventories for the copper, the auxiliaryshielding and parts of the stainless steel vacuum tank of thebeam-dump. These were required as part of the procedurefor obtaining the licence to condition this waste. In view ofthe high activity of the components, the calculation wasalso to provide inventories for samples extracted from thecomponents, which were to be radio-chemically analysedto validate the main inventory calculation results. Anotherconsequence of the high dose-rates was that useablegamma dose-rate measurements were not possible, so thatabsolute calculated inventories were required.

Detailed consideration of the work involved made itnecessary to include the full complex rather than just the

n operation up until 1989. Both sections use different cuts through theing dating from the early 1970s and augmented from other drawing as

Table 1Proton charge (mA h) at monitor MHC1 with the various pE1/lE1configurations used in 1987, 1988 and 1989

Year pE1 Momentum setting (MeV/c) Total

�220 �160 �150 150 155 160 176 220

1987 222 53 235 156 78 7441988 200 10 248 119 314 17 72 6971989 285 17 564 866

Totals 707 53 245 421 119 595 17 150 2307

Note: Momenta shown as negative mean operation of pE1 for negativelycharged particles and with modified optics (parasitic mode).

86 D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95

immediate beam-dump into the calculation: As absolutevalues were required, the transport calculation needed tobe started from the proton beam incident at the actual car-bon target as being the only point where the initial condi-tions for calculating the irradiating fields throughout thesystem were clearly defined. Also, the complicated distribu-tion of materials plus the spreading of the beam passingthrough the actual target coupled with the significance ofthe whole energy range of the secondary neutron irradia-tion made it difficult to truncate the system other than at1 or 2 m below the outer shielding. Some compensationcame from the observation that all the components of thissystem would require disposal as active waste eventually(part was re-used in the re-built version) and several othercomponents also had components directly irradiated by theproton beam; nuclide inventory estimates for the wholesystem would be needed sooner of later. A further positiveaspect was that the results for some components could becompared with the normal PWWMBS methods to yieldsome information about where the interchange betweenthe two calculation methods might lie.

2.2.1. The calculation method in general termsThe particle transport calculation was made using the

PSI version of the HETC package [5]; this outputs anevent-by-event history of the transport that needs to beanalysed to retrieve the information relevant to the prob-lem under study. The analysis in this case was used toobtain collision spectra in the components of the system,which were then converted to nuclide production ratesusing components of the PWWMBS system (Note: at thetime of the calculation the PWWMBS system was not yetcompleted but the essential elements as described in Section2.1 were available and used).

Because only collision spectra were to be extracted, thegeometry and composition of the materials only neededspecifying in sufficient detail so that the propagation ofthe cascade was properly modelled, e.g. the cross-talkbetween the various sources and the reflection of particlesback to components of interest is correctly handled, andthe collision spectra corresponded to that in the fullydefined material. A complication was that transport ofthe charged particles leaving the actual target includes pas-sage through a set of beam-line components including alarge bending magnet, whose setting were in accordanceto the needs of one or other of two secondary beams. A fur-ther departure from simplicity was that several differentproduction targets were used.

Information over the amount of beam at Target-E whilerunning with particular secondary beam configurationscould be extracted from the logging system for the opera-tional periods from 1987 to 1989. During this period, eightmomentum/particle-charge configurations of the second-ary beams were used. Detailed information for earlier yearscould not be accessed. Although different targets wereused, it turned out that only two had significant amountof use: the operation up to the end of 1985 (3135 mA h)

was with a 210 kg/m2 thick carbon target and for 1986–1989 (3047 mA h) this was reduced in thickness to105 kg/m2. The change of target thickness has significantconsequences: (i) the energy loss for the non-interactingprotons is reduced from 48 to 24 MeV, (ii) dispersion bythe bending magnet AHE leads to further alterations ofthe beam positions at the beam-dump, (iii) the interactionprobability in the target is reduced from 26% to 14% and(iv) the Coulomb scattering is reduced by about 30%. Asa result of these various target and beam-optical condi-tions, the beam was spread between 16 separate spatialdistributions. The proton fluence for each of the configura-tions are given in Table 1; because of lack of any alterna-tive knowledge, the same frequencies are used for the twotarget thicknesses. The resulting calculated proton currentdistribution on the surface of the copper of the beam-dumpis shown in Fig. 2; only three peaks and a shoulder areclearly resolved.

2.2.2. The Target-E system geometry

The part of the system represented by the calculationgeometry starts 2.25 m before the carbon target, endsabout 3 m beyond the end of the copper of the beam-dumpand in the transverse direction goes to a depth of 1 or 2 minto the surrounding shielding. This is most of the systemshown in Fig. 1. The total volume in the transport calcula-tion is 496.4 m3 and the materials and volumes involved arelisted in Table 2. Some brief notes about the major compo-nents of the system are given in the next few paragraphs.

(i) The carbon target assembly: The target is a rotatingcone of carbon mounted in an 0.8 · 1.1 · 1.42 m3

void in a shielding assembly consisting of a basic ver-tical steel cylinder of 4.0 m diameter and 3.5 m heightwith 1.0 m and 1.1 m thick steel disks on the top andbottom. The middle region, in the height range1.0–2.42 m, has a more complicated form: the backof the cylinder is cut away to leave a 0.4 m thick castiron shield wall and the (part) annulus in the radialinterval from 1.12 to 2.0 m is formed from interlock-ing cast-iron blocks. Inside this are four regionspacked with hexagonal steel rods. Quadrupole mag-nets (these and others are identified in Fig. 1 withlabels QC/QTA/QTB) for three secondary beams,

Fig. 2. The spatial distribution of proton fluence on the front face of the copper of the beam-dump as calculated.

Table 2Materials and volumes for the target-E system as modelled

Description Density(kg/m3)

Volume(m3)

Weight(t)

1 Mild steel 7850 45.14 354.32 Loose packed (80 V%) mild steel 6420 22.27 143.03 Cast iron 7300 36.46 266.24 Heavy (iron shot loaded)

concrete5700 29.59 168.7

5 Normal concrete 2475 216.01 534.66 Stainless steel 7850 0.89 7.07 Copper 8960 0.96 8.68 Carbon – Target-E material 1750 � �

9 Water pipe (72.25 V%water + steel)

0.16 0.30

10 Cast iron 7300 1.57 11.411 Bundeseisen (steel type ‘‘Box

Ultra’’)7850 21.80 171.1

Totals (4440) 374.85 1665.2

D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95 87

two at right angles to the target and one in the for-ward proton beam direction, were mounted withinthe ‘radial’ arms of the shielding block. These wereall of the ‘compact’ figure-of-eight design (averagedensity of about 5500 kg/m3), close packed withshielding and adequately represented by steel forthe transport calculation. In the forward (proton-beam) direction, a 0.1 m radius hole was includedto represent the aperture of the forward quadrupoletriplet.

(ii) The bending magnet AHE: This is represented by asteel block 3.2 · 0.87 · 2.54 m3 with an apertureabout the beam axis 0.18 m high and uniformly vary-ing from 0.9 to 1.08 m horizontal width over its0.87 m length. No details (e.g. magnet coils, etc.)are necessary or included. A collimator was mountedbetween the target and AHE to define the phase-space of the secondary particle beam produced byinteractions and to reduce the beam loss on AHE.The collimator consists of a block of copper with aflared beam hole about the proton beam directionsurrounded by steel shielding. Primary beam losses

in this region are comparatively large; the transportcalculation estimated that 12.3 mA h primary protonbeam charge (2.8 · 1020 protons) were lost on thecollimator and 6.6 mA h proton beam charge(1.4 · 1020 protons) in the aperture of AHE.

(iii) The main vacuum tank: The vacuum vessel was notexpected to have too strong an influence on the irra-diating fields but included into the model to providehooks for making the collision spectrum estimates.In the model the vessel was built up from simple20 mm thick stainless steel plates (localised thicken-ings due to the flanges, strengthening ribs, etc. werenot included and their effect was corrected for inthe nuclide inventory estimate). The vessel extendsfrom AHE to the entrance of the beam-dump system.As may be seen in Fig. 1, the form is irregular toallow mounting of the secondary beam-line quadru-pole magnets and shielding.

(iv) The beam-dump assembly: The basic element is a cop-per assembly of weight about 8000 kg which was irra-diated directly by the major part of the proton beamand by secondary particles; calculating the nuclideinventory for this was the main goal. The assemblyalso includes various blocks of shielding materialmounted inside and outside the vacuum tank. Somedetails of the layout of this part of the system mayalso be seen in Figs. 3 and 4.The actual copper assembly was built from 40 piecesof 30 mm thick copper plate (20 each for the upperand lower parts), mounted with distance pieces to cre-ate a re-entrant beam hole and with water cooling onthe horizontal edges furthest from the beam axis. Asmounted, there was a 2 mm clearance between eachplate, giving an overall length of 0.618 m and it wastraversed by a small beam hole for the nE1 neutronbeam. In the model, the part struck by the protonbeam was represented by a 3.5 · 0.6 · 0.45 m3 blockof copper; the re-entrant structure of the first fourplates was simulated exactly (openings of 116, 82,58 and 42 mm height extending the full width anddepth of each plate) and the rest of the re-entrant holerepresented by a wedge. The block was water cooled

Fig. 4. A sketch of the beam-dump assembly. The samples from the topplate were taken from the St-37 of the strengthening I-beams and thestainless steel of the vacuum tank lid from positions as close together aspossible.

Fig. 3. A sketch of the inner parts of the former beam-dump aftertransport from the operating position. The concrete filling was added justbefore this transport. The approximate positions from where the samplesfor these components were taken are shown; samples A11 and A12 fromthe cast-iron shield block were taken from two depths of the same core.

88 D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95

and this was represented by 2 mm thick by 600 mmwide slabs of water and steel mixture directly aboveand below the copper and extending over the wholesurface area. These slabs extend outwards and thenturn vertical to represent the sections in the vacuumvessel.A 1.6 m3 cast iron shield block was mounted abovethe copper with a vertical distance between the adja-cent faces of 135 mm. This shielding block and thecopper sat inside a second vacuum tank, again mod-elled with 20 mm stainless steel plate. None of the

support structure (steel pillars, framework, etc.) wasincluded. There were several other bits of shieldingassociated with the beam-dump assembly: It sat ona 4.36 m3 block of normal concrete; a 9.75 m3 blockof heavy concrete supported by a 50 mm thick steelplate was mounted above the inner vacuum tankand between the vacuum tank vertical extensions car-rying the water manifolds (see Fig. 3); irregularlyshaped iron shielding was packed around the vacuumtank and the secondary beam-line components; a3 m3 block of normal concrete sat below the mainvacuum tank.

(v) Some components of the secondary beams, pE1 andlE1, were mounted very close to the beam-dumpand for the purposes of the calculation only act asparticle reflectors. The quadrupole magnets (compactfigure-of-eight design) and a shutter/energy-degraderunit in the lE1 beam were modelled as simple blocksof steel.

(vi) The shield walls: In all except the forward direction, a1.0 m thick layer of the shielding was included in themodel geometry. The floor and roof were modelled asnormal concrete and the side walls variously loose-packed steel, ordinary steel and concrete as in thedesign drawings. In the forward direction (past thebeam-dump), the shielding in the calculation modelwas extended to a depth of 2.0 m. This was madeup from steel, heavy concrete and Bundeseisen.

2.3. The transport calculation

The transport was split between two codes – HETC forthe medium-energy cascade and O5R_PSI for fast neutrontransport. The HETC code handles the transport from the587 MeV primary protons incident at the carbon targetthrough all generations of product particles, until theyeither escape the system, or are slowed by ionisation-lossto rest or, if neutrons, are below the minimum transportenergy. HETC makes a dual level random-walk – throughthe nuclei to determine the interaction cross-sectiontogether with a sample outcome of an interaction (usingthe Bertini code [6]) and through the material arrangementas represented by the geometry routines. The transport cal-culation for the neutrons below the HETC cut-off energy ismade using O5R_PSI in which the development of the ran-dom-walk in under the control of cross-section data. Thisfollows the neutrons from their birth in medium-energyinteractions through to their eventual absorption, normallyin the thermal energy region. Collisions in the energyregion below about 1 MeV involve only neutrons andsimple reactions – (n,c), (n,a), (n, p), etc. – but are compli-cated by the huge variation in the size of cross-section.For the transport calculation it is found that 72 scatterersare sufficient to represent the approximately 1300 foundin the material assay. These are built up from all the indi-vidual elemental cross-sections to yield the right capturerate.

D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95 89

2.4. Sampling of the starting coordinates

There are eight sets of values for settings of the dipolemagnet AHE and the three quadrupoles, which togetherwith the two thicknesses for the carbon target gives 16 con-figurations in total. To simplify matters somewhat, thetransport through the target and beam-line componentsis carried out as part of the particle starting procedurefor the transport calculation.

The energy of the protons incident at the carbon targetis 587 MeV with a FWHM energy spread of 0.5 MeV. Thisspread is modelled using a 6 Æ X Æ (1 � X) distribution,which is a good approximation to the expected truncatedcosine distribution. The phase-space areas are taken as 1and 2p mm mrad in the horizontal and vertical directionswith 95% of the beam inside a 5 mm diameter circle. Thespatial starting coordinates are sampled out of anuniformly filled 4-D hyper-ellipsoid with semi-axes2.8373 mm, 0.3525 mrad, 2.8373 mm and 0.7049 mrads,respectively.

Transport for the target consists of randomly selectinglength (49.3% probability for 60 mm and 50.7% for120 mm), then making a normal exponential sampling tosee if an interaction is to occur. Coulomb scattering andionisation loss are computed on the basis of the shorterof the target-length and distance to the interaction. Cou-lomb scattering is treated by sampling from the Williams,Bethe and Ashkin [7] distribution. To reduce somewhatthe complication, the reasonably small probability thatCoulomb scattering causes the proton to leave throughthe sides of the target is ignored. A constant specific ionisa-tion loss of 2.3 MeV cm2/g is used to compute the finalenergy of the proton.

If an interaction in the target is predicted to occur, theBertini Intra-nuclear cascade routines in HETC areinvoked to compute an interaction and the secondary par-ticles above the HETC cut-off energy are successively trans-ported. If there is no interaction, the exiting proton only istransported further.

Medium-energy neutrons are passed directly to HETCfor further transport. All charged particles (primary or sec-ondary) within the diameter of the beam line were sub-jected to a beam transport calculation up to the end ofthe bending magnet AHE, using standard first-ordermatrix transforms and aperture checking at the start, mid-dle and end of components, before being passed to HETC.If the particle was predicted to have struck the aperture ofone of the components, the particle is passed to HETC withposition and direction projected back to the start of thatcomponent. Beam-line settings for the eight operatingmodes are used with probabilities based on the operationalfrequencies listed in Table 1.

2.5. Auxiliary analysis

Both transport calculations only give an event-by-eventhistory of the transport of each particle (the event type, the

type, position, direction and momentum of the particle plusvarious pieces of information about the environment of theevent). This is analysed, either on- or off-line, to obtain theresults actually wanted.

The primary results required are the collision spectraand energy grouped neutron absorption rates averagedover the volume of each of the 776 material sectors (eachconsists of one material) of the geometric representationof the system. The collision spectra are collected into 49bins with an energy width increasing on a 2n basis. Theabsorptions are also collected into energy bins on a fac-tor-of-two width basis; these start from 19.2835 MeV andend at 35.92 meV with a last bin for the thermal neutronreactions. These require further analysis to retrieve the con-tribution by the individual scatterers.

The next stage of the analysis is to fold the collision-rates with the cross-sections from the PSIMECX libraryto form the nuclide production rates and at the same timeto restore full material definitions and correct for othermissing details; design of the calculation geometry has toensure that such details really cause only minor perturba-tion (slightly incorrect dimensions, missing features ofany support structure or other details). As an example, amagnet has about 90 wt% steel, 8 wt% copper and 2 wt%other materials; the mean free paths of copper and theiron-based materials for medium-energy neutrons vary byabout 6% (1400 ± 30 kg/m2) and for thermal neutron cap-ture by about 20% (300 ± 30 kg/m2). The reaction rate (pergram) for the copper will be very close to that for the iron itwould displace.

Another job is to unfold the absorption into values forthe individual nuclei. As the majority of the componentsconsist of large lumps, most of the transport will be mod-eration within a single medium. Slowing down is character-ised by a constant average lethargy gain per collision (n).The probability of events in some specific channel c(= Pc) after a particular lethargy gain is the sum of thechannel probabilities at each lethargy but reduced by thenon-absorption probability at this and all previous scatters.That is, after k scatters starting from zero lethargy

P c ¼Xk

l¼1

RcðlnÞRðmÞt ðlnÞ

Yl

n¼0

1� RðmÞa ðlnÞRðmÞt ðlnÞ

" #: ð1Þ

The subscripts to the cross-sections (R) c, a and t stand forthe wanted-channel, absorption and total macroscopiccross-sections respectively and the superscript (m) indicatesthat it corresponds to a suitable sum over all scatterers inthe material. This expression is evaluated for the full ele-mental composition of each material on a 1-group persuper-group basis starting from 19.28 MeV, to create adata-set that may be interrogated to give all the productsand their fraction of the total number of absorptions withineach energy bin and the thermal group. It has about 19,000entries. The quality of the numerical approximation ischecked by simultaneously generating infinite dilution res-

Table 5Calculated and measured power deposition in the plates of the beam-

90 D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95

onance integrals for all nuclei in the material and compar-ing these with tabulated values [8].

dump

Plateno.

Calculated power(kW)

Measured power(kW)

Difference(%)

1 1.17 1.11 +52 2.37 2.16 +103 3.30 2.64 +254 6.89 3.78 +825–9 16.0 16.8 �510–16 6.97 6.48 +8

Total 36.6 33.0 +11

2.6. Results checking

When making a ‘‘blind’’ absolute prediction of specificquantities in such a complicated a system, it is helpful tofind some measured quantities that help to support thecredibility of the results. A difficulty is that as the Target-E system was a working facility, very few independentresults suitable for cross-checking the transport calculationwere available. Naturally, obvious checks on energy andbaryon number conservation were made together with spa-tial distributions and later, the activation comparison forthe samples would be available.

The distribution of the interactions between the variouscomponents of the complex together with the fast-neutronproduction and absorption give a first feel for the gross dis-tribution of activation and energy. A compressed distribu-tion of the interactions is given in Table 3. A usefulindication from these results is that all parts of the systemcontribute. Also, the difference between the birth compo-nent and the absorption site is a good indication that therather detailed model of the full system was necessary toobtain a reasonable estimate for the activation. The neu-tron production by inelastic interactions during the fastneutron transport and also the escape particles from themodelled system are show in Table 4. Adding the fast neu-tron 1st generation production to those in Table 3, the totalproduction of neutrons is 5.8683 and, similarly with theabsorptions and escapes added, the ‘lost’ neutrons

Table 3Numbers of medium-energy interactions, fast neutrons produced andneutron absorptions per proton incident at the carbon target

ME interactions Fast neutrons

Primary Secondary Production Absorption

Target assembly 0.05751 0.4479 0.92543 0.92375Collimator jaws 0.00199 0.00754 0.01987 0.005815Collimator shielding – 0.00359 0.005685 0.03938Magnet AHE 0.00144 0.03917 0.05745 0.85439Beam-dump copper 0.64781 1.4470 4.32193 1.50122Beam-dump

(other parts)– 0.19163 0.24982 1.76172

Biological shielding 0.13945 0.20889 0.74662

Sums for system 0.70876 2.2763 5.7891 5.8329

Table 4Numbers of neutrons created and escaping the Target-E geometry duringthe medium-energy transport per proton incident at the carbon target

Particle transport stage Fast n0

createdEscapes Escape energy

(MeV)

Fast neutron 1 0.07861 0.01011 0.00332Fast neutron 2 0.00060 0.00133 0.00055Medium-energy transport (5.7891) (0.00057) 0.03909

Totals 5.8683 0.01144 0.04296

accounted for 5.8443. That is, the calculation and analysisyield a neutron balance at the 0.4% level. Similarly, theenergy deposition is also a useful indication of how the‘strength’ of the activation will be distributed; the totalaccounted for, 582.7 MeV/proton with about 95% depos-ited as heat and most of the rest going to provide the bind-ing energy, is about 4 MeV (0.6%) lower than the587 MeV/proton entering the system.

One useful check on the calculation comes from com-paring the power extracted by the cooling system fromthe copper plates of the beam-dump with measurement[9]; these were made in 1982 with the system operating witha 120 mm thick carbon target. Removing the thin target(60 mm) contribution from the calculated results givesquite good absolute agreement with measurement (seeTable 5).

3. The samples

3.1. Sample extraction

Small samples (from 100 to 200 g each) were extractedfrom five positions in and around the beam-dump assem-bly; these positions are shown in Figs. 3 and 4. Becauseof the high level of dose-rate, the work had to be carriedout remotely in a hot cell.

• Two samples came from the copper; one (A06) at a posi-tion as close as possible to the place with the maximumactivation, the other (A09) at a position within theregion of lowest specific activation. As the innermostpart was filled with concrete before removal from theexperimental hall, the boring was made by dead reckon-ing using dimensions based on the calculated protoncurrent distribution.

• Two samples from the top plate of the vacuum tank, onefrom the actual top (steel type 304) and the other fromthe stiffening (steel type 37) I-beams. They were takenfrom points as close together as possible.

3.2. Calculation of the nuclide inventories for the samples

The inventory calculations for the samples were carriedout with a PWWMBS build-up and decay calculation,

Table 7The irradiation sequence used in the build-up/decay calculation for thesamples

Beam-on time (h) Average current (lA) Beam-off time (h)

38,745 100 42394510 165 42564760 146 40565200 167

D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95 91

using production rates obtained from folding the specificinteraction rate spectra, their material compositions andcross-section data from the PSIMECX library; the elemen-tal compositions used are listed in Table 6 and were allobtained from assays of samples of the specific materials.The inventories were calculated using the PWWMBS Bat-eman equation solver with the four cycle irradiationsequence shown in Table 7; as inventories after 10 yearsdecay are being calculated, greater detail is not necessary.

The interaction rate for sample A06 has two parts, fromthe protons (calculated as if caused by 21.7 mA h/cm2 pro-ton current) and from the secondary particles createdthroughout the system. The contribution from the protonswas extracted directly from the activation maximum andthat of the secondary particles is an average over a 5 cmside cube about the sample point. The contribution of the

Table 6Elemental compositions (wt ppm) for the samples extracted from thebeam-dump assembly

Element Cast-irona

(A11 and A12)Steel-37b

(A16)Steel-304c

(A15)OFHC-Copperd

(A06 and A09)

C 28000.0 1477.5 610.0Na 2.8 22.0 2.0Mg 5.3 6.4 3.7Al 42.0 34.8 15.0Si 12500.0 1964.5 5250.0P 2620.0 170.0 360.0S 280.0 265.0 70.0 7.0K 1.2 1.1 1.4Ca 2.2 23.5 7.8 0.3Ti 412.0 37.5 17.9V 272.0 44.5 803.0Cr 252.0 1067.5 171000.0Mn 4490.0 6020.9 9670.0Fe 950328.3e 984736.9e 718554.1e 0.7Co 54.0 101.5 1610.0Ni 170.0 1067.8 87000.0Cu 422.0 2470.0 3080.0 999972.6e

Zn 42.0Ga 98.0As 130.0 95.0Rb 3.0 4.8 5.0Mo 179.3 1810.0Ag 17.4Sn 125.0Cs 16.0 15.3 11.0Ba 0.2 1.2Pb 47.5

a This is the material of the shield block above the copper assembly. Asingle sample was assayed; an extra 3625 wt ppm of Ni has been added, torepresent the contribution from the 0.4 mm anti-corrosion coating.

b The composition is the average of the assays of four samples of steel 37and 37K drawn from the PSI stores and is unchanged from that used inthe transport calculations.

c The elemental composition used in the transport calculation is theaverage of the assays of four samples of steel 4435 (316L). The stainlesssteel in the assembly was type 304L which has rather less molybdenum,and the results of an assay of a sample have been used for the nuclideinventory calculations.

d A single sample of the same copper as specified for the manufacture ofthe beam-dump has been assayed and used for calculating the activity.

e Determined by subtracting the sum of all other elements from one.

proton interactions to the activity of sample A06 was madeusing a direct intra-nuclear cascade plus evaporation calcu-lation with the elemental composition.

The collision-rate for sample A09 was extracted fromthe average over the back half of the copper block (roughly4843 kg) and corrected for self absorption using a shieldinglength of 1400 kg/m2; this gives an intensity reduction atthe sample position of a factor of 100.

The specific interaction rates for samples A11 and A12are taken from an average over the whole component(11,487 kg) and corrected for absorption through theblock; the activation for sample A11 is a factor of 3.4 lowerthan the average and A12 a factor of 1.8 lower.

As samples A15 and A16 were extracted from compara-tively thin material, the interactions rates are taken as theaverage over the total amount; 1409 kg steel-304 for sampleA16 and 408 kg of steel37 for sample A15.

4. Radiochemical analysis

4.1. Chemical separation procedures

In general, the samples could be dissolved in 7 M HNO3

within 2–3 h using light heating. Only the stainless steelsamples had to be boiled under reflux for 20 h until com-plete dissolution was obtained.

For the separation of elements foreseen for AMS mea-surements, additional treatment to remove stable isobaricisotopes is necessary in some special cases, because theycan disturb the measurement. Details of the separationtechniques can be found in [10,11].

4.1.1. 129I and 36Cl

Chlorine and iodine can be separated simultaneouslyfrom the target material by distillation in a N2 stream whilebeing dissolved. The iodine is distilled into a hydrazinesolution at 55 �C and the Cl into an AgNO3 solution at70 �C. A schematic view of the equipment is shown inFig. 5.

The hydrazine solution containing the Iodine was acid-ified with HNO3, AgI was precipitated, filtrated, washedwith bi-distilled water and dried at 80 �C. The precipitateof AgCl was resolved in NH3 and Ba(NO3)2 was addedin order to remove the stable isotope 36S in form of BaSO4.Then the AgCl was re-precipitated by acidifying and thentreated in the same way as the iodine samples.

For the AMS measurements the iodine samples weremixed with Ag powder and pressed into special target

Fig. 5. Equipment for simultaneous determination of chlorine and iodine.

92 D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95

holders. Chlorine samples were pressed into the holderswithout addition of silver.

4.1.2. 26Al and 10Be

For determination the Al and Be isotopes in the coppersamples their hydroxides were precipitated with NH3 solu-tion. Under these conditions the copper remains in solutionas an ammonium complex and is, thereby, nearly com-pletely removed.

The hydroxides were dissolved in 0.1 M HNO3 solutionand fed onto a cation exchange column (0.5 · 3 cm, DOW-EX 50 · 8, 150–200 mesh, H+-form). The column waswashed with 20 ml of 0.1 M HNO3 to remove stable boron.Beryllium was then eluted with 15 ml of 1.1 M HCl, afterthat the Al with 4 ml 4 M HCl.

The hydroxides were precipitated with NH3, washedwith bi-distilled water and glowed at 800 �C. The oxideswere mixed with copper powder and pressed into specialtarget holders for the AMS measurement.

After dissolution of the steel and iron samples in 7 MHNO3, the iron hydroxide was precipitated with ammoniasolution; this also carries the aluminium and berylliumhydroxides. The residues were dissolved in 7 M HCl andthe iron was extracted into methylisobutylketone (MIBK).The solution was passed through a DOWEX 1 · 8 columnfor further purification from Fe. The aluminium and beryl-lium hydroxides were then again precipitated and dissolvedin 0.1 M HNO3. The final separation was made on a cationexchange resin DOWEX 50 · 8, as described above.

4.1.3. 55/60Fe

The dissolved samples were evaporated to dryness. Fivemilligrams of Fe carrier were added to the copper samples.The residues were dissolved in 7 M HCl and the iron wasextracted into MIBK. The extraction was repeated twiceusing fresh extraction agent each time and the fractions

were combined. Back extraction was carried out with1 M HCl; this procedure also completely extracts theSb5+. Stable nickel is not extracted under these conditions.

The 55Fe was measured by using LSC on this solution.The chemical yield was determined by use of atomicabsorption spectrometry (AAS).

Determination of 60Fe was made by AMS. The ironhydroxide was again precipitated with NH3 solution. Thisalso gives an additional stage of removal of Nickel, whichforms soluble ammonia complexes. The residue was driedat 100 �C.

4.1.4. 59Ni

Samples of from 10 to 30 mg were dissolved as describedabove. To the copper samples 30 mg of iron powder wereadded to reduce Cu2+ to elemental Cu. The metal precipi-tate was removed. The solution was evaporated to drynessand fumed several times with concentrated HCl to free it ofHNO3. The residue was dissolved in diluted HCl and Fe2+

was oxidised to Fe3+ with H2O2. From this solutionFe(OH)3 was precipitated with NH3. Under these condi-tions, Ni remains in solution as NiðNH3Þ2þ4 complex. TheNi was separated with dimethylglyoxime as a dark red pre-cipitate, which was glowed to Ni/Ni2O3 at 600 �C.

The iron and stainless steel samples were directly treatedwith ammonia solution after dissolution, followed by thedescribed procedures.

4.1.5. 108mAg

Four milligrams of Ag carrier were added to an aliquotof the respective sample solution and silver was precipi-tated with 1 M HCl. The precipitate was washed with0.1 M HCl and dried at 80 �C. The chemical yield wasdetermined by AAS in a way similar to that used for theiron samples.

4.1.6. 3H

The separation of tritium was performed under drynitrogen from separated weighted samples. They were dis-solved in a three-neck bottle under stirring in a 10% excessof the calculated amount of HNO3 under efflux conditions;only the stainless steel sample was dissolved in Aqua Regia.After that, the solution was carefully distilled to drynesscollecting the distillate. The residue was taken up by50 ml bi-distilled water and a second time distilled to dry-ness. Both distillates were combined and measured withLSC.

4.2. Measurements

The c-spectra were made using a standard HPGe-detec-tor. Tritium and 55Fe were measured with liquid scintilla-tion counting technique (LSC) using Ultima Gold LLT�

as cocktail.26Al, 36Cl, 129I, 10Be, 59Ni and 60Fe were determined

after chemical separation by Accelerator Mass Spectrome-try (AMS) using the facilities at ETH Zurich (Van de

D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95 93

Graaff EN tandem accelerator at IPP [13]) and at theBeschleunigerlabor of TU Munchen [14].

5. Results

After dismounting, the samples were put into a centralstorage system. Each sample was, in fact, in several piecesand dose-rate measurements made during preliminary han-dling are given in Table 8. These results give an indicationof the probable systematic errors in the activitymeasurements.

The experimental results and the calculated values arelisted together with their ratio (always the larger over thesmaller) in Table 9, those with half-life less than 500 yearsand in Table 10 for the long half-life nuclides.

As expected, the activities are significantly higher insample A06 than in the others; it alone was activated bythe primary 590 MeV proton beam. It is also readily seenthat the agreement between calculated and measured datais markedly worse than for the samples activated by sec-ondary particles. This is qualitatively understandable on

Table 8Deviations of the gamma dose-rates from the samples

Sample A06 A09 A11 A12 A15 A16

Number of measurements 13 4 10 10 10 101-Sigma-dose-rate variation (%) 10 43 12 17 16 18

Table 9Calculated and measured nuclide inventories in the samples for isotopes with

Half-life(year) [12]

3H 22Na 44Ti 54Mn 55Fe12.32 2.6019 60 0.854 2.737

A06

Calculated 2.2 · 108 9200 5.5 · 106 3400 2.1 · 107

Measured 2.8 · 105 930 4.2 · 104 370 1.7 · 106

Ratio 786 10 131 9.1 12

A09

Calculated 230 0.01 10.8 0.2 720Measured 150 0.63 3.8 0.088 200Ratio 1.5 32 2.8 2.3 3.6

A11

Calculated 130 10.9 35.5 1.5 5.4 · 104

Measured 450 4.5 44.7 2.8 1.7 · 104

Ratio 3.5 2.4 1.3 1.9 3.2

A12

Calculated 250 20.6 67.1 2.8 1.0 · 10s

Measured 1400 4.1 68.4 2.4 2.5 · 104

Ratio 5.6 5 1 1.2 4

A15

Calculated 36 2.8 25.6 0.7 4.8 · 104

Measured 6300 2.8 30.1 3.4 3200Ratio 175 1 1.2 4.9 15

A16

Calculated 23 0.7 10.8 0.6 4.9 · 104

Measured 2700 4.5 110 2.9 1800Ratio 117 6.4 10 4.8 27

Values are Bq/g on January 1st, 2004.

the basis that the positional variation of the secondary neu-tron irradiating field is relatively small in comparison withthat of the proton beam (q.v. Fig. 2) and the likelihood thatthe samples are from a position displaced from the protoncurrent maximum is rather high. The calculated values forsample A06 are systematically higher than those measured.However, as 60Co dominates the dose-rate, the factor of 4higher value for the calculated specific activity suggests thatthe sample came from a region with a beam current densityabout a factor of 4 less than the maximum: this wouldbring the differences to a similar level to that of the othersamples.

The agreement between measurement and calculation inthe case of the long half-life nuclides is generally satisfac-tory (it should not be forgotten that we are dealing with‘‘real’’ materials rather than analytic samples). The calcu-lated values for 36Cl, one of the significant nuclides in wastemanagement, are quite significantly lower than measure-ment for the secondary particle activated samples; how-ever, in this case it contributes about 30% of the radio-toxicity of the complete inventory.

The 129I quantities are more than 6 orders of magnitudebelow the level where they have significance for repositorysafety. The most plausible production mechanism is ura-nium fission and the results may be used to give estimatesfor the upper limit for the U content in the various samples.For sample A06, the cross-section for production of 129Ifrom uranium by 590 MeV protons is about 40 mb [15],

half-lives <500 years

57Co 60Co 65Zn 108mAg 110mAg 125Sb0.744 5.2713 0.668 418 0.684 2.759

2100 2.2 · 107 11.7 15.8 0.003 051.7 5.5 · 106 0.04 26.5 0.02 1.541 4 293 1.7 6.7

0.113 3500 0 0.3 0.0007 00 590 0 0.7 0.0002 2.6

6 1 2.3 3.5

0.0031 2800 3.4 · 10�10 0 0 00 1800 0.08 <NWG <NWG 16.1

1.6 1 1

0.006 2500 6.5 · l0�10 0 0 05.3 2500 0.06 <NWG <NWG 23.9883 1 1 1

0.045 8.4 · 104 1.3 · 10�6 0 0 00 2.5 · 104 0.0005 0.4 <NWG 3.2

3.4 380 1

0.00041 5500 1.5 · 10�6 0 0 5.30.8 9200 0.017 0.8 <NWG 3.41950 1.7 11600 1 1.6

Table 10Calculated and measured nuclide inventories in the samples for isotopes with half-lives >500 years

Half-life (ky) [12] 36Cl 10Be 26Al 60Fe 59Ni 129I303 1510 717 1500 101 15,700

A06

Calculated 943 16.4 14.8 50.1 64000 0Measured 306 0.27 0.76 1.2 6630 3.1 · 5

Ratio 4.6 63 19 44 9.6

A09

Calculated 0.00078 1.3 · 10�5 4.3 · 10�6 0.0021 4.8 0Measured 0.05 1.7 · 10�5 0.00048 0.0029 0.6 6.6 · 10�7

Ratio 64 1.3 112 1.3 8.6

A11

Calculated 0.00091 0.0016 0.014 3.2 · 10�6 2.4 0Measured 0.08 0.0010 0.0074 1.7 · 10�5 5.8 5.1 · 10�6

Ratio 88 1.6 1.9 5.3 2.4

A12

Calculated 0.00091 0.003 0.025 6.0 · 10�6 4.5 0Measured 0.06 0.0025 0.011 1.7 · 10�5 6.2 7.9 · 10�6

Ratio 66 1.2 2.3 1.2 1.4

A15

Calculated 0.00064 2.1 · 10�5 0.0030 3.9 · 10�6 64.1 0Measured 0.59 – 0.00012 4.7 · 10�6 30.8 –Ratio 920 25 1.2 2.1

A16

Calculated 0.00020 2.9 · 10�5 0.00078 1.1 · 10�7 0.6 0Measured 0.1 4.5 · 10�5 2.4 · 10�5 8.5 · 10�6 2.1 1.5 · 10�8

Ratio 500 1.6 33 77 2.5

Values are Bq/g on January 1st, 2004.

94 D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95

and the measured specific activation (3.1 · 10�5 Bq/g)translates to an uranium concentration in the copper of<0.03 wt ppm; a value of the order of 0.0001 wt ppm Uwould be expected on the basis of [16].

6. Discussion

A major requirement from the side of the radioactivewaste repository planners is that the radionuclide inventoryis complete. High accuracy is not necessarily required butknowledge of the tolerance on the nuclide concentrationsis. The goal is to provide a radioactive nuclide inventorysufficient for the needs of the safety of the repository dur-ing the operational phase and for the safety analysis for theperiod after closure. Both the requirements are influencednot only by the quality of the nuclear physics models atpredicting nuclear reaction products and particle spectrabut also by the materials’ composition. Practical reasons,like simply the large amounts of material involved, suggestthat calculation is going to have to be relied on: the calcu-lation method must be validated. Some amelioration willcome from the combination of waste from one source into,probably large capacity, repository units, leading to thewaste it holds being in some senses an average over thatproduced by the source.

A validation programme is going to have to rely heavilyon samples taken from components in the normal opera-

tional-waste stream. This has the advantages that theinventory of actual materials will be examined and a pic-ture of the average inventory based on measurement canbe built up. It also has the advantage that samples withadequately long irradiation times to make it possible tomeasure the long half-life repository safety-relevant nuc-lides can be obtained (anyway here at PSI).

Such measurements cannot be considered as tests ofnuclear physics theory – although agreement can only beobtained when those used are reasonably correct – as sam-ples will come from ‘‘real materials’’ and the irradiationconditions will usually be rather poorly defined. The goalof a validation program is to provide a reliable estimatefor the uncertainty in the inventory calculations; when thisis too high the models involved will need to be replacedrather than corrected.

From the point of view of the disposal of the beam-dump elements, the results indicate that the calculatedinventories for the components of the beam-dump areprobably sufficiently accurate. Also, despite being a ratherspecial component, the results do have some relevance tothe validation of the PWWMBS system in general:

• The calculated inventory for sample A06 (at the positionwith the maximum specific activity) is higher than mea-surement; if it had had a lower value, it would have beenan unambiguous indicator of a failure in the calculationmethod.

D. Schumann et al. / Nucl. Instr. and Meth. in Phys. Res. B 264 (2007) 83–95 95

• The inventory for sample A06 includes the first compar-ison of measurement and calculation involving very-long half life nuclides. These values normalised to(say) the 60Co activity provide a relevant test.

• The low number of instances of a nuclides being foundin the measurements but not in the calculated inventoryis a relevant check.

• The few cases where the calculated inventory does notinclude a nuclide, which has been search for but notfound (i.e. those indicated with <NWG in Table 9) isalso a positive point for the validation.

Acknowledgement

The help and encouragement of Martin Jermann duringexecution of the work on the development of thePWWMBS system and of the setting up of the validationprogram is gratefully acknowledged.

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