Reaction rate measurements for nuclear reactor analyses and critically data

~ucl. hf.

~rrrcks J.

Rodiul.

Rodioi.

Meos..

Appi.

Irz.vrrwu..

Vol.

14. No.

PWI

3. pp.

387408.

0191-278X/88

1988

$3.00

+ 0.00

Per~amon Press plc

D

Primed in Great Britain

REACTION REACTOR

RATE MEASUREMENTS FOR NUCLEAR ANALYSES AND CRITICALITY DATA

RAYMOND GOLD*, JAMES H. ROBEKTS~, LLOYD S. KELLOGG*, WILLIAM Y. MATSUMOTO*, WILLIAM N. MCELROY*, CHRISTOPHER C. PRESTON* and ROBERT L. SIMONS Westinghouse

Hanford

Company,

Hanford Engineering WA 99352, U.S.A.

Development

Laboratory,

Richland,

and SIDNEY R. BIERMAN

Battelle,

Pacific

Northwest

Laboratories,

(Received 28 February

P.O. Box 999. Richland,

WA 99352. U.S.A

1988; in revised .form 25 March 1988)

Abstract-Neutron reaction rate measurements with solid state track recorders (SSTR) and radiometric (RM) neutron dosimeters have been conducted at the Pacific Northwest Laboratory (PNL) Critical Mass Laboratory (CML) as part of the U.S. Department of Energy (DOE) and the Power Reactor and Nuclear Fuel Development Corporation of Japan (PNC) Criticality Data Development Program. These reaction rate measurements represent benchmark data that can rigorously test the adequacy of neutron transport calculations performed for nuclear reactor analyses as well as for criticality safety assessments. In the 220 series of experiments, fast test reactor (FTR) plutonium fuel pins were assembled in a 0.761 cm square lattice array, which was immersed in an organic moderator. In-fuel and in-moderator dosimetry measurements were conducted near axial midplane. To obtain results at a single axial location, corrections were applied for the spatial variation (axial buckling) of the reaction rates. For the in-fuel measurements, dosimeters were placed between fuel pellets thereby creating gaps in the fuel pin column. Consequently, for these in-fuel measurements, the gap-perturbation effect was measured so that reaction rate data could be corrected to zero fuel gap, i.e. the reaction rates in the unperturbed fuel. Experimental uncertainties range from a low of 2-3 percent for U-238 and Th-232 fission rates to a high of 15-16 percent for U-238 capture rates. The uncertainty in the U-238 (n, y) moderator results is dominated by the uncertainty in the neutron self-shielding correction factor, which has been estimated to be approximately Uncertainties in U-235, Np-237 and Pu-239 fission rates range from . 15 percent. . .. approximately 4 to 7 percent. These latter uncertainties are larger than uncertainties normally achievable in SSTR neutron dosimetry and reflect the fact that the quality of the SSTR electrodeposits prepared for these isotopes was not completely satisfactory. Least-squares spectral analyses of these data were performed with the FERRET-SAND II computer code. These analyses confirm the general consistency of the experimental data and furnish absolute neutron Auxes with assigned uncertainties.

SSTR neutron dosimetry was conducted with mica track recorders and fissile deposits of Th-232, U-235, U-238, Np-237 and Pu-239. Absolute in-fuel fission rates measurements were measured by direct insertion of mica track recorders in FTR fuel pins. Capture rate measurements in U-238 were measured by RM dosimetry. Reaction rate measurements performed as part of the Task 220 series of experiments are described herein. Table 1 provides a description of the FTR fuel pin array used for reaction rate measurements in the Task 220 series of experiments. A photograph of this array is displayed in Fig. 1. Figure 2 is a schematic cross section of the 220 assembly showing the axial locations of the in-fuel and in-moderator dosimeters within the assembly. The in-fuel and in-moderator irradiations are described in Section 2. Experimental

1. INTRODUCTION

experiments have been conducted in the Battelle Pacific Northwest Laboratory’s (PNL) Critical Mass Laboratory (CML) using a variety of fast test reactor (FTR) fuel pin configurations and fissile solution concentrations. These experiments are part of a broad collaboration between the U.S. Department of Energy (DOE) and the Power Reactor and Nuclear Fuel Development Corporation, Japan (PNC) concerning criticality data development that has been carried out under a Memorandum of Agreement between DOE and PNC (August 1983). As part of the Task 220 series of experiments, absolute neutron reaction rate measurements (bare and cadmiumcovered) were carried out with solid-state track recorders (SSTR) and radiometric (RM) dosimeters. CRITICAL

*Present tPresent

address: address:

Battelle, Pacific Northwest Laboratories, Metrology Control Corporation (MC’),

P.O. Box 999, Richland, WA 99352, U.S.A. P.O. Box 944, Richland, WA 99352, U.S.A.

387

388

RAYMOND

GOLD

er ui.

Table 1. Experimental assembly for TASK-220 Lattice spacing:

0.761 cm square

Fuel: Type 3. i: Type 3.2:

PuOl-UOz FTR pins (27.6 wt% PuO,) Pu02-UOI FTR pins (22.5 wt% PuOz)

Moderator: Number of pins:

38 wt% tributylphosphate (TBP) 62 wt% normal paraffin hydrocarbon

(NPH)

1055

methods are discussed in Section 3 and experimental results are presented in Section 4. A least-squares analysis of these data is given in Section 5. Section 6 provides a brief conclusion.

2. DESCRIPTION OF THE IRRADIATIONS IN THE TASK 220 SERIES OF EXPERIMENTS 2.1. In -fuel measurements SSTR and RM dosimeters were wrapped in aluminum foil and placed between FTR fuel pellets that were, in turn, loaded into fuel pins. The load diagram for FTR fuel Pin 2 is given in Table 2. In-fuel SSTR were equally spaced with five FTR fuel pellets separating each SSTR. As can be seen in Table 2, the gap between the fuel pellets created by introduction of these SSTR varied from 8.0 up to 10.7 mils. Since the perturbation created by such a gap could be non-negligible, it was necessary to quantify this gap-perturbation effect. Consequently, in-fuel measurements in Pins 4 and 6 were dedicated to obtaining empirical correction factors for this gapperturbation effect. To explore the energy dependence of this effect, a threshold SSTR monitor (U-238) and a broad-based SSTR monitor (U-235) were used. The load diagram for Pin 4, which used the U-238 threshold monitor, is given in Table 3. It can be seen that the fuel gap varied from 8.5 up to 25.8 mils, so that the spatial dependence of the gap-perturbation effect for threshold monitors could be ascertained. The load diagram for Pin 6. which used the U-235 broad-based monitor, is given in Table 4. It can be seen that the fuel gap varied from 10.5 up to 30.0 mils, so that the spatial dependence of the gapperturbation effect for broad-based monitors could be ascertained. Locations of Pin Assemblies 2, 4 and 6 are shown in Fig. 3. The radiograph in Fig. 4 shows FTR Fuel Pins 2, 4 and 6 loaded with SSTR before the in-fuel irradiation. The midplane of the fuel region lies at a distance of approximately 66.3 cm from the bottom of the Type 3.2 fuel pins. Consequently, the in-fuel measurements were conducted slightly above midplane. The in-fuel irradiation (25 June 1985) used a period of 85 s to attain a constant power level, at which point the control blade was removed 44.7cm from

the bottom of the fuel pins, as indicated in Fig. 3. The duration of the exposure at this power level was 2 h. 2.2. In-moderator

measurements

Irradiation capsules of aluminum and cadmium were fabricated for the in-moderator measurements. Figure 5 provides the dimensions of these moderator irradiation capsules. Bare measurements were carried out at Location I using the Al capsule, whereas the cadmium capsule provided Cd-covered measurements at Location 3. The locations of moderator capsules 1 and 3 are shown in Fig. 6. These two capsules were positioned in the moderator on the end of hollow 0.25 in (OD) acrylic tubes. These capsules were located at an elevation of 81.97 cm above the bottom of the fuel pins or 15.67 cm above midplane. These in-moderator capsules were not positioned closer to midplane because of the possible perturbation from the lattice support plate, which was located near midplane. Load diagrams for the Al-capsule at Location 1 and the Cd-capsule at Location 3 are presented in Tables 5 and 6, respectively. Each mica SSTR and fissile deposit was wrapped separately in aluminum foil before insertion into the capsule bucket. These two capsules were loaded top to bottom in the order enumerated in Tables 5 and 6. To prevent leakage of the moderator into the capsules, the lids were sealed with epoxy. The moderator irradiation (10 July 1985) used a period of 103 s to attain a constant power level; at which point, the control blade was removed 44.7 cm from the bottom of the fuel pins, as indicated in Fig. 6. The duration of the exposure at this power level was 2 h. 2.3. Angular

orientation

To investigate gradient effects as well as any possible angular anisotropy, all mica SSTRs were marked with a black dot on the periphery for alignment purposes. FTR fuel pins were loaded so that the black dots of the in-fuel SSTRs were aligned. In a similar fashion, the black dots of the in-moderator SSTRs were aligned when the moderator capsules were loaded. For the in-fuel irradiation, the FTR fuel pins were oriented so that the black dots on the in-fuel SSTRs faced north. Similarly for the moderator irradiation, the moderator capsules were oriented so

WI

9

.

P

RAYMOND

390

252.35

i

202.57

0.18

f

Polypropylene

cm____.--_-__-__-

0.15 cm

Lattice

GOLD

c’f al.

Top of duel Pin -t---------

/+-+3l

i

0.02 cm

i

0.02

I I

Plate

cm

Polypropylene

Lattice Plate

I

* 0.02 cm GO 71 rm

I

-Carbon

Polypropylene

Lattice

(al Elevation (bl Elevation (cl Elevation FIG. 2. Schematic

cross

Plates.

Steel Tank 112 cm I.D.

for Type 3.2 Fuel Pins. Type 3.1 Fuel Pins are 0.5 cm Less of lowest SSTR in fuel column when present of reaction rate capsules in moderator when present

section of the Task 220 FTR fuel pin assembly showing the dosimeters relative to major assembly components.

Table

2. Load

diagram

for FTR

the axial elevation

pin 2 Deposit

SSTR

ID

26 24 23-SSTR 23-RM§ 22 21

Axial* location

Fuel gap (mils)

81.77 78.52 75.37 75.37 72.17 68.92

9.6 8.0 8.0 8.0 10.7 10.6

Isotope Np-237 Th-232 U-238 U-238 (I foil) U-235 Pu-239

Deposit 74 K s, s, S, 58 K 78 K

IDt

Total (/J g) 2.042 7687 12,583 12,583 0.34 0.0558

(1.8) (0.8) (0.8) (0.8) (6.3) (I .8)

mass: -... ___ Mass densit) (/Cgicm? 40.3

I

6.70 I.101

*Distance in cm from the bottom of the fuel pin to the bottom of the dosimeter. tS, denotes an asymptotically thick foil was used. fValue in parentheses is the mass uncertainty in percent at the lu level. $The same asymptotic foil used in the SSTR was also counted for the U-238 RM capture measurement.

rate

of

REACTION

RATE MEASUREMENTS Table

3. Load

FOR NUCLEAR

diagram

for FTR

REACTOR

ANALYSES

391

in pin 4 Deposit

mass5

Fuel Total

SSTR ID

Axial* location

gap (mils)

Isotope

49 47 No mica: 44 43 42 41

88.25 85.0 81.80 78.60 75.40 72.20 68.95

25.8 21.0 16.1 8.5 15.6 11.8 8.6

U-238 U-238 U-238 U-238 U-238 U-238 U-238

Deposit S, S, S, S, S, S, S,

1Dt

Mass density (p g/cm’)

(p g) 16,629 (2.1) 15,543 (2.1) 51,782 (2.3) 12,758 (2.3) 15,773(2.1) 14,039 (2.2) 17,893 (2.1)

(3 foils)

-

*Distance in cm from the bottom of the fuel pin to the bottom of the dosimeter. TS, denotes an asymptotically thick foil was used. fin-fuel capture rate measurement in U-238. jWalue in parentheses is the mass uncertainty in percent at the 10 level. Table 4. Load

diagram

for FTR

pin 6 Deposit

mass11

Fuel SSTR ID

Axial* location

gap (mils)

Isotope

Deposit

69 67 No micaf 64 63 62 61

88.15 84.9 81.70 78.55 75.30 72.10 68.90

30.05 24.1 14.1 11.3 19.7 14.8 10.5

U-235 U-235 U-238 U-235 U-235 U-235 U-235

90 K 89 K S, (3 foils) 65 K 88 K 66K 63 K

*Distance in cm from the bottom of the fuel tS, denotes an asymptotically thick foil was fln-fuel capture rate measurement in U-238. §Part of the aluminum foil came off in loading ID No. 1) was used in an attempt to maintain distance of 30.0mils is not a direct measurement //Value in parentheses is the mass uncertainty

ID7

Total

Mass density

(gg)

(p g/cm’)

0.99 0.90 43,688 0.30

(4.9) (5.1) (2. I) (4.6) 1.09(5.4) 0.35 (7.1) 0.30 (6.9)

pin to the bottom used.

19.56 17.71 5.83 21.44 6.90 5.89

of the dosimeter.

this SSTR and a mica spacer of 5.5 mils (SSTR the fuel gap distance. Consequently the fuel gap but only an estimate. in percent at the la level.

Experiment:

066

Lattice

Pitch: 0.761

Control

Blade: Out 44.7

+ 0.001

From Safety

Blade:

Bottom

of Fuel Pin

Out of System

Fuel Pins: 1055 Comments:

cm

cm

Same

(See Comments) Experimental

Assembly Two

as 065

Additional

with

Type

3.1

Fuel Pins for Irradiation of Reaction

FIG. 3. Overhead

schematic

of the Task

220 assembly showing 4 and 6.

the locations

Rate Devices

0 Reaction

Rate Assembly

2

c) Reaction

Rate Assembly

4

0 Reaction

Rate Assembly

6

of in-fuel pin assemblies

2,

RAYMOND

392

N

c

ci

rt c

ti

GOLD

cr crl

REACTION

RATE

MEASUREMENTS

FOR NUCLEAR

REACTOR

393

ANALYSES

(Young. 1958). In his original work, Young demonstrated that a large increase in chemical etch rate existed in the region of damage created by energetic and highly ionizing charged particles such as fission fragments. In spite of this rather profound and pioneering discovery, little, if any, work was pursued along these lines until well into the decade of the sixties. Since then. however, the use and applications of track recorder techniques have expanded exponentially as is well documented in the text of Fleischer ct cl/. (1975) who are perhaps the most notable contributors to this field of endeavor. The range of scope of applications for this technique now cover almost the complete breadth of the natural and physical sciences, as well as certain limited applications in biological science. In neutron dosimetry work, detectors using this technique have become commonly known as solid state track recorders (SSTRs). Such detectors have offered fundamental advantages for in-core reactor dosimetry, health physics and environmental science. Absolute SSTR reaction rate measurements have been employed for some time now in neutron dosimetry (Gold et al., 1968) and cover an enormous intensity range, from the low levels arising in environmental applications to the high levels found in power reactor environments. Indeed, the domain of SSTR applications in United States’ nuclear reactor energy from the harsh highprograms now extends temperature environments found in high power reactor cores to very low flux environments arising in terials

-

FIG. 5. Cross-sectional in the 220 experiment.

Lid

view of the moderator capsule used All dimensions are given in inches.

that the black dots on the in-moderator

SSTRs faced

north.

3. EXPERIMENTAL 3.1. Solid-state dosimetrj,

track

METHODS

recorder

(SSTR)

neutron

Almost three decades have elapsed since the discovery of radiation damage tracks in dielectric ma-

Experiment:

066R

Lattice

Pitch: 0.761

Control

Blade:

+ 0.001

Out 44.7

cm

cm

From Bottom

of Fuel Pin

Safety Blade: Out of System Fuel Pins: 1055 (See Comments) Comments:

Same

Experimental

Assembly as 065 with Two Additional Type 3. 1 Fuel Pins for Irradiation of Reaction

FIG. 6. Overhead

schematic

of the 220 assembly

showing

1 and 3.

locations

Rate Device ?5

0

Reaction

Rate Assembly

1

A

Reaction

Rate Assembly

3

of the moderator

capsule

assemblies

RAYMOND

394 Table

5. Load

diagram

GOLD

et ul.

for Al moderator

capsule

at location

Deposit

mass:

Total SSTR ID T S No mica? P 0 N

Isotope

Deposit

Np-237 Th-232 U-238 U-238 U-235 Pu-239

ID*

Mass densit! (p g/cm’)

(/1 g) 0.4269 (2.1) 3380 (0.5) 16,508 (0.5) 733 1(0.5) 1.059 (3.9) 0.0240 (1.9)

108 s, S, (3 foils) s, 91 K 99 K

*S, denotes an asymptotically thick foil was used. tin-moderator capture rate measurement in U-238. fValue in parentheses is the mass uncertainty in percent

out-of-core

locations,

critical

assemblies,

or

away

from reactors (AFR) experiments. The neutron energy region arising in these applications is very broad, covering more than eight decades from thermal up to fusion energies. The range of neutron flux/fluence intensity encountered in these applications is even greater, extending over more than thirteen decades. As a consequence, use of a variety of SSTR has been entailed in U. S. Fast Breeder Reactor, Light Water Reactor, and Magnetic Fusion Energy Reactor programs (Roberts et al., 1977; Gold et al., 1980a, b). An ASTM standard has been established for SSTR neutron dosimetry (ASTM, 1982a). The successful use of SSTR neutron dosimetry to obtain data for Three Mile Island Unit 2 (TMI-2) reactor recovery operations (Gold et al., 1983a; Ruddy et al., 1983; Gold et al., 1983b, 1984a, b, 1985) is a particularly noteworthy low-flux endeavor, since these efforts extend downward to extremely low neutron intensity levels, i.e. of the order of cosmic-ray neutron flux intensity at sea level. A wide variety of SSTR materials such as minerals, glasses and plastics can be used for SSTR neutron dosimetry. Indeed, we have found that each track recorder material possesses unique properties that can often be exploited for specific applications. Only through attention to a great many details has it been possible to attain absolute accuracy of l-2 percent (lcr) in SSTR neutron dosimetry applications. To this end, such factors as: (1) etching procedures (Gold et

Table

6. Load

diagram

3.2. SSTR

of Cd moderator

A Z No mica? X W V

Np-237 Th-232 U-238 U-238 U-235 Pu-239

Deposit

ID*

101 S, S,

(3 foils)

S% 93 K 109

21.332 0.4743

at the 1~ level.

detector

configurations

and deposits

SSTR are usually placed in firm surface contact with a fissionable nuclide that has been deposited on a pure non-fissionable metal substrate (backing). This typical SSTR geometry is depicted in Fig. 7. For the in-fuel measurements in the 220 series of experiments, there was no space for the conventional cap and case shown in Fig. 7. Instead, the mica and deposit were wrapped together using thin aluminum foil (h 2 mils). Larger gaps were created in the FTR fuel column by increasing the successive layers of aluminum foil wrapping.

capsule

at location

Deposit Isotope

8.425

al., 1979; Roberts et al.. 1982a); (2) objectivity in track counting (Gold, 1977a; Roberts et al., 1982b); (3) annealing (Roberts et al., 1979; Gold et al., 1981a, b); and (4) radiation damage (Gold et al., 1980~) have been extensively studied in our SSTR laboratory at Hanford. These efforts have provided the incentive to develop automated computercontrolled systems for the quantitative scanning of nuclear tracks. Indeed, our laboratory has been privileged to contribute to this particular specialization over the years (Gold ef al., 1982, 1983~; Roberts et al., 1984). As any in-depth review of the SSTR method would be inappropriate here, the reader is referred to the above cited references and in particular the ASTM standard (ASTM, 1982a) for further details.

Total SSTR ID

I

(pg) 0.7501 (2.1) 3345 (0.5) 18,404 (0.5) 4565 (0.5) 1.14(3.9) 0.0282 (1.3)

*S, denotes an asymptotically thick foil was used. tin-moderator capture rate measurement in U-238. fValue in parentheses is the mass uncertainty in percent

3

mass: Mass density (p g/cm’) 14.82

22.37 0.5571

at the lu level.

REACTION

RATE

MEASUREMENTS

FOR

Al OR Cd CASE /

FISSION DEPOSIT

TRACK RECORDEli

I Al OR Cd CAP

FIG. 7. Typical geometrical configuration

used for SSTR

neutron dosimetry.

For thin deposits, the thickness (mass density) of the deposit is much less than the range of fission fragment in the deposit material. Under these conditions, self-absorption is negligible and sensitivity depends linearly on mass density. For deposit thicknesses greater than about 100 pg/cm2, self-absorption of fission fragments by the deposit becomes increasingly important. For deposit thicknesses greater than twice the range of a fission fragment in the deposit material, the effective thickness may be represented by a constant value. This constant value is referred to as the asymptotic sensitivity, s,. The SSTR asymptotic sensitivity is the highest SSTR efficiency that can be attained. It can be expressed in units of atoms per cm2 or grams per cm2. It is essentially the number of atoms per cm2 that can give rise to observable tracks at the surface of the SSTR (after suitable etching). The asymptotic sensitivity for mica SSTR using U-238 and Th-232 foils has been measured to an absolute accuracy of approximately 2 percent (la) (Gold et al., 1968, 1977b). Deposit thicknesses in the approximate range from 0.1 to 30 mg/cm2 should be avoided because of problems arising from self-absorption of fission fragments in the source. While it is possible to work in this range, additional error will be incurred because of the need to correct for self-absorption. In the region beyond 30mg/cm2, one should use the asymptotic sensitivity. Electrodeposition and vacuum deposition are the most frequently used and the most effective techniques. The latter method normally results in more uniform deposits, but economy of material and convenience may favor the former. In both cases, actinide deposits are produced more easily in the oxide than in the metallic form. Adherence of the deposit to the backing material can often be accomplished by heating the deposit to red heat in an inert atmosphere. Uniformity can be demonstrated by a-autoradiography using an u-sensitive SSTR such as cellulose nitrate or by fission track radiography with uniform neutron field irradiations.

NUCLEAR

REACTOR

ANALYSES

395

For 220 series of experiments, SSTR deposits were prepared by electrodeposition for fission rate measurements in U-235, Pu-239 and Np-237. These electrodeposits were prepared on very pure (better than 99.992%) Marz-grade nickel. The nickel backing was 5 mm thick and possessed a 0.168 in dia., whereas the deposit diameter was 0.100 in. For U-238 and Th-232 fission rate measurements, asymptotically thick foils were available. These foils were 0.002 in thick. For the moderator measurements 0.1875 in dia. foils were used, whereas the in-fuel measurements were conducted with 0.125 in dia. foils. The electrodeposits of U-235, Pu-239 and Np-237 were not completely satisfactory with respect to both total mass and uniformity. The quality of SSTR deposits is a crucial factor in the ability to attain accurate absolute results from SSTR neutron dosimetry. This fact was recognized at the very outset of SSTR neutron dosimetry (Gold et al., 1968), and has since been emphasized (ASTM, 1982a; Gold, 1977a). As a consequence, reaction rates observed for U-235, Pu-239 and Np-237 are not as accurate as those of U-238 and Th-232 in the 220 series of experiments. 3.3. Radiometric (RM) ments

U-238 capture rate measure-

The absolute U-238 (n, y) reaction rate was measured by observing the decay of the Np-239 reaction rate product with high-resolution gammaray spectrometry. ASTM El81 (ASTM, 1982b) was adhered to in this work except for calibration of the intrinsic Ge gamma-ray detector. A special method summarized below was used to calibrate the detector for Np-239 using the 228.2 and 277.6 keV gamma photopeaks. Corrections for radioactive decay of the sample during the relatively long counting times used, and from the end of the irradiation until start of counting, were made in accordance with procedures in ASTM El 8 1. Attenuation of gamma-rays through the finite thicknesses of the U-238 dosimeters was also corrected for in accordance with procedures in ASTM E181. The intrinsic Ge detector was calibrated directly for response to the 228.2 and 277.6 keV gamma-rays from Np-239 decay by using highly enriched Am-243 sources that had been absolutely counted in a low geometry alpha counter at Argonne National Laboratory (ANL). In this way, the Am-243 alpha emission rate of these sources was determined with an uncertainty of approximately 0.4 percent (la). The Am-243 sources were allowed to age for greater than 30 days to ensure that the Np-239 daughter would be in secular equilibrium with the Am-243 parent at the time the Np-239 gamma spectrometer calibration measurements were made. This method of direct calibration for Np-239 eliminates uncertainties in the Np-239 decay scheme and branching intensities (for the Np-239 gamma photopeaks) and thereby improves accuracy over indirect methods of calibration.

396

RAYMOND

GOLD

et al.

Table 7. In-fuel FTR pin 2 data Ftlel SSTR ID 26 24 23-SSTR 23-RMt 22 21

Axial* location

gap (mils)

81.77 78.52 75.37 75.37 72.17 68.92

9.6 8.0 8.0 8.0 10.7 10.6

*Distance in cm from tThe same asymptotic measurement. fValue in parentheses $Total observed tracks. JIValue in parentheses

Wapture

Isotope Np-237 Th-232 U-238 U-238 U-235 Pu-239

l

U-238 Np-237 Th-232

545-&1.35) 14984 (2.58)

is the experimental

uncertainty

at the lc level.

7.07E 3.65E 1.572E 1.328E I .202E 1.481E

-

17 (2.6) I8 (2.7) I7 (2.3) 16 (3.3)$ 15 (6.4) 15 (3.2)

is the experimental s).

uncertainty

in percent

rate

at the la level.

rate in captures/(atok

Direct effects of gamma radiation on the mica component of the SSTR are completely negligible. We have shown that gamma-ray exposures in excess of IO9 R have no subsequent effect on either the recording or etching properties of mica. A background from the gamma-ray component of the reactor radiation field can be produced by photofission. For broad-based monitors that possess high neutroninduced fission rates, such as U-235 or Pu-239, photo-fission is negligible. However, for threshold monitors (such as Th-232, U-238 or Np-237) photofission may not be negligible compared with other sources of experimental error. Estimating the photofission contribution for these threshold monitors requires a knowledge of the gamma-ray spectral intensity, especially above roughly 5 MeV where the photofission cross section first becomes significant. Unfortunately, efforts to define the gamma-ray component of the mixed radiation field in reactors have seriously lagged in contrast to the vigorous activity that has been applied to define the neutron component of the mixed radiation field. This situation was discussed in-depth at special workshops held during the last two ASTMEURATOM International Symposia on Reactor Dosimetry (Gold and Lloret, 1985; Gold and Najzer, 1987). In lieu of well-defined data, one can only obtain crude estimates based on knowledge that is available from comparable environments. Perhaps the most extensive examination of photofission background contribution to threshold fission neutron monitors has been performed in Light Water Reactor (LWR) Pressure Vessel (PV) environments (McGarry et al., 1984). At the 1/4-T location, which is two inches from the inner PV surface, it has been shown that the relative photofission background component is roughly as follows:

l

26375 (1.9) 3.004 x 105(1.8) 1.3099 x lOh(O.95)

the bottom of the fuel pin to the bottom of the dosimeter. foil used in the SSTR was also counted for the U-238 RM capture

3.4. Gamma-ray effects

l

Fission /I rate (fissions/atom/s)

Trackf density (tracks/cm’)

2-4 percent I1 percent 5-8 percent.

It is also well-known that neutrons are attenuated more rapidly than gamma-rays in the large water gap that exists between the LWR core and the PV. Consequently, the photofission background component that would arise in the LWR core is considerably less than that which exists at the 1/4-T location. On this basis, it is concluded that gamma-ray effects are negligible in the neutron dosimetry measurements conducted with mica SSTR in the Task 220 series of experiments. 4. EXPERIMENTAL

RESULTS

4.1. In -fuel data 4.1.1. Axial buckling. In-fuel reaction rate results for Pins 2, 4 and 6 are given in Tables 7, 8 and 9, respectively. Inspection of the U-238 fission rate data in Table 8 reveals a significant difference between SSTR 41 and SSTR 44, even though each possesses a nearly identical fuel gap (-8.5 mils). The U-235 fission rate data in Table 9 reveal a similar behavior pattern. There exists a significant difference between SSTR 61 and SSTR 64, even though each possesses a near identical fuel gap (_ 11 mils). These differences exist because of a non-negligible axial buckling that must be taken into account. This is not really surprising, since a five fuel pellet spacing was used between in-fuel dosimeters to avoid any interperturbation from one dosimeter to the next. As a result of this spacing, a rather extended axial range was entailed, namely 12.85, 19.3 and 19.25 cm for Pins 2, 4 and 6, respectively. Consequently, correction for axial flux variation must be anticipated. The shape of the axial intensity profile is shown more clearly in Figs 8 and 9, which present the U-238 and U-235 fission rate data, respectively. Points from Table 4 have been included so that the U-238 data in Fig. 8 corresponds to a fuel gap of approximately 8.5 mils, whereas the U-235 data in Fig. 9 corresponds to a fuel gap of approximately 11 mils. Actually, the fuel gap varies from 8.0 up to 8.6 mils for the U-238 data set, whereas the fuel gap variation for the U-235 data set is from 10.5 up to 11.3mils. It has

REACTION

RATE MEASUREMENTS

REACTOR

FOR NUCLEAR

ANALYSES

397

Table 8. In-fuel FTR pin 4 data Fission§ rate (fissions/atom/s)

SSTR ID

Axial* location

Fuel gap (mils)

Isotope

Trackf density (tracks/cm*)

49 47 No mica? 44 43 41

88.25 85.0 81.80 78.60 75.40 68.95

25.8 21.0 16.1 8.5 15.6 8.6

U-238 U-238 U-238 U-238 U-238 U-238

1.0436 x 106(1.81) 1.1619 x 106(l.80) 1.2199 x 106(l.8) 1.3512 x 106(1.8) 1.387 x 106(1.3)

1.252E 1.403E 1.11E 1.464E1.621E 1.664E -

17 (2.8) 17 (2.8) 16(5.1)1) 17 (2.5) 17 (2.8) 17 (2.5)

*Distance in cm from the bottom of the fuel pin to the bottom of the dosimeter. tin-fuel capture rate measurement in U-238. $Value in parentheses is the experimental uncertainty in percent at the la level. $Value in parentheses is the experimental uncertainty in percent at the lu level. [[Capture rate in captures/(atom.s). Table 9. In-fuel FTR pin 6 data

SSTR ID

Axial* location

69 67 No mica? 64 63 62 61

88.15 84.9 81.70 78.55 75.30 72.10 68.90

Fuel gap (mils) 30.01 24.1 14.1 11.3 19.7 14.8 10.5

Fission§ rate (fissions/atom/s)

Isotope

Tracks5 counted

U-235 U-235 U-238 U-235 U-235 U-235 U-235

14,989 (0.82) 15,467 (0.80) 4993 (I .42) 21,862 (0.68) 6037 (1.28) 6037 (1.28)

8.21E 9.32E 5.68E 9.03E 10.9E 9.36E 12.OE-

16 (5.0) 16(5.2) 17 (4.8)/l 16 (4.8) 16 (5.4) 16 (7.2) 16 (7.0)

*Distance in cm from the bottom of the fuel pin to the bottom of the dosimeter. tin-fuel capture rate measurement in U-238. $Part of the aluminum foil came off in loading this SSTR and a mica spacer of 5.5 mils (SSTR ID No. 1) was used in an attempt to maintain the fuel gap distance. Consequently the gap distance of 30.0 mils is not a direct measurement but only an estimate. §Value in parentheses is the experimental uncertainty in percent at the lo level. l/Capture rate in captures/(atom . s).

been assumed that the gap-perturbation effect (see Section 4.1.2) is negligible over such small spatial ,driations. The smooth curves in Figs 8 and 9 are least-squares’ fits of these SSTR fission rate F(z) data to the fundamental mode form F(z) = a, cos(z/a,)

(1)

where z is the axial distance from fuel midplane.

r

1.0

The parameters a, and a2 are obtained from a least-squares’ fitting procedure. In this report, least-squares analyses of SSTR data from the 220 experiment have been carried out with the computer program FATAL (Salmon and Booker, 1972). For U-238, the track density can be used directly and one finds F,,(z) = 1.4017 x 106cos(z/24.106).

(2)

Full rcala = 1.5257OE+06

0.7 0.6 0.s 0.4 0.3 -

“:f

0.2 -

(

0.1 3

I 4

I 5 Axial

I 6 location

I 7

I 6

I 9

in cm from fuel

I IO

I II

I 12

midplane

FIG. 8. U-238 track density axial buckling data for a fuel gap of approximately 8.5 mils.

4

,

,

,

5

6

7

Ax101 location

(

(

,

6

9

IO

in cm from fuel

,

,

II

I2

mldplone

FIG. 9. U-235 fission rate axial buckling data for a fuel gap of approximately 11 mils.

398

RAYMOND Table Parameter No.

squares

Initial estimate 1.4000E+ 06 2.0000E + 01

0, 0, Observed values 2.6500E + 00 9.0700E + 00 1.2300E + 01

10. Least

Estimated weights 3.0758E - 09 6.4517E - 09 6.7197E - 09

GOLD

fit of the U-238

Final value 1.4017Ef06 2.4106E +Ol

Observed F(z) values 1.3870E + 06 1.3099E + 06 1.2199E+06

matrix

Parameter No. *i a, Observed z values 2.6OOOE + 00 5.87OOE + 00 1.2250E + 01

squares

Initial estimate 1.2000E - 15 2.4000E + 0 1

Estimated weights 1.3998E + 32 1.6898E + 32 5.3020E + 32

Table

12. Axially

portion

adjusted

need be given.

in-fuel

FTR

pin 2 data*

SSTR ID

gap (mils)

Isotope

Fission1 rate (fissions/atom/s)

26 24 23-SSTR 23-RMt 22 21

9.6 8.0 8.0 8.0 10.7 10.6

Np-237 Th-232 U-238 U-238 U-235 Pu-239

7.03E 3.33E 1.35E 1.14E 9.86E 11.9E-

-

17 (2.8) 17 (2.9) 17 (2.6) 16(3.5)§ 16 (6.5) 16(3.4)

*Reaction rates adjusted to an elevation of 81.97 cm above the bottom of the fuel pins. tThe same asymptotic foil used in the SSTR was also counted for the U-238 RM capture rate measurement. fValue in parentheses is the experimental uncertainty in percent at the lu level. @Capture rate in units of captures/(atom.s).

fuel pins, which corresponds to the axial location of the moderator capsules. These adjusted reaction rates are given in Tables 12, 13 and 14. The additional uncertainty component entailed in this axial correction was slightly larger than 1 percent for all reaction rates. The location of the three in-fuel pins, as shown in Fig. 3, was chosen close to the center of the assembly so that the radial variation of the neutron spectrum, in both intensity and energy, could be neglected. 4.1.2. Gap-perturbation effect. The axially adjusted SSTR fission rates given in Table 13 for U-238

fit of the U-235

Final value 1.2518E - 15 1.6063E + 01

buckling

data

SD 6.739OE - 17 1.7324E + 00

Fitted F(z) values 1.2355E15 1.3692E - 15 9.0510E - 16

Observed F(z) values 1.2040E - 15 1.2020E- 15 9.0290E - 16

matrix

Differences (%) -4.4446E - 01 4.8307E - 01 -2.6274E-01

Fuel

Variance-covariance 4.5413E - 33 -9.2850E - 17 *Since the variance-covariance

Differences -6.1922E + 03 6.2974E + 03 -3.2137E+03

(3)

11. Least

l.l691E+OO 5.7624E + 00

only the lower triangular

As can be seen from a comparison of Figs 8 and 9, the fit for the U-238 data is excellent whereas the fit for the U-235 data is not as good. This is shown in greater detail in Tables 10 and 11, which provide the computer results from these leastsquares’ fits for U-238 and U-235, respectively. In addition, the variance-covariance matrices given in Tables 10 and 11 permit calculation of the uncertainty entailed when one corrects these data for axial buckling. The higher quality of the U-238 data can be directly attributed to the fact that only the track density data could be used; whereas for U-235, it is necessary to employ the SSTR mass data and its associated uncertainty. Consequently, the fit of the U-238 data was used to make axial corrections for all SSTR fission rate data. This is justifiable, since the series of 220 experiments was conducted under critical conditions where a single fundamental mode form should provide a good approximation over the axial range of interest here (z I 22 cm), because any neutron spectral variation over this axial range is negligible. Consequently, the axial correction of the in-fuel dosimeters was obtained by use of equation (2) and Table 10. All in-fuel reaction rates were adjusted to an axial location of 8 1.97 cm above the bottom of the

Table

SD I .6387E + 04 1.3891E + 00

1.9295E + 00

is symmetric,

= 1.2518 x 10-‘scos(z/16.063).

data

matrix*

For U-235, the fission rate must be used and one finds F&)

buckling

Fitted F(z) values 1.3932E + 06 1.3036E + 06 1.223lE+06

Variance-covariance 2.6852E + 08 - 1.929OE + 04 *Since the variance+ovariance

et al.

5.3833E + 00 1.0785E+ 01

Differences -3.1457E3 17 3.2842E - 17 -2,1945E18

Differences W) -2.5462E+OO 2.8090E + 00 -2.4246E-01

matrix* 3.0013E + 00

is symmetric,

only the lower triangular

portion

need be given.

REACTION

RATE MEASUREMENTS

FOR NUCLEAR I.0

Table 13. Axially adjusted in-fuel FTR pin 4 data*

SSTR ID

Fuel gap (m&s)

Isotope

49 47 No micat 44 43 41

25.8 21.0 16.1 8.5 15.6 8.6

U-238 U-238 U-238 U-238 U-238 U-238

Fission3 rate (fissions/atom/s)

399

ANALYSES

r

Full scola~ 1.767SlE-17

0.7 -

1.625E- 17 (2.9) 1.564E- 17 (2.9) l.lOE1.336E 1.388E 1.331E -

REACTOR

2

0.6 t

16(5.2)§ 17 2.7) 17 (3.0) 17 (2.7)

*Reaction rates adjusted to an elevation of 81.97 cm above the bottom of the fuel pins. tin-fuel capture rate measurement in U-238. SValue in parentheses is the experimental uncertainty in percent at the lo level. §Capture rate in units of captures/(atom.s).

i

-:L,, g (gap

26

in mild

FIG. 10. U-238 gap-perturbation

data.

Table 14. Axially adjusted in-fuel FTR pin 6 data*

SSTR ID

Fuel gap (mils)

Isotope

Fissions rate (fissions/atom/s)

69 67 No mica? 64 63 62 61

3o.q 24.1 14.1 11.3 19.7 14.8 10.5

U-235 U-235 U-238 U-235 U-235 U-235 U-235

1.06E I .04E 5.63E 8.23E 9.30E 7.678 9.64E-

15 (5.0) 15 (5.3) 17 (4.9)/l 16 (4.9) 16 (5.6) 16 (7.3) 16(7.11)

*Reaction rates adjusted to an elevation of 81.97 cm above the bottom of the fuel pins. ?In-fuel capture rate measurement in U-238. $Part of the aluminum foil came off in loading this SSTR and a mica spacer of 5.5 mils (SSTR ID No. I) was used in an attempt to maintain the fuel gap distance. Consequently the fuel gap distance of 30.0 mils is not a direct measurement but only an estimate. §Value in parentheses is the experimental uncertainty in percent at the lo level. (/Capture rate in units of captures/(atom.s).

observed

in Pin 4 are plotted

as a function

of fuel gap

In Fig. 10. The smooth curve in Fig. 10 is a linear

:ast-squares’

fit of the data in the form &(g) = b, + b2.g.

(4)

Here, F**(g) is the U-238 fission rate [fissions/ (atom.sec)] for a gap distance g (in mils), where b, and 6, are coefficients determined from the leastsquares’ fitting procedure. Computer results of this linear least-squares’ fit are summarized in Table 15. These least-squares results provide the correction factor needed to account for the gap-perturbation effect in threshold monitors. For broad-based monitors, a similar analysis has been performed with the adjusted SSTR fission rates in Table 14 observed with U-235 in Pin 6. These U-235 fission rates are plotted in Fig. 11 as a function of fuel gap. The smooth curve in Fig. 11 is a least-squares’ fit of the data in the form

4&)

= bl + b, ‘g.

Here, F,,(g) is the U-235 fission rate [fission/ (atom.s)] for a gap distance g (in mils), where 6, and bz are coefficients determined from the least-squares fitting procedure. Computer results of this linear least-squares’ fit are summarized in Table 16. These least-squares results provide the correction factor needed to account for the gap-perturbation effect in broad-based monitors.

Table 15. Linear least-squares fit of the U-238 gap-perturbation Parameter No. b, b, Observed g values 8.0OOOE+ 00 8.5OOOE+ 00 8.6OOOEf 00 I .5600E + 01 2.1OOOE+Ol 2.5800E + 01

Initial estimate 1.2500E - 17 1.5OOOE- 19

Estimated weights 8.805lE + 36 9.7048E + 36 6.2499E + 36 5.7784E + 36 4.8516E + 36 2.7685E + 36

Final value 1.1996E - 17 1.5916E - 19

SD 3.754OE - 19 2.749lE-20

Observed

Fitted

F,, values

Fz8values

1.3460E 1.336OE 1.3330E 1.3880E 1.5640E 1.6250E -

17 17 17 17 17 17

1.3269E 1.3348E 1.3364E 1.4478E1.5338E 1.6102E -

17 17 17 17 17 17

data 0 3.1295E + 00 1.7272E + 01

Differences Differences (%) 1.9121E - 19 144llE+00 l.l631E-20 8.7133E - 02 -3.4286E - 20 -2.56558 - 01 -5.9843E19 -4.1332E+OO 3.0209E - 19 1.9696E + 00 1.4812E - 19 9.1990E - 01

Variance-covariance matrix* 1.4093E - 37 -9.3113E - 39 7.5575E -40 *Since the variancecovariance

matrix is symmetric, only the lower triangular portion need be given.

RAYMOND

GOLD

r

et al.

Table

1.0

17. Axially adjusted and fuel-gap corrected reaction-rate results for FTR pin 2

SSTR

ID

26 24 23-SSTR 23-RM’ 22 21

II

I3

I5

17

19 g

FIG. 11. U-235

21

23

25

27

Np-237 Th-232 U-238 U-238 U-235 Pu-239

6.236E 3.010E 1.217E 1.031E 8.633E 1.043E

*The same asymptotic foil used was also counted for the U-238 RM measurement. TReaction rates adjusted to an 8 1.97 cm above the bottom of the fuel

29

(gap on mild gap-perturbation

Isotope

Correctedtf fission rate (fissions/atom/s) -

17 (3.6) 18 (3.5) 17 (3.2) 16 (4.0)5 16 (6.9) 15 (4.2)

in the SSTR capture rate elevation of and corrected

for the fuel gap-perturbation effect. IValue in parentheses is the experimental

data.

un-

certainty in percent at the lo level. §Capture rate in captures/(atom.s).

Comparison of the linear least-squares’ fits for the U-238 and U-235 data, see Figs 10 and 11, reveals that the U-238 fit is clearly superior. This superiority can again be attributed to the larger uncertainty introduced with the mass data of the U-235 SSTR deposits. Using this linear model of the gapperturbation effect, both equations (4) and (5) can be written in the form F(g) = b,[l +

Wh).gl.

(6)

Since b, = F(O), one can write F(g)IF(O) = 1 + w4~tT.

(7)

Consequently, the relative gap-perturbation correction factor, C(g), can be expressed in the form C(g) = F(O)IF(g) = [l + @,l~,)~gl-‘.

(8)

Hence, one finds that the relative gap-perturbation correction depends only on the ratio (b,/b,) of the least-squares coefficients. From the computer results given in Table 15, one finds that bJb, = 0.01327 for U-238, whereas the computer results in Table 16 yield bz/bl = 0.01378 for U-235. These two bJb, ratios

Table Parameter No. b, b, Observed g values 1.0500E + 1.0700E + l.l3OOE+Ol 1.4800E + 1.9700E + 2.4100E + 3.0000E +

01 01 01 01 01 01

16. Linear

least-squares

Initial estimate 7.8OOOE - 16 8.9OOOE - 18

Estimated weights 2.0762E + 2.2276E + 6.1572E + 3.0996E + 3.684OE + 3.3178E + 2.9421E +

32 32 32 32 32 32 32

differ by less than 4 percent. The agreement between these two ratios is certainly well within experimental uncertainties and this concordance implies that the relative gap-perturbation effect is essentially independent of energy for this environment. As a consequence, the more accurate linear least-squares’ fit obtained from the U-238 data, see Fig. 10 and Table 15, can be used to correct all reaction rate data, whether from threshold or broad-based monitors. On this basis, the corrected in-fuel reaction rate results for Pin 2 are summarized in Table 17. The error introduced through the gap-perturbation correction can be calculated from the variance-covariance matrix given in Table 15. This error component varies from approximately 1.9 percent up to 2.4 percent as the gap g increases from 8 to 10.7 mils. 4.2. Moderator data Moderator reaction rate results for Capsules 1 and 3 are given in Tables 18 and 19, respectively. The

fit of the U-235 Final value 7.4444E - 16 1.0259E - 17

Observed Fz5 values 9.64OOE 9.8590E 8.2270E 7.6720E 9.3020E 1.0350E 1.06OOE -

16 16 16 16 16 15 15

gap-perturbation

SD 9.0979E - 17 4.9457E - 18

Fitted Fzs values 8.5216E 8.5421E 8.6037E 8.96288 9,4655E9.9169E 1.0522E -

16 16 16 16 16 16 15

data ;), 1.2221E + 01 4.8207E + 01

Differences l.l184E1.3169E -3.7665E - 1.2907E -1.6344E4.3315E7.7846E -

16 16 17 16 17 17 18

Differences W) 1.3125E+Ol 1.5417E+Ol -4.3778E + 00 - 1.44OlE + 01 -1.7267E+OO 4.3678E + 00 7.3983E - 01

Variance-covariance matrix* 3,1266E33 - 1.5798E - 34 9.2397E - 36 *Since the variance-covariance

matrix

is symmetric,

only the lower triangular

portion

need be given.

REACTION

RATE MEASUREMENTS Table

SSTR

18. Data

from

ID

Isotope

T S No mica* P 0

Np-237 Th-232 U-238 U-238 U-235

FOR NUCLEAR

the Al moderator

capsule

REACTOR at location

ANALYSES

401

1

Fission§ rate (fission/atom/s)

Trackt density (tracks/cm*) 563$ (4.2) 2.762E + 05 (2.0) 1.080E+06(1.1) 5.359E + 05 (1.2)

7.20E 3.31E 5.13E 1.29E 1.36E

-

17 (4.7) 18 (2.8) 16(16)\1 17 (2.3) 15 (4.1)

*In-moderator capture rate measurement in U-238. tValue in parentheses is the uncertainty in percent at the la level. ITotal observed tracks. $Value in parenthesis is the uncertainty in percent at the la level. IiCapture rate in captures/(atom.s). Correction for neutron selfshielding has been applied.

capture rate results reported in Tables 18 and 19 have been corrected for neutron self-shielding using a slab geometry approximation. In this approximation (Simons and McElroy, 1985), the neutron self-shielding factor, NSS (which is the ratio of the observed capture rate, &, to the infinitely dilute capture rate, R,,) is given by

U-238

NSS = +

= [l + 1.2 x 104(px)]-“2.

(9)

ID

Here, p is the density in atoms per cm3 and x is the thickness of the slab in cm3 per barn. In contrast, no self-shielding correction has been applied to the U-238 capture rate measurements in the fuel pins, for in this case, it is the in situ reaction rate in the fuel that is desired. Based on comparison of equation (9) with actual measurements, the uncertainty introduced through this self-shielding correction is estimated to be roughly 15 percent (1~) for the U-238 capture rate foils used in moderator Capsules 1 and 3. 4.3. Gradient observations A number of the in-fuel and moderator SSTR irradiated in experiment 220 were scanned to investigate the existence of reaction rate gradients. This

Table

19. Data

study of gradient effects was restricted to SSTR obtained with uniform deposits, which for the 220 series of experiments was only U-238 and Th-232. The deposits prepared by electrodeposition, i.e. U235, Np-237 and Pu-239, were non-uniform and consequently not well-suited for use in gradient studies. The black dot on the periphery of the SSTR was used to orient the scan across the diameter of the SSTR. One scan was made across the SSTR diameter going north-to-south through the black dot. This scan is defined as the 0” scan. Another scan was made across the SSTR diameter at an angle of 45” with respect to the 0” scan. Typical scan results are shown in Figs 12 and 13, for the 0” and 45” scans, respectively, of SSTR 23, i.e. the U-238 in-fuel measurement in Pin 2. In Figs 12 and 13, the smooth curve is a linear regression fit of the scan data. In both cases, the slope of the regression line is not significantly different than zero. Similar scans were performed with in-moderator SSTR. In all such in-fuel and in-moderator scans, no radial or angular dependence of the track density could be detected. Hence, the SSTR data show that no significant gradients exist in the U-238 and Th-232 reaction rates observed in the CFRP/PNC 220 series of experiments.

from the Cd moderator

SSTR ID

Isotope

A 2 No mica* X V

Np-237 Th-232 U-238 U-238 Pu-239

caosule

Track? density (tracks/cm*) 7263 (6.6) 2.525E + 05 (1.9) 1.064E + 06 (I .O) 393f (5.0)

at location

3

Fissions rate (fissions/atom/s) 5.28E 3.02E 4.98E 1.24lE 7.67E

-

17 (7.0) 18 (3.5) 16(15)11 17 (2.2) 16 (5.2)

*In-moderator capture rate measurement in U-238. tValue in parentheses is the uncertainty in percent at the lu level. $Total observed tracks. §Value in parenthesis is the uncertainty in percent at the lo level. l/Capture rate in captures/(atom.s). Correction for neutron selfshielding has been applied.

402

RAYMOND

GOLD

PNC23-EC

et al

taneously

adjusted.

For example, R, = CQ$.

FIG.

12. 0” scan data for the in-fuel U-238 SSTR 23 measurement in Pin 2.

5. LEAST-SQUARES 5.1. FERRET-SAND

SPECTRAL

ANALYSIS

II data analysis procedures

Derivation of in-fuel and in-moderator neutron spectra was performed with the FERRET-SAND II codes (McElroy et al., 1967; Schmittroth, 1979; Simons et al., 1985; McElroy, 1985). These HEDL codes use the measured reaction rate data to adjust the calculated group fluxes. The FERRET lognormal least-squares algorithm weights both the a priori values and the measured data in accordance with the assigned uncertainties and correlations. In general, the measured values fare linearly related to the flux @ by some response matrix A :

Table

20. FERRET

neutron

PNc23-45 o

15.4 H

14.41

P

I

FIG. 13. 45” scan data for the in-fuel U-238 measurement in Pin 2.

SSTR

23

1 2 3 4 5 6 I 8 9 IO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 *Group

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 ELB

0.16905 + 002 0.14918 + 002 0.13499 + 002 0.11618+002 0.10000 + 002 0.86071 + 001 0.74082 + 001 0.60653 + 001 0.49659 + 001 0.36788 + 001 0.28650 + 001 0.22313 + 001 0.17377 + 001 0.13535 + 001 0.11080+001 0.82085 + 000 0.63928 + 000 0.49787 + 000 0.38774 + 000 0.30197 + 000 0.18316 + 000 0.11109+000 0.67379 - 001 0.40868 - 001 0.25540 - 001 0.19890 - 001 0.15034-001 53 lower

bound

energy

group

structure

Group upper bound (UB) (MeV)

Group upper bound (UB) (MeV)

where i indexes the measured values belonging to a single data set s, g designates the energy group and a delineates separate spectra that may be simul-

(11)

relates a set of measured reaction rates R, to a single spectrum CJ~by the multigroup cross sections G,~. In this case, FERRET also adjusts the cross sections (Schmittroth and Lippincott, 1983). The lognormal approach automatically accounts for the physical constraint of positive fluxes, even with large assigned uncertainties. Hence reaction rates, reaction rate cross sections and the spectrum are all adjusted within assigned uncertainty limits to obtain adjusted least squares results. For analysis of dosimetry data, the continuous quantities (i.e. fluxes and cross sections) were approximated in 53 groups. The group structure is given in Table 20. The calculated flux-spectra were expanded/contracted into this group structure using the SAND II code. The procedure is carried out by first expanding the spectrum into the SAND II 620-group structure using a SPLINE interpolation procedure for interpolation in regions where group boundaries do not coincide. The high end of the spectrum is extrapolated using a fission spectrum form and the low end by either a l/E + thermal (Maxwellian with temperature T) or an E form. The 620-point spectrum is then easily collapsed to the 53 groups required by FERRET. The cross sections were also collapsed into the 53 energy-group structure using SAND II with calculated spectra (as expanded to 620 groups) as weight-

(LB).

0.91188 - 002 0.55308 - 002 0.33546 - 002 0.28395 - 002 0.24038 - 002 0.20347 - 002 0.12341 - 002 0.74852 - 003 0.45400 - 003 0.27536 - 003 0.16702 - 003 0.10130-003 0.61442 - 004 0.37267 - 004 0.22603 - 004 0.13710-004 0.83183 -005 0.50435 - 005 0.30590 - 005 0.18554 -005 0.11254-005 0.68256 - 006 0.41399 - 006 0.251 IO - 006 0.15230 - 006 0.92370 - 007 0.10000 - 009*

REACTION

RATE

MEASUREMENTS

FOR

ing functions. The cross sections were taken from the ENDF/B-V dosimetry file. Uncertainty estimates and 53 x 53 covariance matrices were constructed for each cross section. Correlations between cross sections were neglected because of data and code limitations, but are expected to be unimportant. For each set of data or a priori values, the inverse of the corresponding relative covariance matrix M is used as a statistical weight. In some cases, as for the cross sections, a multigroup covariance matrix is

NUCLEAR

REACTOR

ANALYSES

403

in the 220 series of experiments, except the moderator used in these earlier experiments was water (Lippincott et al., 1979).

5.2. In-fuel results While Table 17 summarizes the corrected in-fuel reaction rates for Pin 2, additional measurements of the U-235 (n, f), U-238 (n, f), and U-238 (n, y) reaction rates have been conducted in Pins 4 and 6 with nearly the same gap spacing as that used in Pin 2.

Table 21 provides a comparison of the in-fuel results for these three reaction rates. Whereas the U-238 (n, f) results exhibit good agreement, there exists Pin Mlg= R;+R,R;pig (12) 6 results for the U-235 (n, f) and U-238 (n, y) reactions that he outside a 2a statistical uncertainty where R, specifies an overali fractional normalization band from the average. Consequently, these results uncertainty (i.e. complete correlation) for the correhave been ignored in forming the average value of the sponding set of values. The fractional uncertainties reaction rate. R,specify additional random uncertainties for group The uncertainty shown for the average values in g that are correlated with a correlation matrix: Table 21 is merely the statistical standard deviation (13) of the results from the average value. Since this p&=(1 -B)S,+Bexp[ -*I. statistical uncertainty does not account for sources of The first term in equation (13) specifies purely systematic experimental uncertainty, it should be less random uncertainties, while the second term dethan the overall experimental uncertainty. While this scribes short-range correlations over a range y (0 is true for the U-235 (n, f) and U-238 (n, f) reaction, specifies the strength of the latter term) and ait is the it is not true for the U-238 (n, y) reaction. Taking this Kronecker delta. behavior into account together with systematic exFor the a priori calculated fluxes, a short-range perimental uncertainties, total (lo) uncertainties of correlation of y = 3 groups was used. This choice 6.6, 2.9 and 9.0 percent have been assigned to the U-235 (n, f), U-238 (n, f) and U-238 (n, y) in-fuel implies that neighboring groups are strongly correaction rates, respectively, for use in FERRETrelated when 8 is close to 1. For the integral reaction rate covariances, simple normalization and random SAND II analyses. For the Th-232, Np-237 and uncertainties were combined as deduced from Pu-239 in-fuel fission rates, the values and assigned experimental uncertainties. Specific assignments of uncertainties in Table 17 have been used in uncertainty values were made as follows. FERRET-SAND II analyses. On this basis, in-fuel reaction rate experimental results are summarized in Flux normalization uncertainty (RN) 100% Table 22. Flux group uncertainty (R,,R;) 50% Results of the FERRET-SAND II analysis for the Short range correlation fraction (0) 0.8 in-fuel measurements are given in Tables 23-25. Reaction rate uncertainties: RM 9.&16% Table 23 compares the a priori and adjusted neutron SSTR 2.2-7.0% spectra. Table 24 provides integral flux quantities For the a priori spectrum used as input in and associated uncertainties. Comparison of the the FERRET-SAND analysis, a spectrum calculated measured reaction rates (used in this least-squares earlier at Oak Ridge National Laboratory (ORNL) adjustment procedure) with both a priori and adwith the KENO-IV code was employed. This spec- justed calculated reaction rates are given in Table 25. trum was calculated for a lattice identical to that used The adjusted meas/calc. reaction rate ratio given in used. used:

More

often,

a simple

parameterized

form

Table 21. Comparison U-235 (n, f)

Average

is

of corrected in-fuel reaction rates*t U-238 (n. f)

U-238 (n, y)

Pin 2, g = 10.7 8.633E - 16 (6.9)

Pin 2, g = 8.0 1.217E - 17 (3.2)

Pin 2, g = 8.0 1.031E - 16 (4.0)

Pin 6, g = 11.3 7.154E- 16(5.5)$

Pin 4, g = 8.5 1.20lE- 17(3.4)

Pin 4, g = 16.1 0.9064E - 16 (6.3)

Pin 6, g = 10.5 8.46lE- 16(7.5) 8.547E- 16(1.4)

Pin 4, g = 8.6 l.l97E17(3.4) 1.205E - 17 (0.9)

Pin 6, g = 14.1 0.4743E - 16 (5.9)$ 0.9687E - 16 (8.8)

*Units of reactions (fissions or capture)/(atom.s). tValue in parentheses is the experimental uncertainty $Not used in forming the average value.

in percent

at the lu level.

RAYMOND

404 Table

22. CFRP/PNC

Reaction U-235 U-238 U-238 Np-237 Th-232 I+239

TASK

220 in-fuel

*Not corrected

8.547E 1.205E 9.687E 6.236E 3.010E 1.043E for neutron

-

16 17 17 17 18 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

6.6 2.9 9.0 3.6 3.5 4.2

self-shielding.

Table 23. In-fuel Group

et al.

the last column of Table 25 shows an improvement over the a priori values for all reaction rates. The U-235 reaction rate ratio possesses the largest deviation from unity and this is the only in-fuel reaction rate that deviates from unity by more than experimental uncertainty. This result is not surprising, however, since the effects of the larger mass uncertainty associated with the U-235 SSTR deposits have already been stressed.

rates

% experimental uncertainty

Reactions/atom/s (n, f) (n. f) (n, y)* (n, f) (n, f) (n, f)

reaction

GOLD

FERRET-SAND

Energy (MeV 1.492 + 001 1.350 + 001 1.162+001 1.000+001 8.607+000 7.408 +oOQ 6.065+000 4.966+000 3.679 + 000 2.865 + 000 2.231 + 000 1.738 + 000 1.353 +OOO 1.108+000 8.208 - 001 6.393 - 001 4.979 - 001 3.877 - 001 3.020 - 001 1.832 - 001 1.111 -001 6.738 - 002 4.087 - 002 2.554 - 002 1.989 - 002 1.503 - 002 9.119-003 5.531 - 003 3.355 - 003 2.839 - 003 2.404 - 003 2.035 - 003 1.234 - 003 7.485 - 004 4.540-004 2.754-004 1.670 - 004 1.013 - 004 6.144 - 005 3.727 - 005 2.260 - 005 1.371 - 005 8.315 - 006 5.043 - 006 3.059 - 006 1.855 - 006 1.125 -006 6.826 - 007 4.140 - 007 2.511 - 007 1.523 - 007 9.237 - 008 1.000-010

II spectral

A priori flux* W/cm2/s) 2.182 + 003 4.536 + 003 2.103 + 004 6.382 + 004 1.615 + 005 3.484 + 005 9.293 + 005 1.248 + 006 2.716 + 006 3.545 + 006 4.325 + 006 4.439 + 006 4.471 + 006 3.386 + 006 4.731 + 006 3.645 + 006 3.322 + 006 2.940 + 006 2.532 + 006 4.030 + 006 3.048 + 006 2.508 + 006 2.205 + 006 1.919 + 006 9.789 + 005 1.056 + 006 1.784 + 006 1.684 + 006 1.622 + 006 5.302 + 005 5.245 + 005 5.200 + 005 1.537 + 006 1.515 + 006 1.506+006 1.500+006 1.478 + 006 1.418 + 006 1.325 + 006 1.237 + 006 1.166+006 1.113+006 1.073 + 006 1.048 + 006 1.099 + 006 1.174+006 9.727 + 005 5.135+005 6.596 + 005 1.439 + 005 1.928 + 005 3.418 + 005 8.822 + 005

results

for the 220 experiment

Adjusted flux V/cm?+ 1.153+003 2.438 + 003 1.161 f004 3.672 + 004 9.852 + 004 2.300 + 005 6.777 + 005 1.011 +006 2.486 + 006 3.632 + 006 4.828 + 006 5.184+006 5.263 + 006 3.794 + 006 4.931 + 006 3.372 + 006 2.720 + 006 2.145 + 006 1.678 + 006 2.481 + 006 1.779 •t- 006 1.413 + 006 1.215+006 1.045+006 5.298 + 005 5.705 + 005 9.648 + 005 9.124 + 005 8.796 + 005 2.860 + 005 2.808 + 005 2.738 + 005 7.862 + 005 7.318 + 005 6.708 + 005 5.910 + 005 4.866 + 005 3.780 + 005 2.794 + 005 2.185 + 005 1.571 + 005 1.294 + 005 1.458 -t 005 1.332 -t 005 1.927 + 005 2.444 + 005 2.383 + 005 1.469 + 005 2.145 + 005 5.281 + 004 9.316+004 2.237 f 005 9.635 + 005

% uncertain (1 c) 54.0 54.0 53.0 52.0 50.0 47.0 42.0 37.0 30.0 24.0 22.0 24.0 28.0 30.0 31.0 36.0 41.0 46.0 49.0 52.0 53.0 53.0 54.0 54.0 54.0 54.0 54.0 54.0 53.0 53.0 53.0 53.0 52.0 51.0 50.0 49.0 46.0 44.0 40.0 36.0 29.0 26.0 32.0 33.0 41.0 45.0 46.0 45.0 41.0 35.0 30.0 26.0 12.0

REACTION

RATE MEASUREMENTS

FOR NUCLEAR

REACTOR

ANALYSES

405

Table 24. In-fuel integral flux values for the 220 experiment Adjusted value

8.714 + 007

6.181 + 007

13.0%

2.220 + 006 5.044 + 007 2.728 + 007

1.548 + 006 4.666 + 007 2.894 + 007

6.0% 13.0% 6.0%

Flux, E > 0.0 MeV Flux, E < 0.414 eV Flux, E > 0.1 MeV Flux, E > 1.0 MeV Table 25. Comparison

U-238 U-238 Np-237 Th-232 U-235 Pu-239

5.3. In-moderator

of in-fuel measured and calculated reaction rates for the 220 experiment Meas.

Reaction (N, y) (N, F) (N, F) (N, F) (N, F) (T’J,F)

Reaction rate (DPS/nucleus) A priori talc. Adj talc.

9.69 - 017 1.20-017 6.24 - 017 3.01 - 018 8.55 - 016 1.04 -015

6.94 - 016 1.18 -017 5.78 - 017 2.95 - 018 1.21 - 015 1.89-015

results

In-moderator reaction rate experimental results are summarized in Table 26. Results of the FERRETSAND II analysis for the in-moderator (bare and cadmium-covered) measurements are given in Tables 27-29. Table 27 compares the a priori and adjusted neutron spectra. Table 28 provides integral flux quantities and associated uncertainties. Comparison of the measured reaction rates (used in this least-squares adjustment procedure) with both a priori and adjusted calculated reaction rates are given in Table 29. The adjusted reaction rate ratio given in the last column of Table 29 lies within experimental uncertainty of unity for all reaction rates except Np-237. Examination of Tables 18 and 29 reveals that the in-moderator Np-237 SSTR possessed very low track density. In fact, to maximize available track counting statistics for these in-moderator Np-237 measurements, it was necessary to scan the entire SSTR surface. In contrast, SSTR measurements normally provide adequate statistics by sampling only a small fraction of the SSTR surface, so that results can be taken from different regions of the SSTR surface and suitably averaged. The absence of this capability together with the poorer track counting statistics of

Table 26. CFRP/PNC Reaction U-235 (n, f) U-238 (n, f) U-238 (n. y)* Np-237 (n, f) Th-232 (n. f) U-238 (n, f) U-238 (n, y)* Ng237 (n. f) Th-232 (n. f) Pu-239 (n, f)

% Uncertain (1 o)

A priori value

1.07-016 1.21 -017 6.19-017 3.00 - 018 7.23 - 016 1.11 -015

Bare Bare Bare Bare Bare Cadmium Cadmium Cadmium Cadmium Cadmium

0.14

1.02 1.08 1.02 0.70 0.55

0.90 1.00 1.01 1.00 1.18 0.94

these in-moderator Np-237 SSTR is, in all likelihood, the reason that the Np-237 reaction rate ratio shows the largest deviation from unity for the in-moderator FERRET-SAND II analysis.

6. CONCLUSIONS Least-squares spectral adjustment with the FERRET-SAND II code produces a distinct improvement in the ratio of measured-to-calculated reaction rates. For the in-fuel reaction rates, which are shown in Table 25, all adjusted reaction rate ratios are distinctly better (i.e. closer to unity) than the a priori ratios. For the in-moderator reaction rates, which are shown in Table 29, all adjusted reaction rate ratios are again better than the corresponding a priori ratios, except for the cadmiumcovered fission rate in Np-237. This particular result is not surprising and in fact has already been attributed to the lack of quality in the SSTR electrodeposit that was employed. There is another possible explanation for this anomalous Np-237 result. From the measured values in Table 29, one can calculate the cadmium coveredto-bare fission rate ratios for the threshold monitors.

TASK 220 in-moderator

Cover

Ratio meas./calc. A priori Adj. talc.

Reactions/atom/s 1.36E 1.29E 5.13E 7.20E 3.31E 1.24E 4.98E 5.28E 3.02E 7.67E -

*Corrected for neutron self-shielding.

15 17 16 17 18 17 16 17 18 16

reaction rates % experiment uncertainty 4.1 2.3 16.0 4.7 2.8 2.2 15.0 7.0 3.5 5.2

RAYMOND

406 Table

27. In-moderator

Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

FERRET-SAND experiment

the 220

% uncertain (1 0)

1.492 + 001 1.350+001 1.162+001

2.261 + 003 4.700 + 003 2.179+004 6.613 + 004 1.673 + 005 3.610 + 005 9.617 + 005 1.267 + 006 2.129 + 006 3.594 + 006 4.379 + 006 4.481 + 006 4.510+006 3.430 + 006 4.809 + 006 3.710+006 3.391 + 006 3.016 + 006 2.619 + 006 4.224 + 006 3.253 + 006 2.704 + 006 2.389 + 006 2.087 + 006 1.069 + 006 1.157+006 1.966 + 006 1.860 + 006 1.782 + 006 5.793 + 005 5.719 + 005 5.673 + 005 I.692 + 006 I.689 + 006 1.685 + 006 1.681 + 006 1.678 + 006 1.653 + 006 1.553 + 006 1.460 + 006 1.401 + 006 1.349 + 006 1.285 + 006 1.241 + 006 1.266 + 006 1.324 + 006 1.217+006 9.627 + 005 9.731 + 005 7.242 + 005 6.823 + 005 7.326 + 005 2.210 + 006

1.939 + 003 4.058 + 003 1.899 + 004 5.842 + 004 1.504 + 005 3.320 + 005 9.095 + 005 I.231 + 006 2.755 + 006 3.786 + 006 4.800 + 006 5.099 + 006 5.321 + 006 4.097 + 006 5.743 + 006 4.307 + 006 3.784 + 006 3.216 + 006 2.672 + 006 4.150+006 3.090 + 006 2.502 + 006 2.167 + 006 1.865 + 006 9.445 + 005 1.016+006 1.717 fOO6 1.622 + 006 1.554 + 006 5.072 + 005 5.049 + 005 5.075 + 005 1.544+006 1.571+ 006 1.607 + 006 1.616+006 1.588 + 006 1.493 + 006 1.350 + 006 1.146+006 9.255 + 005 8.564 + 005 9.110 + 005 8.112+005 9.710 + 005 1.115+006 1.087 + 006 8.519 + 005 8.183 +005 5.039 + 005 3.904 + 005 3.634 + 005 9.136+005

54.0 53.0 52.0 51.0 48.0 45.0 40.0 35.0 28.0 24.0 22.0 25.0 28.0 30.0 30.0 34.0 39.0 44.0 48.0 50.0 52.0 52.0 53.0 53.0 53.0 53.0 53.0 53.0 53.0 53.0 53.0 52.0 51.0 50.0 48.0 47.0 45.0 42.0 39.0 36.0 30.0 24.0 30.0 31.0 39.0 41.0 41.0 39.0 36.0 34.0 31.0 27.0 16.0

28. In-moderator

z < z >

for

Adjusted flux (N/cm’/s)

1.000+ 001

E E E E

results

A priori flux Wicm’is)

integral

A priori value Flux, Flux, Flux, Flux,

11 spectral

Energy WeV)

8.607 + 000 7.408 + 000 6.065 + 000 4.966 + 000 3.679 + 000 2.865 + 000 2.231 + 000 1.738 + 000 1.353 + 000 l.lOS+OOO 8.208 - 001 6.393 - 001 4.979 - 001 3.877 - 001 3.020 - 001 1.832 - 001 1.111-001 6.738 - 002 4.087 - 002 2.554 - 002 1.989 - 002 1.503 - 002 9.119-003 5.531 - 003 3.355 - 003 2.839 - 003 2.404 - 003 2.035 - 003 1.234 - 003 7.485 - 004 4.540 - 004 2.754 - 004 1.670 - 004 1.013 - 004 6.144 - 005 3.727 - 005 2.260 - 005 1.371 - 005 8.315-006 5.043 - 006 3.059 - 006 1.855 - 006 1.125 - 006 6.826 - 007 4.140 - 007 2.511 -007 1.523 - 007 9.237 - 008 1.000 - 010

Table

GOLD et al.

0.0 MeV 0.414 eV 0.1 MeV 1.0 MeV

9.619 5.322 5.157 2.762

+ + + -t

007 006 007 007

flux values

for the 220 experiment

Adjusted 9.287 2.990 5.605 3.053

value + + + +

007 006 007 007

% uncertain (1 0) 13.0% 16.0% 14.0% 6.0%

REACTION

RATE

MEASUREMENTS

FOR

NUCLEAR

REACTOR

ANALYSES

407

Table 29. Comparison of in-moderator measured and calculated reaction rates for the 220 experiment Reaction rate (DPS/nucleus) Meas. A priori talc. Adj. talc.

Reaction U-238 U-238 Np-237 Th-232 U-235 U-238 Np-237 Th-232 Pu-239 U-238

(N, (N, (N, (N, (N, (N, (N, (N, (N, (N.

y) F) F) F) F) F)* F)* F)* Fj* Y)*

*Cadmium-covered

5.13 -016 1.29-017 7.20 - 017 3.31 - 018 1.36-015 1.24-017 5.28 - 017 3.02 - 018 7.67 - 016 4.98 - 016

8.29 - 016 1.20-017 5.88 - 017 3.00-018 2.35 - 015 1.17-017 5.72 - 017 2.93 - 018 9.00 - 016 8.02 - 016

5.58 - 016 1.28 - 017 6.63 - 017 3.22 - 018 1.38-015 1.25 -017 6.45 - 017 3.15 -018 7.40-016 5.40-016

Ratio meas./calc. Adj. talc.

A priori

0.62 1.07 1.22 1.10 0.58 1.06 0.92 1.03 0.85 0.62

0.92 1.01 1.09 1.03 0.99 0.99 0.82 0.96 1.04 0.92

reaction rates.

and 0.912 for Np-237; U-238 and Th-232, respectively. All of these ratios are below unity and this consistency implies the existence of a systematic effect between the bare and cadmium-covered in-moderator capsules. Perhaps the most apparent systematic effect could be a thermal neutron flux depression created by the presence of the cadmium capsule. The existence of such a depression would reduce the local fission rate in the fuel in the vicinity of the cadmium capsule. This localized reduction in fuel fission rate would, in turn, lower the fast neutron flux and thereby explain the systematic behavior in the cadmium covered-to-bare fission rate ratios observed for the three threshold monitors. Group flux uncertainties given in Tables 23 and 27 appear to be reasonable, with the possible exception of the in-fuel thermal flux component that is assigned a 6 percent uncertainty. This low uncertainty should be contrasted with the in-fuel adjusted reaction rate ratio for U-235, which at 1.18 is rather high. It is possible that the uncertainties estimated for the infuel broad-based U-235 (n, f) and U-238 (n, y) were overly optimistic, since one out of three in-fuel measurements was found statistically deficient and was therefore rejected for each of these two reaction rates (see Table 21). On the other hand, this in-fuel thermal flux result could reflect the limitation of the least-squares analysis with a group structure of only 53. In this event, the accuracy of the in-fuel thermal flux may be realistic and difficulties could be entailed through resonance region adjustments of the U-235 (n, f) and U-238 (n, y) reaction rates because of the lack of suitable group structure. One finds ratios of 0.733,0.961

dedication to track scanning of P. D. Bright, M. D. Gold and R. C. McElroy is sincerely acknowledged. We are indebted to F. C. Brectd, M. J. Perry and L. H. Roberts of Test Pin Fabrication for loadina and retrieval of the in-fuel SSTR. Acknowledgements-The

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(SSTR) monitors

for reactor surveillance. In 1982 Standards, Part 45. ASTM,

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Philadelphia, PA. ASTM E181-82 (1982b) ASTM standard for general methods for detector calibration and analysis ofradionuclides. In I982 Annual Book of ASTM Standards. Part 45, Section 12, Vol. 12.02. ASTM Philadelphia; PA. Fleischer R. L., Price P. B. and Walker R. M. (1975) Nuclear Tracks in Soliris. University of California Press, Berkley, CA. Gold R. and Lloret R. (1985) Workshop: gamma dosimetry and calorimetry. In Proc. 5th ASTM-EVRATOM Symp. Reactor Dosirnerry, GKSS Research Centre, Geesthacht, FRG, 24-28 September 1984, Vol. 2, p. 1017, D. Reidel Publishing, Dordrecht. Gold R. and Najzer M. (1987) Workshop on gamma-ray dosimetry. In Proc. 6th ASTM-EcRAT&M Symi. Reactor Dosimerrv. Jackson Hole. WY. 31 Mav-5 June 1987. _’ Gold R. (1977a) Critical requirements of the solid-state track recorder (SSTR) method. In Proc. lsf Int. ASTM-EVRATbM

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and Kramer D.), pp. 402-423. ASTM STP 683, American Society for Testing and Materials, Philadelphia, PA. Gold R., Ruddy F. H. and Roberts J. H. (1980a) Applications of solid state track recorders in U.S. nuclear reactor energy programs. In Proc. 10th Int. Conf: Solid-State Nuclear Track Detectors, Lyons, France, 2-7 July 1979, pp. 533-547. Pergamon Press, Oxford. Gold R., Ruddy F. H. and Roberts J. H. (1980b) Solid-state track recorder applications in U.S. nuclear reactor energy programs. Trans. Am. Nucl. Sot. 34, 146. Gold R., Roberts J. H. and Ruddy F. H. (198Oc) Advances in SSTR techniques for dosimetry and radiation damage measurements. In Proc. 3rd Inf. ASTMEVRATOM Symp. Reacror Dosimetry, Ispra, Italy,

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Gold

Gold

Gold

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Lippincott E. P., Gold R., Ruddy F. H., Long C. L. and Roberts J. H. (1979) SSTR Dosimetry in critical mass measurements. Trans. Am. nucl. Sot. 32, 325. McElroy W. N., Berg S. and Crocket T. (1967) A CompuferAutomated Interactive Method of Neutron Flux Spectra Determined by Foil Activation, AFWL-TR-67-4 1, Vols I-IV. Air Force Weapons Laboratory, Kirkland AFB, NM. McElroy W. N. (Ed.) (1985) L WR-PV-SDIP: L WR Power Reactor Surveillance Physics-Dosimetry Data Base Compendium, NUREG/CR-3319, HEDL-TME 85-3. Hanford Engineering Development Laboratory, Richland, WA.

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