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This guide was issued after consideration of comments received from the public. Comments and suggestions for improvements in these guides are encouraged

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to the Rules and Directives Branch, ADM, U.S. Nuclear Regulatory Commission, Washington, DC 20555-0001. 

Regulatory guides are issued in ten broad divisions: 1, Power Reactors; 2, Research and Test Reactors; 3, Fuels and Materials Facilities; 4, Environmental and Siting;

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Single copies of regulatory guides (which may be reproduced) may be obtained free of charge by writing the Distribution Services Section, U.S. Nuclear Regulatory

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at NRCís home page, along with other recently issued guides, Accession Number ML010890301. 

U.S. NUCLEAR REGULATORY COMMISSION March 2001 

REGULATORY

GUIDE

 OFFICE OF NUCLEAR REGULATORY RESEARCH

REGULATORY GUIDE 1.190

(Previous drafts were DG-1053 and DG-1025)

CALCULATIONAL AND DOSIMETRY METHODS

FOR DETERMINING

PRESSURE VESSEL NEUTRON FLUENCE
iii

TABLE OF CONTENTS

Page

A. INTRODUCTION ............................................................. 1

B. DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

C. REGULATORY POSITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1. NEUTRON FLUENCE CALCULATIONAL METHODS ............................. 3

1.1 Input Data .............................................................. 4

1.2 Core Neutron Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Fluence Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Methodology Qualification and Uncertainty Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2. NEUTRON FLUENCE MEASUREMENT METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1 Measurement Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Validation in Standard and Reference Neutron Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3 Fluence Determination from Detector Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Ex-vessel Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3. REPORTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1 Fluence Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Multigroup Fluences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Integral Fluences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Comparisons of Calculation and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 Specific Activities and Average Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

D. IMPLEMENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

LIST OF TABLES

1. Summary of Regulatory Positions on Calculation and Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . 30

2. Threshold Detectors Recommended for Pressure Vessel Dosimetry . . . . . . . . . . . . . . . . . . . . . . 34

LIST OF FIGURES

1. Discrete Ordinates Calculation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2. Monte Carlo Calculation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3. Calculation Methodology Qualification Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4. Fluence Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Measurement Qualification Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1

A. INTRODUCTION

This regulatory guide has been developed to provide state-of-the-art calculations and

measurement procedures that are acceptable to the NRC staff for determining pressure vessel

fluence.

The U.S. Nuclear Regulatory Commission (NRC) has promulgated regulations that ensure

the structural integrity of the reactor pressure vessel for light-water-cooled power reactors. 

Chapter 15, ìAccident Analysis,î of the Standard Review Plan (NUREG-0800, ìStandard Review

Plan for the Review of Safety Analysis Reports for Nuclear Power Plantsî) assumes the pressure

vessel does not fail. Specific fracture toughness requirements for normal operation and for

anticipated operational occurrences for power reactors are set forth in Appendix G, "Fracture

Toughness Requirements," of 10 CFR Part 50, "Domestic Licensing of Production and Utilization

Facilities." The requirements of Appendix G are imposed by 10 CFR 50.60. Additionally, in

response to concerns over potential pressurized thermal shock (PTS) events in pressurized water

reactors (PWRs), the NRC issued 10 CFR 50.61, "Fracture Toughness Requirements for

Protection Against Pressurized Thermal Shock Events."

To satisfy the requirements of both Appendix G and 10 CFR 50.61, methods for

determining the fast neutron fluence (E > 1 MeV) are necessary to estimate the fracture toughness

of the pressure vessel materials. Appendix H, "Reactor Vessel Material Surveillance Program

Requirements," to 10 CFR Part 50 requires the installation of surveillance capsules, including

material test specimens and flux dosimeters, to provide data for material damage correlations as a

function of fluence.

The fracture toughness of pressure vessel materials is related to a parameter called the

material's "reference temperature for nil-ductility transition," or simply reference temperature, and

is denoted as RTNDT. The RTNDT is defined in Revision 2 of Regulatory Guide 1.99, "Radiation

Embrittlement of Reactor Vessel Materials," by a correlation of the fluence (E > 1 MeV), material

chemistry (concentrations of Cu and Ni), initial reference temperature, and margin to account for

uncertainties in the correlation and input values. In 10 CFR 50.61, evaluation of the reference

temperature based on the best estimate of the fast neutron fluence at the end of the license period

is required, and the corresponding reference temperature is termed RTPTS.

This guide is intended to ensure the accuracy and reliability of the fluence determination

required by General Design Criteria (GDC) 14, 30, and 31 of Appendix A, ìGeneral Design

Criteria for Nuclear Power Plants,î to 10 CFR Part 50. The guide describes methods and

assumptions acceptable to the NRC staff for determining the pressure vessel neutron fluence. 

These methods are directly applicable to the determination of RTNDT and RTPTS. The licensee

may propose alternative methods. Alternative methods will be considered on a plant-specific

basis, especially in cases involving unusual plant characteristics or factors that require different

methods and assumptions. It is recognized that, when the embrittlement of a reactor vessel

material is not significant and there is a large margin to the RTNDT limits, more approximate

methods for determining the fluence may be appropriate (Reference 1).
1

 For a discussion of the terms bias and uncertainty as used in this guide, see Sections 3.2 and 3.3 of Reference 3.

2

Compliance with this guide is not a regulatory requirement of the USNRC. However, if a

licensee elects to use this guide to determine pressure vessel neutron fluence, implementation of

the guide would not be satisfied unless the licensee complies with certain specific provisions

identified in the Regulatory Position of the guide. The use of the following terms is explained to

clarify compliance with these regulatory positions.

Must - Necessary provisions if implementation is to be satisfied.

Should - Provisions that are expected to be complied with unless it is not possible

because of specific circumstances (for example, data needed to meet the

position are not available).

May - Provisions that are acceptable and recommended, but are to be applied at the

option of the licensee.

The information collections contained in this regulatory guide are covered by the

requirements of 10 CFR Part 50, which were approved by the Office of Management and Budget,

approval number 3150-0011. If a means used to impose an information collection does not

display a currently valid OMB control number, the NRC may not conduct or sponsor, and a person

is not required to respond to, the information collection. 

B. DISCUSSION

The methods and assumptions described in this guide are for the calculation and

measurement of vessel fluence for core and vessel geometrical and material configurations that are

typical of current PWR and boiling water reactor (BWR) designs. This guide does not address the

determination of surveillance specimen material properties or the correlation between material

properties and neutron fluence. The methodology presented is intended as a best estimate, rather

than a bounding or conservative fluence determination. For example, in the RTPTS correlation

called for in 10 CFR 50.61, the best-estimate fluence is used to calculate the shift in RTPTS. 

Uncertainty in the shift prediction (e.g., from uncertainty in the fluence, chemistry factor, or shift

correlation) has been included separately in an explicit margin term. While the E > 1 MeV

fluence has been selected as the exposure parameter for the RTNDT and RTPTS correlations, the

procedures described in this guide determine the damage fluence spectrum (from 0.1 to 15 MeV)

and are applicable to other exposure units, such as iron displacements per atom - dpa (Ref. 2).

The determination of the pressure vessel fluence is based on both calculations and

measurements; the fluence prediction is made with a calculation, and the measurements are used

to qualify the calculational methodology. Because of the importance and the difficulty of these

calculations, the methods must be qualified by comparison to measurements to ensure a reliable

and accurate vessel fluence determination. In this qualification, measurement-to-calculation

comparisons are used to identify biases (i.e., systematic errors) in the calculations and to provide

reliable estimates of the fluence uncertainties.1

 When the measurement data are of sufficient

quality and quantity that they allow a reliable estimate of the calculational bias (i.e., they represent

a statistically significant measurement data base), the comparisons to measurement may be used to
3

(1) determine the effect of the various modeling approximations and any calculational bias and, if

appropriate, (2) modify the calculations by applying a correction to account for bias or by model

adjustment or both. Typically, plant-specific data alone are not sufficient to determine a

calculational bias for an individual plant. As an additional qualification, the sensitivity of the

calculation to the important input and modeling parameters must be determined and combined

with the uncertainties of the input and modeling parameters to provide an independent estimate of

the overall calculational uncertainty. 

The prediction of the vessel fluence must be made by an "absolute" fluence calculation in

which the transport of the neutron flux is calculated from the core out to the vessel and cavity,

rather than a simple spatial extrapolation of the fluence measurements.

The calculations of the pressure vessel fluence consist of the following steps: (1)

determination of the geometrical and material input data, (2) determination of the core neutron

source, (3) propagation of the neutron fluence from the core to the vessel and into the cavity, and

(4) qualification of the calculational procedure. These steps are discussed in detail in Regulatory

Positions 1.1 through 1.4. In Regulatory Position 2, the use of surveillance dosimetry as an in situ

verification for the calculations is described. Reporting is discussed in Regulatory Position 3. 

The major regulatory positions are summarized in Table 1, ìSummary of Regulatory Positions on

Calculation and Dosimetry.î

As an indication of current practice, selected codes and cross-section libraries are listed in

the references; however, it is the responsibility of the licensee to demonstrate their acceptability in

a specific application.

C. REGULATORY POSITION

1. NEUTRON FLUENCE CALCULATIONAL METHODS

This guide describes the application and qualification of a methodology acceptable to the

NRC staff for determining the best-estimate neutron fluence experienced by materials in the

beltline region of light water reactor (LWR) pressure vessels, as well as for determining the

overall uncertainty associated with those best-estimate values. Both the deterministic discrete

ordinates method and the statistical Monte Carlo transport method are considered acceptable for

vessel fluence determination and are described in Regulatory Position 1.3.

Appendix B, "Quality Assurance Criteria for Nuclear Power Plants and Fuel Reprocessing

Plants," to 10 CFR Part 50 requires that this methodology be properly qualified. Qualification

includes determination of the uncertainty in the reactor vessel fluence as described in Regulatory

Position 1.4. The uncertainty of the fluence must be 20% (1 σ) or less when the fluence is used to

determine RTPTS and RTNDT for complying with 10 CFR 50.61 and Revision 2 of Regulatory

Guide 1.99, "Radiation Embrittlement of Reactor Vessel Materials," respectively. It should be

recognized that this 20% uncertainty value has been included in the margin term for the RTPTS. 

Uncertainty of fluence for other applications should be determined using Regulatory Position 1.4

and included as an uncertainty allowance in the fluence estimate, as appropriate for the specific
 2

It should be noted that in many applications the ENDF/B-IV and the first three MODs of the ENDF/B-V iron cross-sections

result in as much as ~20% underprediction of the vessel inner-wall fluence and ~35% underprediction of the cavity fluence (Refs.

5-7). Updated ENDF/B-VI iron cross-section data (Ref. 8) have been demonstrated to provide a more accurate determination of

the flux attenuation through iron (Refs. 5, 6) and are strongly recommended. These new iron data are included in ENDF/B-VI.

4

application. For example, when performing probabilistic risk assessment (PRA) evaluations such

as those described in Regulatory Guide 1.154, "Format and Content of Plant-Specific Pressurized

Thermal Shock Safety Analysis Reports for Pressurized Water Reactors," an explicit uncertainty

term is required in addition to the best-estimate fluence values. In this case, it is acceptable to use

the fluence uncertainty determined per the Regulatory Position 1.4 of this guide.

An overview of the calculational methods described in Regulatory Positions 1.1 through

1.3 is provided in Figures 1 and 2. The procedures for qualifying these methods and determining

the pressure vessel fluence are summarized in Figures 3 and 4.

1.1 Input Data

1.1.1 Materials and Geometry

Detailed material and geometrical input data should be used to define the physical

characteristics that determine the attenuation of the neutron flux from the core to the locations of

interest on the pressure vessel. These data include material compositions, regional temperatures,

and geometry of the pressure vessel, core, and internals. The geometrical input data include the

dimensions and locations of the fuel assemblies, reactor internals (baffle, shroud, former plates,

core support barrel, thermal shield, and neutron pads), the pressure vessel (including identification

and location of all welds and plates) and cladding, and surveillance capsules. For cavity

dosimetry, input data should also include the width of the reactor cavity and the material

compositions of the support structure and concrete (biological) shielding, including water content,

rebar, and steel. The data should, to the extent possible, be based on documented and verified asbuilt dimensions and plant-specific materials. The isotopic compositions of important constituent

nuclides within each region should be based on as-built materials data. In the absence of plantspecific information, nominal compositions and design dimensions may be used; however, in this

case conservative estimates of the variations in the compositions and dimensions should be made

and accounted for in the determination of the fluence uncertainty (Regulatory Position 1.4.1). The

determination of the concentrations of the major isotopes responsible for the fluence attenuation

(e.g., iron and water) should be emphasized. The water number densities should be based on plant

full-power operating temperatures and pressures, as well as standard steam tables. The data

should account for axial and radial variations in water density caused by temperature differences

in the core and inside the core barrel, as well as the presence of in-channel and downcomer voids

in the case of BWRs. The in-channel and bypass water and fuel channel may be combined to

determine a homogenized material region. This approximation has been evaluated in Reference 4

and results in less than a ~3% additional uncertainty in the vessel fluence. 

1.1.2 Cross-Sections

The calculational method to estimate vessel fluence should use the neutron cross-sections

over the energy range from ~0.1 MeV to ~15 MeV and should apply the latest version of the

Evaluated Nuclear Data File (currently ENDF/B-VI). These data have been thoroughly reviewed

and tested relative to experimental benchmarks.2

 Cross-section sets based on earlier or equivalent
3

 The ASTM E1018 standard (Ref. 9) provides additional guidance on the selection of dosimeter reaction rate cross-sections.

5

nuclear-data sets that have been thoroughly benchmarked for a specific application may be used

for that specific application.3 However, when the evaluated cross-section data change, the effect

of these changes on the licensee-specific methodology must be evaluated and the fluence

estimates updated when the effects are significant (see reporting requirements in Regulatory

Position 3).

1.1.2.1 Multigroup Libraries. Transport theory codes that are used to determine the

neutron fluence, which employ a multigroup approximation, require cross-section libraries in

which the basic data contained within the ENDF files has been preprocessed into a multigroup

structure. The development of a multigroup library should consider the adequacy of the group

structure, the energy dependence of the flux used to average the cross-sections over the individual

groups, and the order of the Legendre expansion of the scattering cross-section. Sufficient details

of the energy and angular dependence of the differential cross-sections (e.g., the minima in the

iron total cross-section) should be included to preserve the accuracy in attenuation characteristics.

1.1.2.2 Constructing a Multigroup Library. The construction of the multigroup library

involves the selection of a problem-independent, fine-multigroup, master library containing data

for all required isotopes. This master library should include a sufficiently large number of groups

(100) that differences between the shape of the assumed flux spectrum and the true flux have a

negligible effect on the multigroup data. This library typically includes ~50-100 energy groups

above ~0.1 MeV. In addition, a minimum of a P-3 Legendre expansion of the scattering crosssection must be used for typical LWR configurations (Ref. 10). Several libraries satisfying these

provisions are available from RSICC, the Oak Ridge National Laboratory Radiation Safety

Information Computational Center (Refs. 11-13).

The number of groups may be reduced, with little loss in accuracy, by collapsing the data

in the master library over spectra that more closely approximate the true spectra. The vessel

fluence calculations should be performed with a job library that has been determined by collapsing

the master library. This reduction may be accomplished with a one-dimensional calculation that

includes the discrete regions of the core, vessel internals, by-pass and downcomer water, pressure

vessel, reactor cavity, shield, and support structures. The resulting job library should consist of

multigroup cross-sections based on the region-specific isotopic compositions. This job library

should include ~20 energy groups above ~0.1 MeV. The adequacy of the job library must be

demonstrated by comparing calculations for a representative configuration performed with both

the master and job libraries. In these comparisons, the threshold-detector cross-sections and

reaction rates obtained with the fine-group structure should be preserved in the multigroup

calculations. In addition to the validation of the collapsing of the master library, additional

qualification of the job library is provided by the benchmarking comparisons of Regulatory

Position 1.4.2.

There are several ~50-group libraries available from RSICC that were generated using

light-water reactor (LWR) spectra for the group collapsing from master libraries (Refs. 14-16) and

may be used for LWR application. These libraries contain microscopic cross-sections as well as

some premixed macroscopic cross-sections for relevant mixtures. Because these prepackaged
6

libraries were designed specifically for LWR pressure vessel fluence calculations, their

applicability in any atypical application (for example, when an accurate thermal flux is required)

should be verified prior to use.

1.2 Core Neutron Source

The determination of the neutron source for the pressure vessel fluence calculations should

include the temporal, spatial, and energy dependence together with the absolute source

normalization.

The spatial dependence of the source should be based on depletion calculations that

simulate core operation or measured data. The depletion calculations can be performed in either

two or three dimensions. Three-dimensional calculations will provide the source in both the radial

and axial directions. If two-dimensional calculations are used, the axial effects should be based

on measured data.

The core neutron source should be determined by the power distribution (which varies

significantly with fuel burnup), the power level, and the fuel management scheme. The detailed

state-point dependence should be accounted for (Refs. 17, 18); however, if this is not feasible,

averaging over the operating power distribution is acceptable and may be obtained by either (1)

averaging representative power distributions within the cycle or (2) assuming the cycle-average

assembly power distribution is well approximated by the accumulated-exposure distribution at the

end of the cycle.

A best-estimate power distribution may be used for reactor vessel neutron fluence

calculations. However, this best-estimate power distribution must be updated if changes in core

loadings, surveillance measurements, or other information indicate a significant change in

projected fluence values. This updating may be avoided by using a conservative generic average

power distribution, provided no measured distribution yields higher power levels for the important

peripheral assemblies.

The peripheral assemblies, which contribute the most to the vessel fluence, have strong

radial power gradients, and these gradients should not be neglected (Ref. 19). In the case of

PWRs, the fuel pins closest to the core periphery tend to have reduced relative power while for

BWRs the peripheral fuel pins may have increased relative power. The pin-wise source

distribution should be used for best-estimate calculations and the peripheral-assembly pin-wise

source data should be obtained from core depletion calculations. The pin-wise source distribution

should represent the absolute source distribution in the assembly.

The local source should be determined as the product of the fission rate and the neutron

yield. The energy dependence of the source (i.e., the spectrum) and the normalization of the

source to the number of neutrons per megawatt must account for the fact that changes in the

isotopic fission fractions with fuel exposure (caused by Pu build-up) result in variations in the

fission spectra, the number of neutrons produced per fission, and the energy released per fission. 

These effects tend to increase the fast neutron source per megawatt of power for high-burnup

assemblies. The variations in these physics parameters with fuel exposure may be obtained from
4

 Additional information concerning the application of transport methods to reactor vessel surveillance is provided in ASTM

Standard E 482-89 (Ref. 31)

5

 If DOT (Ref. 29) is used, the "θ-weighted" option (MODE-5 in DOT 4.3) is considered to be more accurate than the "weighted"

option (MODE-3 in DOT 3.5 or 4.3) for flux extrapolation and is recommended. Also, a value of θ = 0.3 is generally adequate

(Refs. 4, 32, 33). Reference 34 includes a description of the directional θ-weighted scheme which may also be used.

7

standard lattice physics depletion calculations (Refs. 20, 21). This effect is particularly important

for plants that have adopted the PWR low-leakage refueling schemes (vs. out-in-in three-batch

fuel management) in which once-, twice-, or thrice-burned fuel is located in the high-importance

peripheral locations (Refs. 22-25). The harder spectrum in the BWR fuel regions having a high

void fraction will have a similar effect on the isotopic fission fractions and on the neutron-source

normalization and spectrum.

A planar-octant representation is generally acceptable for the octant-symmetric fuelloading patterns typically employed in LWRs. However, in the case of BWRs in which the jetpump positioning is quadrant-symmetric, a quadrant-symmetric model may be required. For

determining the peak fluence, fuel-loading patterns that are not octant symmetric (e.g., as in

certain low-leakage patterns) may be represented in octant geometry using the octant having the

highest fluence. For evaluating dosimetry, the octant in which the dosimetry is located may be

used.

When the actual planar core rectangular geometry cannot be modeled (e.g., in the case of

(r,θ) discrete ordinates calculations), the core geometry may be described using an (r,θ) planar

representation. To accurately represent the important peripheral assembly geometry, a θ-mesh of

at least 40 angular intervals over an octant must be applied. The (r,θ) representation should

reproduce the true physical assembly area to within ~0.5% and the pin-wise source gradients to

within ~10%. The assignment of the (x,y) pin-wise powers to the individual (r,θ) mesh intervals

should be made on a fractional area or equivalent basis (Ref. 26). Reference 26 is particularly

useful if the radial mesh is a function of (θ). The overall source normalization should be

performed with respect to the (r,θ) source so that differences between the core area in the (r,θ)

representation and the true core area do not bias the fluence predictions. A discussion of the

uncertainties in determining the core neutron source is provided in Reference 27.

Determination of the three-dimensional (3-D) fluence at the vessel using (r,z)- and (r)-

geometry calculations may also be appropriate (see Regulatory Position 1.3.4). If these

calculations are used to provide an axial correction factor, since the (r,z)- and the (r)- dependent

fluences enter as a ratio (see Equation 4), the source specification may be less stringent if

consistent sources are used in both the (r,z) and (r) calculations.

1.3 Fluence Calculation

1.3.1 Discrete Ordinates Transport Calculation

The transport of neutrons from the core to locations of interest in the pressure vessel may

be determined with a two-dimensional discrete ordinates transport program (Refs. 28-30) in (r,θ)

and, when appropriate, in (r,z)- and (r)- geometries.4,5 When calculating a horizontal plane of the

core/vessel geometry in which the rectangular (x,y) geometry of the core boundary and the
8

cylindrical (r) geometry of the vessel are mixed, a more accurate description is provided by the

variable (r,θ) mesh option (Ref. 29) and may be applied.

An azimuthal (θ) mesh using at least 40 intervals over an octant in (r,θ) geometry in the

horizontal plane should provide an accurate representation of the spatial distribution of the

material compositions and source described in Regulatory Position 1.2. The radial mesh in the

core region should be ~2 intervals per inch for peripheral assemblies and may be much more

coarse for assemblies more than approximately two assembly pitches removed from the corereflector interface. In excore regions, a spatial mesh that ensures the flux in any group changes by

less than a factor of ~2 between adjacent intervals should be applied, and a radial mesh of at least

~3 intervals per inch in water and ~1.5 intervals per inch in steel should be used. Because of the

relatively weak axial variation of the fluence, a coarse axial mesh of ~0.5 interval per inch may be

used except near material and source interfaces, where flux gradients can be large. An S8 fully

symmetric angular quadrature must be used as a minimum for determining the fluence at the

vessel. However, in reactor cavity fluence calculations a higher order quadrature may be needed,

depending on the width of the cavity and the axial location at which the fluence is being

calculated.

Where computer-storage limitations prevent the implementation of these mesh densities in

a single-model representation, the calculation should be performed in two or more "bootstrap"

steps rather than compromising the spatial mesh or quadrature (the number of groups used usually

does not affect the storage limitations, only the execution time). In this approach, the problem

volume is divided into overlapping regions. In a two-step bootstrap calculation, for example, a

transport calculation is performed for the cylinder defined by 0 < r < R with a fictitious vacuumboundary condition applied at R. From this initial calculation a boundary source is determined at

the radius R= R - ∆ and is subsequently applied as the internal-boundary condition for a second

transport calculation from Rto R (the true outer boundary of the problem). The adequacy of the

overlap region must be tested (e.g., by decreasing the inner radius of the outer region) to ensure

that the use of the fictitious boundary condition at R has not unduly affected the boundary source

at Ror the results at the vessel.

A point-wise flux convergence criterion of 0.001 should be used, and a sufficient number

of iterations should be allowed within each group to ensure convergence. To avoid negative

fluxes and improve convergence, a weighted-difference model should be used.5

 The adequacy of

the spatial mesh and angular quadrature, as well as the convergence criterion, must be

demonstrated by tightening the numerics until the resulting changes are negligible (Ref. 32). In

discrete ordinates codes, the spatial mesh and the angular quadrature should be refined

simultaneously. In some cases, these evaluations can be adequately performed with a onedimensional model.

The application of the discrete ordinates methods described in this section is illustrated in

detail in Reference 4. 

1.3.2 Monte Carlo Transport Calculation

The transport of neutrons from the core to locations of interest in the pressure vessel may

be determined by using Monte Carlo Transport (Refs. 4 and 35-46). The Monte Carlo method has
9

the advantage of allowing an exact representation of the problem geometry (Refs. 43-44); i.e., the

rectangular fuel assemblies, the barrel, thermal shield and vessel cylindrical regions, and the axial

geometry including upper and lower core reflectors, axial dosimeter locations, and vessel

circumferential weld locations. In addition, the Monte Carlo method allows a continuous (as well

as a multigroup) energy description of the nuclear cross-sections and flux solution. It is

noteworthy, however, that in order to obtain comparable accuracy this method typically requires

substantially longer computing times than the discrete ordinates method.

The cross-section data used in the Monte Carlo calculations should satisfy the

requirements of Regulatory Position 1.1.2. However, if a continuous energy cross-section library

is used, the requirements concerning the Legendre expansion of the scattering cross-sections and

the number of energy groups are not applicable. In addition, to ensure an accurate integration

over the dosimeter cross-section, the energy bin structure used to determine dosimeter response

scoring should satisfy the requirements of Regulatory Position 1.1.2 concerning the selection of

the multigroup library group structure.

While the Monte Carlo programs allow a great deal of flexibility in defining problem

geometry, the input is generally relatively complex, requiring the definition of a large number of

surfaces and cells, and is a potential source of error. Consequently, the geometry input should be

checked thoroughly (using plots, volume checks, etc.) against the model design data to validate

the definition of the geometry.

In pressure vessel evaluations, the flux is required at specific dosimeter and vessel surface

and internal locations. The calculated flux is edited in area and volume tally regions at these

locations. Typically, the size of these tally regions is increased to increase the number of particle

histories and reduce the statistical error in the flux estimate. The sensitivity of the flux estimate to

the volume or area of the tally region should be determined to ensure that the spatial dependence

of the flux does not introduce a bias in the flux estimate. If the size of the tally region introduces

a bias into the flux estimate, the calculation should be rerun with a smaller tally region and an

increased number of particle histories or the Monte Carlo prediction should be adjusted to

eliminate the calculational bias. This adjustment may be made, for example, using a correction

based on a deterministic calculation.

In addition to the area and volume tally regions, point detectors may be used to estimate

the flux at the locations of interest. However, the use of point detectors is complicated and the

following cautions should be observed. To minimize the variance in point detector edits, Monte

Carlo codes may define an average-flux region surrounding the detector within which the collision

estimation is determined. The neutron flux in this region is assumed to be uniform. In order to

ensure that the point estimate is not biased, the flux estimate should be shown to be insensitive to

the selection of the average-flux region. If the size of the average-flux region introduces a bias

into the flux estimate, the calculation should be rerun with a smaller average-flux region and an

increased number of particle histories. No material boundaries should be included in the averageflux region surrounding the point detector. Since the next-event particle tracking used in point

detectors does not account for reflecting, periodic, or white boundary conditions, the point

detector flux estimate is underpredicted when particles from these boundaries can contribute to

the flux estimate. Therefore, point detectors should not be located where particles from these
10

FOM  1

R 2T (Equation 1)

boundaries can contribute to the flux estimate. In order to ensure that a sufficient number of

particle histories are included and that the region close to the detector is adequately sampled, the

statistical edits should be reviewed thoroughly, especially if the relative error is greater than 5%.

In the Monte Carlo analysis, a calculational uncertainty is introduced as a result of the

finite number N of particle histories sampled. The Monte Carlo analysis provides estimates of the

mean flux, relative error (standard deviation/mean) and terms related to the higher moments, such

as the variance of the variance (VOV), based on the calculated particle histories. In order to

ensure that the calculation has converged and the estimated (mean) flux is valid, a reliable

estimate of the sampling uncertainty is required. However, because of the finite sampling of the

physical phase space, important paths in the geometry and peaks in the cross-sections may not be

adequately sampled, resulting in significant errors in the estimated mean and standard deviation.

Monte Carlo programs include statistical criteria to provide assurance that the calculations

have converged and that the estimated mean and relative error are valid. When performing Monte

Carlo pressure vessel fluence calculations, all statistical tests provided by the Monte Carlo code

should be satisfied or justification for accepting the results should be reported. The Monte Carlo

code should provide sufficient statistical testing (in addition to the usual tally standard deviation)

to ensure that the scoring phase space has been adequately sampled. Representative statistical

tests that are used to ensure tally convergence include (e.g., Reference 43):

(1) The flux mean should not have a significant monotonic dependence (either increasing or

decreasing) on N for the last half of the problem,

(2) The percent relative error of the mean flux should be less than ~10%, except for point

detectors for which it should be less than ~5%,

(3) The relative error should have a ~ dependence for the last half of the problem, 1/ N

(4) The figure of merit defined as

where R is the relative error and T is the problem computing time, should not have a

significant monotonic dependence on N for the last half of the problem, and

(5) The VOV should be less than ~0.10 for all tallies and decrease as ~1/N for the last half of

the problem.

As a result of the strong flux attenuation between the core and the pressure vessel, very

few neutrons (~less than one in a thousand) actually reach the vessel. Since the relative error (and

variance) in the Monte Carlo calculation only decreases as , the number of neutrons tracked 1/ N

and resulting computer times required to obtain acceptable accuracy are very large. In practice,

the computing time may be reduced by using variance reduction techniques that increase the

number of neutrons reaching the locations of interest (such as the dosimetry capsules and vessel

inner-wall) or improve the particle tracking efficiency, or both. Typically, the number of particles

that contribute to the tally is increased by increasing the number of particles in the regions of the

particle phase space that are judged (based on prior knowledge) to contribute significantly to the
11

calculation. However, if this judgment is incorrect and the neutrons believed to be unimportant

make a significant contribution to the tally, the Monte Carlo estimated fluence and relative error

(and variance) will be erroneous. Consequently, the variance reduction methods used in

performing pressure vessel fluence analyses should be qualified by comparing the Monte Carlo

variance reduction predictions with estimates made without the application of the variance

reduction technique. Since the calculation without variance reduction will typically involve a

large number of particle histories and long computing times, this comparison can be made using a

simpler representative configuration (e.g., one-dimensional geometry).

The following Monte Carlo variance reduction methods may be used in performing

pressure vessel fluence analyses: (1) neutron energy cutoff, (2) source biasing, (3) geometry

splitting with Russian Roulette, and (4) weight windows. Specific concerns associated with the

application of these methods are described in the following.

In the application of the neutron energy cutoff technique, neutron tracking efficiency is

improved by terminating tracking when the particle weight falls below a selected input energy. 

This method assumes that particles with energy below the cutoff do not contribute to the tally and,

consequently, may underestimate or bias the tally edit. While a cutoff energy of 1-MeV can be

used to calculate the E > 1-Mev fluence without introducing any error, the cutoff energy for the

dosimeter response calculation depends on the specific dosimeter reaction cross-section and

should be selected low enough to ensure that the calculation provides acceptable accuracy. If this

method is employed, the bias introduced by the energy cutoff should be estimated by comparison

with an unbiased calculation and the Monte Carlo calculation adjusted to account for the bias.

The source biasing method increases the number of source particles in the regions of phase

space that are believed (based on prior knowledge) to provide the most significant contribution to

the Monte Carlo tally. For example, the neutrons born in the peripheral fuel assemblies contribute

most to the vessel fluence and the number of these particles can be increased (and their weight

decreased proportionally) to improve the particle tracking efficiency. The space- and energydependent importance of the core neutrons to a specific location on the vessel can be estimated

using a precalculated adjoint flux and used to determine the source biasing (e.g., Refs. 41, 42, and

44). To ensure that the biased sampling of the source is producing reliable Monte Carlo estimates,

the source biasing method should be qualified by comparison with an unbiased calculation for a

representative problem.

Geometrical splitting with Russian Roulette reduces the variance of the tally edit by

increasing the number of neutrons that reach the vessel. This is accomplished by assigning

numerical importance values to each spatial cell such that the cell importance values increase as

the neutrons approach the vessel (Ref. 46). When a neutron travels toward the vessel passing

from a region of lower importance I to a region of higher importance I, it is split into I/I

neutrons. Conversely, when a neutron travels away from the vessel passing from a region of

higher importance I to a region of lower importance I, it undergoes Russian Roulette with a

survival probability of I/I. The reliability of this technique depends on the selection of the cell

importances I. It is recommended that the importance in adjacent cells should not change by more

than a factor of ~3, and the cell radial optical thickness should be less than ~2 mean free paths

(Ref. 43). To ensure that the selection of the cell importance distribution provides reliable Monte
12

Carlo estimates, the geometrical splitting with Russian Roulette method should be qualified by

comparison with an unbiased calculation for a representative problem.

The weight windows method may also be used to improve the efficiency of the neutron

tracking in Monte Carlo pressure vessel analyses (e.g., Refs. 41, 42, and 45). In the weight

windows method, the neutron weight in each space-energy cell is limited to a specific range or

ìweight windowî by splitting and Russian Roulette. The window is defined so that the neutron

weight is inversely proportional to the importance of the space-energy cell so that the scoring

variance is minimized (Ref. 43). In practice, the specification of the weight windows is difficult

and requires a detailed knowledge of the space-energy-dependent cell importance. Consequently,

in order to ensure that the definition of the weight windows is providing reliable Monte Carlo

estimates, it is important that the weight windows method be qualified by comparison with a

calculation performed without variance reduction.

The application of Monte Carlo methods described in this section is illustrated in detail in

Reference 4.

1.3.3 Fluence Determination

The transport calculations (both discrete ordinate and Monte Carlo) may be performed in

either the forward or adjoint modes. When several transport calculations are needed for a specific

geometry, assembly importance factors may be precalculated by either performing forward

calculations with a unit source (with the desired pin-wise source distribution) specified in the fuel

assembly of interest or by performing adjoint calculations. The adjoint fluxes are used to

determine the fluence at a specific (field) location, while the forward fluxes from the unit-source

calculations determine the fluence at all locations in the problem. Once calculated, these factors

contain the required information from the transport solution, and by weighting the assembly

importance factors with the source distribution of interest, the vessel (or capsule) fluence may be

determined without additional transport calculations, assuming the in-vessel geometry, material,

and source distribution within the assembly remain the same.

In performing calculations of surveillance capsule fluence (Regulatory Position 1.4), it

should be noted that the capsule fluence is extremely sensitive to the representation of the capsule

geometry and internal water region (if present), and the adequacy of the capsule representation

and mesh must be demonstrated using sensitivity calculations (as described in Regulatory Position

1.4.1). The capsule fluence and spectra are sensitive to the radial location of the capsule and its

proximity to material interfaces (e.g., at the vessel, thermal shield, and concrete shield in the

cavity), and these should be represented accurately. The core shroud and baffle former plates can

result in a 5-10% reduction in the surveillance capsule dosimeter response and should be included

in the model. 

When fluence reduction schemes have introduced strong axial or azimuthal heterogeneities

into the source (e.g., an axially zoned replacement of fuel with stainless steel for fluence

reduction), these should be modeled in detail. When the transport calculation is performed using

the discrete ordinates method, a finer spatial mesh and tighter convergence criteria may be

appropriate to ensure an accurate solution. These schemes may also entail a 3-D flux calculation.
13

g(r,,z) = g(r,)Lg(r,z) (Equation 2)

Lg(r,z)  P(z) (Equation 3)

Lg(r,z) = g(r,z)/g(r) (Equation 4)

To account for the neutron spectrum dependence of RTNDT when the E > 1 -MeV fluence is

extrapolated from the inside of the pressure vessel to the T/4- and 3T/4-vessel locations, a spectral

lead factor (which accounts for the change in neutron spectrum between downcomer and vessel

internal locations) must be applied to the fluence for the calculation of ∆RTNDT (Ref. 47). This

spectral lead factor has been included in the Equation 3 attenuation formula of Revision 2 of

Regulatory Guide 1.99, and therefore is not required when this formula is used. However, when

this formula is not used, the spectral lead factor must be applied to the fluence at the vessel

internal locations. Displacements per atom is used as the extrapolation parameter in Regulatory

Guide 1.99 and is an acceptable parameter for extrapolating the E > 1-MeV fluence to vessel

internal locations and determining this lead factor.

1.3.4 Synthesis of the 3-D Fluence

When 3-D effects are important and three-dimensional transport calculations are not

practical, a 3-D fluence representation may be constructed by synthesizing calculations of lower

dimensions using the expression

where φg(r,θ) is the group-g transport solution in (r,θ) geometry for a representative plane and

Lg(r,z) is a group-dependent axial shape factor. Two simple methods available for determining

Lg(r,z) are defined by the expressions

where P(z) is the peripheral-assembly axial power distribution, and

where φg(r) and φg(r,z) are one- and two-dimensional group-g flux solutions, respectively, for a

cylindrical representation of the geometry that preserves the important axial source and

attenuation characteristics (Refs. 4 and 48). The (r,z) plane should correspond to the azimuthal

location of interest (e.g., peak vessel fluence or dosimetry locations) or a conservatively θaveraged (r,z) plane. The source per unit height for both the (r,θ)- and (r)- models should be

identical, and the true axial source density should be used in the (r,z) model.

Equation 3 is only applicable when (1) the axial source distribution for all important

peripheral assemblies is approximately the same or is bounded by a conservative axial power

shape and (2) the attenuation characteristics do not vary axially over the region of interest. In

addition, since the axial flux distribution tends to flatten as it propagates from the core to the

pressure vessel, for typical axial power shapes, use of Equation 3 will tend to overpredict axial

flux maxima and underpredict minima. This underprediction is nonconservative and can be large

near the top and bottom reflectors, as well as when minima are strongly localized as occurs in

some fluence-reduction schemes. Because of the neglect of the former plates, this method may

result in an additional 5-10% underprediction of the fluence. 
14

g(r,,z) =

N



i1

aigi(r,)gi(r,z)/gi(r) (Equation 5)

Equation 4 is applicable when the axial source distribution and attenuation characteristics

vary radially but do not vary significantly in the azimuthal (θ) direction within a given annulus. 

For example, this approximation is not appropriate when strong axial fuel-enrichment variations

are present only in selected peripheral assemblies.

In summary, an (r,θ)-geometry fluence calculation and a knowledge of the peripheral

assembly axial power distribution are needed when using Equation 3. Use of this equation may

result in fluence overpredictions near the midplane at relatively large distances from the core, e.g.,

in the cavity, and underpredictions at axial locations beyond the beltline at relatively large radial

distances from the core. Conservatism may be included in the latter case by using the peak axial

power for all elevations.

Both radial and axial fluence calculations are needed when using Equation 4; thus, it is

generally more accurate in preserving the integral properties of the three-dimensional fluence. 

Both Equation 3 and Equation 4 assume separability between the axial and azimuthal fluence

calculations, which is only approximately true.

When these simple synthesis techniques are not applicable, multichannel synthesis

methods may be used. In the multichannel synthesis calculation, the fluence is represented as the

sum

where the φgi are basis flux solutions, typically representing specific regions of the core and vessel

geometries, and the weighting coefficients ai are determined to provide an optimum prediction of

the vessel fluence. It should be emphasized, however, that the accuracy of this method is sensitive

to the selection of the basis functions, especially at region interfaces, and three-dimensional

calculations should be considered where strong axial or azimuthal heterogeneities exist. This

synthesis technique has been applied to a calculational benchmark in Reference 28 and to an

experimental benchmark in Reference 49.

1.3.5 Cavity Fluence Calculations

Accurate cavity fluence calculations are relied on to analyze dosimeters located in the

reactor cavity (Ref. 50). The calculation of the neutron transport in the cavity is made difficult by

(a) the strong attenuation of the E > 1 MeV fluence through the (5.5- to 10.0-inch thick) vessel

and the resulting increased sensitivity to the iron inelastic-scattering cross-section and (b) the

possibility of neutron streaming (i.e., strong directionally dependent) effects in the low-density

materials (air and vessel insulation) in the cavity. Because of the increased sensitivity to the iron

cross-sections, ENDF/B-VI cross-section data should be used for cavity fluence calculations.2

 As

indicated in Regulatory Position 1.1.2, properly benchmarked alternative cross-sections may also

be used. However, for cavity applications, the benchmarking must include comparisons for

operating reactor cavities or simulated cavity environments.
15

Typically, the width of the cavity together with the close-to-midplane locations of the

dosimetry capsules result in minimal cavity streaming effects. Consequently, in discrete ordinates

calculations, an S8 angular quadrature is acceptable. However, when off-midplane locations are

analyzed, the adequacy of the S8 quadrature to determine the streaming component must be

demonstrated with higher-order Sn calculations. In addition, since the radial mesh in the (r,z)

calculation is generally finer than the z-mesh in the cavity resulting in narrow spatial-mesh

intervals, a θ-weighted difference model should be used.5

The cavity fluence is sensitive to both the material compositions (Regulatory Position

1.1.1) and the local geometry (e.g., the presence of detector wells) of the concrete shield, and

these should be represented as accurately as possible. Benchmark measurements involving

simulated reactor cavities that are recommended for methods evaluation are given in Regulatory

Position 1.4.2.2. The measured energy spectrum for a typical PWR cavity is described in

Reference 51. When both in-vessel and cavity dosimetry measurements are available, an

additional verification of the measurements and calculations may be made by comparing the

vessel inner-wall fluence determined from (1) the absolute fluence calculation, (2) the

extrapolation of the in-vessel measurements, and (3) the extrapolation of the cavity measurements. 

Measurements performed in reactor cavities and the associated calculations are described in

References 5 and 6.

1.4 Methodology Qualification and Uncertainty Estimates

The neutron transport calculational methodology must be qualified, and flux uncertainty

estimates must be determined. The neutron flux undergoes several decades of attenuation before

reaching the vessel, and the calculation is sensitive to the material and geometrical representation

of the core and vessel internals, the neutron source, the nuclear cross-section data, and the

numerical schemes used in its determination. The uncertainty estimates are used to determine the

appropriate uncertainty allowance to be included in the application of the fluence estimate. While

adherence to the guidelines described here will generally result in accurate fluence estimates, the

overall methodology must be qualified in order to quantify uncertainties, identify any potential

biases in the calculations, and provide confidence in the fluence calculations. In addition, while

the methodology, including computer codes and data libraries used in the calculations, may have

been found to be acceptable in previous applications, the qualification ensures that the licensee's

implementation of the methodology is valid.

The methods qualification consists of three parts: (1) the analytic uncertainty analysis

(Regulatory Position 1.4.1), (2) the comparison with benchmarks and operating reactor

measurements (Regulatory Position 1.4.2), and (3) the estimate of uncertainty in the calculated

fluence (Regulatory Position 1.4.3). These three steps in the overall qualification procedure are

discussed below and are outlined in Figure 3.

1.4.1 Analytic Uncertainty Analysis

To demonstrate the accuracy of the methodology, an analytic uncertainty analysis must be

performed. This analysis includes identification of the important sources of uncertainty. For

typical fluence calculations, these sources include:
6

 The systematic errors affect the fluence prediction in a specific direction (i.e., increase or decrease the estimate). Consequently,

when these errors (or biases) are applied, the signs (or directions) must be recognized and they must be combined algebraically. 

The independent random uncertainties have no specific direction (i.e., an increase or decrease) associated with them, and they are

combined without recognizing the sign of the error.

16

 Nuclear data (transport and dosimeter reaction cross-sections and fission spectra),

 Geometry (location of internals and deviations from the nominal dimensions),

 Isotopic composition of material (density and composition of coolant water, core, core

barrel, former plates, thermal shield, pressure vessel with cladding, and concrete shield),

 Neutron sources (space and energy distribution, burnup dependence),

 Methods error (mesh density, angular expansion, convergence criteria, macroscopic group

cross-sections, fluence perturbation by surveillance capsules, spatial synthesis, and cavity

streaming).

This list of uncertainty components is not necessarily exhaustive, and other uncertainties

that are specific to a particular reactor or a particular calculational method should be considered. 

In typical applications, the fluence calculational uncertainty is dominated by a few easily

identified uncertainty components, such as the geometry and core neutron source, which results in

a substantial simplification of the uncertainty analysis.

The sensitivity of the flux to the significant component uncertainties should be determined

by a series of transport sensitivity calculations in which the calculational model input data and

modeling assumptions are varied and the effect on the calculated flux is determined. (A typical

sensitivity would be 10-15% decrease in vessel E > 1 MeV fluence per centimeter increase in

vessel inside radius.) Estimates of the expected uncertainties in these input parameters must be

made and combined with the corresponding fluence sensitivities to determine the total analytically

determined calculation uncertainty σa

c

 (i.e., standard deviation) as indicated in Figure 3. The

uncertainties should be combined in a statistical (root-sum-of-the-squares) fashion to determine

the total fluence uncertainty, accounting for the correlation between uncertainties when necessary

(see, e.g., Section 5.2 of Ref. 3). The known systematic errors (or biases) should be combined

algebraically, recognizing the sign of each contribution, to determine the overall calculational bias

Ba

c

 (Ref. 52).6 The component uncertainties should be based on measurement or on the acceptable

deviations included in the design specifications. The sensitivity calculations may be performed in

one dimension when the model sensitivity does not require a two-dimensional representation. 

If the sensitivities are determined using Monte Carlo transport calculations, the magnitude

of the model variations and the number of particle histories may have to be increased to provide

reliable estimates of the calculation sensitivities. If the increased model variations are large,

several calculations may be required to determine the non-linear dependence of the sensitivity. 

Perturbation calculations using correlated sampling may also be used to determine the sensitivity

to model geometry, material compositions, and cross-sections. Adjoint Monte Carlo calculations

may be used to determine the sensitivity to input such as fission spectra. Alternatively, if the

sensitivities can be determined with sufficient accuracy in one-dimensional geometry, the

sensitivities can be determined using a one-dimensional model.
17

A sensitivity analysis, in which the influence of each of these uncertainties on the

calculated group fluences has been considered, is included in References 5 and 6. Since the

uncertainties used in these analyses are common to many pressurized water reactors, the

sensitivities (including correlations) may be used to determine initial uncertainty estimates. These

variance estimates should be modified as the methods and cross-section data change or if the

reactor of interest differs substantially from the reactors analyzed in these references. The

referenced sensitivity analysis provides guidance for such modifications.

1.4.2 Comparisons with Benchmark Measurements and Calculations

Calculational methods must be validated by comparison with measurement and

calculational benchmarks. The fluence calculation methods must be validated against (1)

operating reactor measurements that provide in-vessel surveillance capsule dosimetry or ex-vessel

cavity measurements or both, (2) a pressure vessel simulator benchmark that provides

measurements at the inner surface and at the T/4 and 3T/4 positions within the vessel (see

Regulatory Position 1.4.2.2 for a discussion of such benchmarks), and (3) the fluence calculation

benchmark. The results of the validation should include comparisons of reaction rates, fluences,

and group fluxes for the locations of interest (Refs. 53, 54).

The methods used to determine the plant-specific data and calculate the benchmarks must

be consistent (to the extent possible) with those used to calculate the vessel fluence. That is, the

same cross-sections, transport techniques, and transport code parameters that are to be used in the

reactor licensing application must be employed in the calculation of the benchmark measurements

and calculations.

Differences between measurements and calculations should be consistent with the

combined uncertainty estimates for the measurements and calculations. (Note that the

uncertainties in both the calculations and measurements will contribute to the observed

measurement-to-calculation differences.) The calculated reaction rates (using the methods

described in Regulatory Positions 1.1 through 1.3) typically agree with the measurements to

within about 20% for in-vessel surveillance capsules and 30% for cavity dosimetry. Deviations

greater than these values must be investigated and, when the cause of the deviation is determined

to be an error in the calculation, the calculations must be modified.

If the calculation is modified using a least-squares statistical approach (Refs. 55-62), the

measurement-to-calculation (M/C) ratios should be reviewed, prior to adjustment, in order to

identify any systematic trends in the M/C data. Specific examples include systematic

overprediction (or underprediction) of the dosimeter response for (1) dosimeters with low-energy

thresholds, (2) dosimeters in the cavity (versus inner-wall and accelerated capsule locations), (3)

dosimeters with long half-life reaction products, and (4) dosimeters monitoring specific cycles. If

systematic trends, interdependence, or correlations appear in the M/C data, these should be

explained and removed (prior to adjustment) or accounted for in the statistical adjustment
7

 For example, if the M/C data for the Np-237 dosimeters tends to be high, indicating a systematically low calculation or high

measurement, the errors in the Np-237 calculated or measured responses are correlated. If this error is not removed prior to the

adjustment, the important sources of correlated error should be identified (e.g., the Np-237 dosimeter reaction cross-section,

reaction product half-life and Np-237 photo-fission correction) and included in the adjustment procedure to allow the proper

treatment of this error. 

8

 The adequacy of the measurement data base for determining a bias in the calculations depends on the magnitude of the bias and

is therefore problem dependent. For example, if the bias is small an accurate estimate of the bias will require either (1) a large

number of reasonably accurate measurements or (2) a small number of very accurate measurements. Specifically, the uncertainty

in the bias should be substantially less than the bias itself. For example, if the calculated fluence is to be increased by 10% , the

uncertainty in this increase should be substantially less than 10%.

9

 Additional guidance on benchmark testing is provided in the ASTM standard E2005-99 (Ref. 64) and examples of operating

reactor benchmark measurements are provided in Reference 65.

18

procedure.7 Also, since the fluence adjustment is sensitive to the input uncertainties, realistic

uncertainty values should be used and documented. The dosimeter measurement uncertainty

should include the response uncertainty caused by dosimeter mislocation. Additional guidance on

least-squares adjustment methods is provided in Ref. 63. It should be noted, however, that the

available least-squares statistical adjustment codes differ substantially in their approach and their

capabilities. Consequently, the selection of the least-squares code and the details of the analysis

are highly application-specific and are outside the scope of this guide. 

The simulator benchmarks provide accurate measurements but typically do not provide an

accurate representation of the actual plant configuration. The operating reactor measurements, on

the other hand, represent the actual as-built plant configuration but, typically, include substantial

measurement uncertainties. The simulator benchmarks together with the operating reactor

measurements generally provide an acceptable measurement data base. The comparisons of the

calculations to the measurement benchmarks should be used to estimate the calculational bias Bb

c

and uncertainty σb

c

. If the bias estimate is considered reliable, a correction equal to the bias may be

applied to the calculation to determine a best-estimate fluence.8 If the calculations or

measurements are adjusted to improve the M/C agreement, using either a least-squares approach

or a direct multiplicative bias, the adjustment and basis must be reported. 

1.4.2.1 Operating Reactor Measurements. Well documented fluence dosimetry

measurements for operating power reactors may be used for methods and data qualification.9

Descriptions of these configurations include three-dimensional geometry, reactor operating

conditions and, in some cases, both in-vessel and ex-vessel measurement data.

Comparisons of measurements and calculations must be performed for the specific reactor

being analyzed or for reactors of similar design. Plant-specific measurements have the advantage

of including the as-built materials and geometry and the actual reactor operating conditions. An

especially accurate determination of the fluence can be obtained when both in-vessel and cavity

dosimetry are available.

These measurements should not be used to bias or adjust the fluence calculations unless a

statistically significant number of measurements is available, the various dosimeter measurements

are self-consistent, and a reliable estimate of the calculational bias can be determined.8,9

Similarly, plant-specific biases should not be used unless sufficient reliable measurement data are

available. As capsule and cavity measurements become available, they should be incorporated
19

into the operating reactor measurements data base, and the calculational biases and uncertainties

should be updated as necessary.

1.4.2.2 Pressure Vessel Simulator Measurements. Several pressure vessel simulator

benchmarks are available (Refs. 7, 49, 65-82) and may be used for methods qualification. These

benchmark experiments were carried out by several laboratories, and dosimetry measurements

using different techniques were compared to provide experimental results with well known and

documented uncertainties. Three configurations were used in these experiments.

 Pressure Vessel Simulator Experiments. The Oak Ridge National Laboratory (ORNL)

Pool Critical Assembly (PCA) is a full-scale-section mockup of a pressure vessel with

dosimetry measurements at the inner surface of the vessel and at the T/4, T/2 and 3T/4

locations within the vessel wall (Refs. 72-75). The PCA benchmark experiment includes a

simulated surveillance capsule that allows the determination of the effect of the capsule on

the dosimetry measurements. This benchmark is characterized by a relatively simple

geometry with generally less uncertainty in region compositions, temperatures, and source

distributions than in operating power reactor benchmarks.

 Experiments Simulating Operating Reactor Conditions. The CEN/SK Laboratory

VENUS benchmark experiment (Refs. 49, 76-79) and the ORNL Pool Side Facility (PSF)

benchmark experiment (Refs. 80-82) simulate the operating reactor: (1) pin-wise power

distributions in peripheral fuel assemblies, (2) three-dimensional effects caused by partiallength shield assemblies, and (3) heterogeneities caused by neutron pads attached to the

core barrel. 

 Pressure Vessel Cavity Measurements. The H.B. Robinson-2 cavity measurement

(Refs. 65-67) and the NESDIP cavity simulator experiment (Refs. 7, 68-71) may be used

as benchmarks to qualify cavity fluence calculational methods. Calculations of dosimetry

measurements performed in an operating reactor cavity are described in References 5

and 6.

1.4.2.3 Calculational Benchmark. The vessel fluence benchmark problems provided by

the NRC in NUREG/CR-6115 (Ref. 4) should be used for methods qualification. This report

provides the detailed information defining the problems and corresponding numerical solutions

for a set of PWR and BWR pressure vessel fluence benchmark problems. The geometry,

materials, and space- and energy-dependent source are fixed by the problem specification. PWR

benchmark problems have been specified for (1) a standard core loading pattern, (2) a low-leakage

core loading pattern, and (3) a partial-length shield assembly core design. Since BWR fuel

loading patterns are presently not being designed for vessel fluence reduction, only a single BWR

problem is specified. In addition, MCNP Monte Carlo calculations have been performed for both

the BWR problem and the PWR problems for the standard core and partial-length shield assembly

core loadings. Comparisons of the vessel fluence determined by using both the MCNP and

DORT computer codes are included. 

The calculation of the benchmark problems allows a detailed assessment and verification

of the numerical procedures, code implementation, and the various modeling approximations
10 The calculation being used as the benchmark must be the NUREG/CR-6115 original referenced benchmark calculation, and

not just a second independent calculation of the benchmark. 

11 Because the weighting of the analytic and benchmark uncertainty estimates depends on the details of the specific application

that can vary widely, it is not possible to specify a practical and generically valid prescription for determining the weights.

However, the following example illustrates factors that should be considered. When as-built measurements of the vessel

diameter are available and reasonable estimates of the core neutron source and other input uncertainties can be determined, the

analytic uncertainty estimate should be reliable and have an uncertainty of 15% (1 sigma). Assume that there are a statistically

significant number of accurate (σ <~

 5%) operating reactor measurements and the uncertainty estimate based on this data has an

uncertainty of 20%. The uncertainty estimate based on the vessel simulator measurements is assumed to be less certain and has

an uncertainty of 25%. Using a weighted mean in which the weight is inversely proportional to the square of the standard

deviation of the estimate (i.e., σ-2), the weights are wA = 0.5, wo = 0.3 and wS = 0.2.

20

   1Bc [c(%) 20]/100c (Equation 6)

relative to state-of-the-art solutions for representative operating configurations.10 If the

differences between the benchmark problem calculation and the reference solution are

substantially larger than what would be expected based on the differences in the methods

approximations and nuclear data used in the two calculations, the agreement is considered

unacceptable. In this case, the calculation should be reviewed and the differences between the

two solutions explained. (Note that NUREG/CR-6115 includes sensitivity calculations and

comparisons with Monte Carlo predictions which provide an indication of the accuracy of the

methods approximations used in the NUREG/CR-6115 reference calculations.) When the cause

of the deviation is determined to be an error in the calculation, the calculational method must be

revised.

1.4.3 Estimate of Fluence Calculational Bias and Uncertainty

The overall fluence calculation bias Bc

 and uncertainty σc must be determined by an

appropriate combination of (1) the analytic uncertainty analysis results of Regulatory Position

1.4.1 (Ba

c

 and σa

c

) and (2) the results of the uncertainty analysis based on the comparisons to the

operating reactor and simulator benchmark measurements of Regulatory Position 1.4.2 (Bb

c

 and σb

c

). 

This combination may be a weighted average that accounts for the reliability of the individual

estimates.11 The bias Bc

 may be applied as a multiplicative correction to the calculated fluence to

determine the best-estimate value, and σc should be used (when required) as the (1-sigma)

uncertainty in the calculated best-estimate fluence. 

The fluence accuracy requirements are generally application specific; however, a vessel

fluence uncertainty of 20% (1 sigma) is acceptable for RTPTS and RTNDT determination. In the

determination of RTNDT and RTPTS, if the overall calculation uncertainty σc is greater than 20%, the

calculational model must be adjusted or a correction must be applied to reduce the difference

between the fluence prediction and the upper 1-sigma limit to within 20%. For example, if σc is

greater than 20% but less than 30%, the fluence φ should be determined from the calculated

fluence φc by the relation

If σc

 is greater than 30%, the methodology of this regulatory guide is not applicable and the

application will be reviewed on an individual basis. The procedure used to determine the fluence

is illustrated in Figure 4.
21

The fluence calculation methods of this section are summarized in Table 1, ìSummary of

Regulatory Positions on Calculation and Dosimetry.î

2. NEUTRON FLUENCE MEASUREMENT METHODS

Dosimetry measurements provide independent estimates of specific activities and isotopic

production rates that are used for validating the neutron transport calculations. Fluence is

obtained from the response of passive integral detectors placed in surveillance capsules and, more

recently, in the ex-vessel cavity. Procedures for performing the measurements and assessing

uncertainty, including the validation of measurement methods and detector response in standard

neutron fields, is described in this section.

The fluence measurement methods of this section are summarized in Table 1, ìSummary

of Regulatory Positions on Calculation and Dosimetry.î The procedure used to qualify the

measurement methods is presented in Figure 5. The guidance provided in this Regulatory

Position is intended for new dosimetry and, to the extent practical, for existing dosimetry.

2.1 Measurement Procedures

Power reactor dosimetry measurement methods use passive integral detectors, which are

typically activation detectors and solid-state track recorders. Most of the detectors respond to

neutrons with energies above a characteristic reaction threshold. These detectors should be

selected with substantial nonoverlapping energy regions (i.e., with well-separated thresholds) to

provide coarse spectrum information as well as an estimate of the neutron fluence.

2.1.1 Specification and Application of Dosimeters

Neutron dosimetry for pressure vessel surveillance may consist of as-built packages of

threshold dosimeters placed in surveillance capsules during reactor construction. The selected

dosimeter set should provide adequate spectrum coverage. A common set of fast neutron integral

detectors that may be employed in these packages is listed in Table 2. These neutron detectors are

discussed in References 83 through 89. The 54Fe(n,p)54Mn and 58Ni(n,p)58Co activation reactions

are useful for monitoring neutrons with energies above ~2 MeV. The 46Ti(n,p)46Sc reaction is

useful for monitoring neutrons with energies above approximately 4 MeV, and the 63Cu(n,α)

60Co

reaction is useful for measuring neutrons with energies above approximately 5 MeV. Fission

monitors are important since they typically have reaction thresholds below 1 MeV. Activities

determined by assaying one or more fission products from the 238U(n,f)FP fast-neutron fission

reaction are useful for monitoring neutrons with energies from approximately 1.5 to 7 MeV. 

Activities determined by assaying fission products from the 237Np(n,f)FP reaction are useful for

measuring neutrons with energies from approximately 0.7 to 6 MeV; however, there is a

significant gamma-ray background associated with neptunium dosimetry that is due to the large

quantity of naturally occurring 233Pa existing in secular equilibrium with 237Np. Compton

scattering of the protactinium decay photons generates a large background continuum, which

reduces the effective signal-to-noise ratio and lowers the accuracy of the radioassay. The

93Nb(n,ní)93mNb activation reaction is useful for monitoring neutrons with energies above

approximately 1 MeV, but involves the counting of a very soft photon, which can complicate the
22

corrections made to the measured activity to compensate for photon attenuation within the

dosimeter.

In addition to the fast-neutron threshold monitors, a thermal monitor such as 59Co should

be included among the selected dosimeters to allow the determination of the thermal neutron

fluence. The thermal fluence is needed to assess the effects of interfering activities in threshold

monitors produced by low-energy activation of impurity elements. In instances where the thermal

flux is relatively high, it can also be used for assessing the effects of burnout of the activated

species.

Taken together with a low-energy detector such as cobalt (to estimate the thermal neutron

fluence for determining interference from low-energy activations), the Table 2 dosimeter set

provides satisfactory neutron energy spectrum coverage for pressure vessel dosimetry. Alternative

detector sets that are used should provide equivalent spectrum coverage. Detector selection

criteria and related recommendations in ASTM E 844 (Ref. 90) and E 1005 (Ref. 91) should be

followed (see Table 2).

The application of the dosimeter should be evaluated relative to the expected neutron flux

and the total irradiation time in order to assess the effects of dosimeter burnout, and the burnout

and burn-in of reaction products. For example, when using 58Ni monitors in the presence of a

high thermal flux, the burnout of the nickel dosimeter as well as the 58Co and 58mCo reaction

products should be considered. The resonant absorption of epithermal neutrons in 238U and the

breeding of 239Pu, which can undergo thermal fission and contribute to the fission product activity,

should also be considered.

Application of activation detectors involves aspects of the measurement process that must

be carefully controlled and documented to obtain accurate results and establish reasonable

uncertainty estimates. Where applicable, procedures in ASTM Standards E 181 (Ref. 92), E 844

(Ref. 90) and E 1005 (Ref. 91) and methods devoted to individual radiometric sensors must be

used as indicated in Table 2. Specific regulatory positions associated with the dosimetry

measurements are indicated in the following.

2.1.1.1 Dosimeter Nuclear and Material Proprieties. The dosimeter nuclear and

material properties are important considerations in the selection and composition of the

surveillance dosimetry package. The physiochemical properties of the dosimeter materials should

be compatible with the prevailing service conditions. Dosimeter melting, for example, can result

in the loss of monitor activity and unreliable measurements. Consequently, the melting point of

the dosimeters and any associated materials should be carefully considered relative to the service

environment ambient temperature and the radiation heating within the dosimeter. Although the

melting point of typical radiometric monitors is sufficiently high to preclude melting, even mild

heating can be problematical for certain dosimeters. For instance, diffusion losses of 54Mn

activity from iron dosimeters can occur when heated to temperatures greater than 700C. In

addition, the dosimeter should be chemically stable and corrosion resistant. Fissionable materials

are especially prone to oxidation and, consequently, fission monitors should be hermetically

sealed to prevent oxidation and subsequent loss of material.
23

The nuclear properties to be considered in dosimeter selection include the reaction crosssection, decay half-life, gamma-ray yield, and the fission yield when employing fission

dosimeters. The reaction cross-section should be of sufficient magnitude to allow the dosimeter

to be used as a fluence monitor, consistent with other requirements on the dosimeter mass and

geometry, as discussed in following sections.

The photon yield associated with the nuclear decay should be large enough to allow an

accurate radio assay, and the energy of the particular photons counted should minimize

interference from neighboring spectral lines. For example, the 24Na reaction product, created from

the 27Al(n,α) reaction, emits photons with energies of 1.369 and 2.754 MeV. Since there is less

interference from the contaminant gamma rays associated with the higher-energy photon, it is

preferable to count the high-energy line during the radioassay. In the case of fission product

radioassay involving the 95Zr-95Nb fission product, three dominant spectral lines are observed at

724, 756, and 765 keV. However, the two high-energy lines are in close proximity and

complicate the determination of the background subtraction. Consequently, counting the 724 keV

line provides the more accurate result.

The half-life of the activated species should be long enough, relative to the elapsed time

from the end of the irradiation to the time at which the dosimeters are actually counted, to permit

nuclear counting to proceed with reasonable counting statistics. This time interval is often a

significant consideration. The half-life should also be long enough to provide an accurate

indication of the fluence during the irradiation period.

The fission product yields associated with fission dosimeters should be of sufficient

magnitude to permit an accurate radioassay. The yields (and decay constants) of the fission

products 99Mo and 140Ba-140La are known with greater accuracy than most fission products;

however, their half-life is generally too short for these isotopes to be useful as neutron fluence

monitors in power reactor applications. Useful fission products include 95Zr-95Nb, 103Ru, 144Ce,

and especially 137Cs-137mBa, because of its 30-year half-life.

2.1.1.2 Material Composition. The dosimeter materials should be pure enough to

ensure there is no significant error in the response of the dosimeter from extraneous activities. 

Cursory specifications of materials regarding impurities are often unreliable. Specifically, fissile

residuals in 237Np and 238U and minute amounts of cobalt in copper and nickel dosimeters

(fractional parts per million) should be determined by mass spectrography or radioactivation

analysis. Tracking the principal decay half-life is also a useful technique for determining the

presence of extraneous activities from impurity elements.

Dosimetric materials should be handled with care to prevent cross contamination of the

dosimeters and, when necessary, the dosimeters should be cleaned of surface contaminants. For

example, the handling of aluminum monitors can introduce sodium (24Na) as an external surface

contaminant. Neutron activation of the sodium will produce 24Na activity that will interfere with

the radioassay of the 24Na activity produced from the desired dosimetric reaction.

Post-irradiation quality assurance may be accomplished at the National Institute for

Standards and Technology (NIST) for dosimeters already in surveillance capsules by additional
24

irradiation in a thermal neutron field or a standard fission spectrum. These additional exposures

and analyses can provide data on the dosimeter masses and impurities (for example, the original

cobalt-59 impurity content in copper used for the copper-63 (n, α) reaction).

2.1.1.3 Encapsulation. The detector capsule design must take into account possible

activation interference and neutron spectrum perturbation. Thermal neutron shields that eliminate

interference from thermal neutron reactions in some detectors must be designed to accommodate

radiation heating and should be placed apart from low-energy detectors (see ASTM Standard E

844, Ref. 90). The thickness of the thermal shield should be selected based on the expected

thermal flux and duty cycle. (Note that the effective cadmium cutoff energy is a function of shield

thickness.) The design of the shields and their placement relative to other dosimeters should be

carefully considered in order to minimize their impact on neighboring foils. For example, the use

of a cadmium shield will generate a local gamma field that could affect adjacent fission foils by

producing a photofission component in the measured activity.

2.1.1.4. Isotopic Mass. The mass of the dosimeters should be selected to permit the

production of sufficient activity to allow an accurate radioassay. However, a dosimeter mass that

is too large can lead to high activities that result in excessive dead-time losses during nuclear

counting and should be avoided. Metal alloys can be used for diluting materials that have high

nuclear cross-sections (e.g., dilution of cobalt in an aluminum alloy). However, stoichiometry and

isotopic analysis should be well documented for dosimeters that are not of pure natural elements. 

2.1.1.5. Geometry and Location. The geometric configuration of the dosimeters can

have a significant effect on the dosimeter response. Most radiometric monitors are in the shape of

thin circular activation foils, although other shapes are available. Dosimeters should be small

enough to allow placement at the desired location and large enough to provide sufficient activity

to allow an accurate measurement. The dosimeter thickness can have a significant effect on the

dosimeter self-shielding (of the neutron flux) and the dosimeter response for strongly absorbing

foils. In addition, increased dosimeter thickness increases the effects of scattering and photon

attenuation within the dosimeter and can lead to large response corrections. When selecting

fissionable dosimeters, it should be recognized that reduced foil thickness increases fission

product loss from nuclear recoil out of the foil, which reduces the measured dosimeter activity. 

The placement of the dosimeters can also have a significant effect on the dosimeter

measurement. The surroundings of a dosimeter (e.g., adjacent dosimeters or material interface)

can influence detector response. Strongly and weakly absorbing foils that respond over the same

energy range should be sufficiently separated within the dosimetry package to minimize

interference effects. The arrangement of the dosimeters within the package should minimize

scattering effects (viz., thick dosimeters should not be stacked so that large scattering corrections

are required for adjacent foils). 

The location of individual dosimeters must be determined accurately and recorded,

because fluence gradients in out-of-core positions are generally severe. In the pressure vessel

cavity, establishing azimuthal position can be as important as the radial location. Specially

designed mounting arrangements that ensure accurate radial, azimuthal, and vertical positions
25

should be used for cavity dosimetry. Vertical wires may be used. Comprehensive and accurate

detector location information should be maintained.

2.1.1.6 Solid-State Track Recorders. Solid state track recorders (SSTRs) are integral

detectors that employ fission reactions. These sensors directly record the tracks of fission

fragments from a thin fissionable deposit (Refs. 93 and 94). The principal advantages of these

detectors are wide sensitivity ranges and a permanent measurement record. Because the

application of SSTRs employs fissionable deposits in the nanogram to picogram range, details of

the measurements should be well documented, and standard neutron field calibration should be

performed prior to the application. ASTM Standard E 854 (Ref. 95) provides additional

information concerning the use of SSTRs.

2.1.1.7 Helium Accumulation Fluence Monitors. The helium accumulation fluence

monitor (HAFM) is another type of stable-product neutron monitor. These monitors rely on the

generation of helium gas via (n,α) reactions that occur in a variety of materials when exposed to a

neutron field. The amount of helium generated in a specific material is a function of the neutron

fluence and is determined by vaporizing the sample and measuring the helium content by mass

spectrometry. HAFMs are routinely used in conjunction with radiometric monitors and, in fact,

several commonly used radiometric monitors also undergo (n,α) reactions and can be analyzed for

helium accumulation as well as for radiometric activity. ASTM Standard E910 (Ref. 96) provides

additional guidance on the use of HAFMs.

2.1.2 Detector Response Measurements

A measured response must be provided to allow comparison of the calculations and

measurements. Typical measured responses include the specific activity at end-of-irradiation

(given in disintegrations per second per nucleus), the measured isotopic production (for example,

helium atoms per initial atom of material), and the total reactions (for example, fissions per initial

atom of material). When comparing calculations with measurements, corrections should be

included for detector response perturbations, interfering reactions, and, when applicable, burnup

and photofission. In the calculation of end of irradiation activities (or in the conversion of end of

irradiation activities into reaction rates), the power-history and the half-life of the dosimeter

activation products must be included (Ref. 91). Photofission corrections can vary considerably

(from 2-15%) depending upon the location of the dosimetry and the type of reactor. Fission yields

should be those specified in the relevant ASTM Standards, the ENDF library, or the validated job

library. In situ neutron field perturbations (e.g., by the surveillance capsule and detector

encapsulation) must be accounted for if they are not an integral part of the neutron transport

calculation.

When reporting measurements, these corrections should be described and quantified along

with any other effects that have a significant impact on the measurements. This is especially

important because pressure vessel surveillance dosimetry often involves comparison of

measurements carried out by different organizations and over long periods of time.

2.1.3 Measurement Uncertainties

Regulatory Position 1.4 states that the calculations must be validated by comparison with

measured benchmarks. In order to perform this validation, the uncertainty associated with the
12 This measurement validation procedure does not require transport calculations.

26

measured response must be determined for each dosimeter type. The uncertainty must be

included in the documentation of the measured results.

The important uncertainties must be quantified and included in an uncertainty table that

summarizes the specific components of uncertainty contributing to each detector response. 

Typical sources of uncertainty include (1) background counting, counting efficiency, counting

statistics, and fraction of the sample counted, (2) decay constant and fission yield uncertainty, (3)

uncertainty in detector weight, geometry, composition and isotopic purity, (4) power history and

time of irradiation, (5) dosimeter location uncertainty, and (6) cross-section uncertainty when the

fluence is determined. Additional sources are identified in Regulatory Positions 2.1.1 and 2.1.2

and in the dosimeter-specific ASTM Standards of Table 2. The entries in the table should be

identified as standard deviations, upper bounds, or appropriate fractions of the correction. Each

entry should be described, along with the method used to combine the entries and determine the

total response uncertainty. The evaluation of the measurement uncertainty for each dosimeter is

important for ensuring a meaningful comparison with the calculations.

2.2 Validation in Standard and Reference Neutron Fields

The dosimeter measurements used to benchmark the calculations must meet the

requirements in Appendix B to 10 CFR Part 50 for a quality assurance program (for surveillance

measurements). To ensure long-term measurement consistency and confirm measurement

uncertainties, dosimetry measurements must be performed every few years12 in well characterized

neutron fields. If there are changes in dosimeter evaluation procedures, equipment, or personnel

that could have a significant effect on the dosimetry, the validation must be updated. This

validation may be performed using the Materials Dosimetry Reference Facility (MDRF) or using

reference fission neutron sources (Refs. 97, 98). Neutron field referencing may be used as a

detector response calibration (Ref. 99).

The validation is accomplished by exposing each type of detector to a certified neutron

fluence in the reference neutron field and by determining the fluence using the measurement

method to be validated. A calculated spectrum-averaged cross-section, generally specified along

with the certified neutron fluence, must be used to derive the measurement value. If measured

and certified neutron fluence agree (to within the combined uncertainty of the measured and

certified fluence), the detector measurement method, including the detector cross-section, is

validated. If the fluences disagree, this calculation-to-experiment (C/E) ratio represents a bias

associated with the detector response measurement or the detector cross-section or both. In this

case, the detector measurement methods and input parameters should be re-examined in order to

eliminate the bias. If after re-examination the bias is still present, the bias may be used directly as

a detector response calibration factor.

The results of the neutron field validation procedure should be reported in terms of C/E

ratios for the individual detectors and should include an uncertainty table. The standard neutron

field validation may be used, as appropriate, to simplify the uncertainty table called for in
27

Regulatory Position 2.1.3 by reducing or eliminating many uncertainties in the activity

measurement, nuclear decay parameters, and detector cross-sections.

Aside from validating the measurement method, standard and reference neutron fields may

be used for quality assurance of critical features of the detector response. Examples are activation

interference by impurities, proper determination of fission product activities, and mass assay of

fissionable deposits for track recorders.

Interlaboratory comparisons, such as those carried out under the NRC-sponsored LWR

Surveillance Dosimetry Improvement Program (Refs. 7, 49, 72, 80, 81), have been useful in

validating the quality assurance programs of various laboratories. These interlaboratory

comparisons have been used to identify problems in the measurement procedures and establish

consistency between the various participating laboratories.

2.3 Fluence Determination from Detector Measurements

As stated in Regulatory Position 1.4, the calculated fast-neutron fluence values must be

validated by comparison with measurement benchmarks. These comparisons validate the

calculational methodology by determining the bias and uncertainty in the calculated fluences, E >

1 MeV. A fast-neutron fluence, E > 1 MeV, must be obtained for each detector as the quotient of

the measured reaction probability and the effective E > 1-MeV spectrum averaged cross-section

(Ref. 100) based on a neutron transport calculation. These fluences and a suitably weighted

average fluence must be reported together with the associated measurement uncertainty

determined using the methods of Regulatory Positions 2.1.3 and 2.2 and accounting for the crosssection uncertainty. An alternative to deriving a neutron fluence from the detector responses is to

directly compare specific end-of-irradiation activities, measured reaction probabilities, isotopic

production, total reactions, average reaction, or measured reaction rates with results from the

neutron transport calculation. The response selected should provide a reliable indication of the

uncertainty and bias in the E > 1 MeV fluence calculation. 

The measurement biases and uncertainties must be documented for the selected detector

response. Based on the measurement-to-calculation (M/C) comparisons, an average M/C ratio

should be determined as a suitably weighted average of the individual M/C values. In determining

the weighting for this average, as a minimum the measurement and spectral average cross-section

uncertainties should be considered. An estimate of the uncertainty in the neutron spectrum may

be included as an additional contributor to the dosimeter weighting. 

 When justification can be provided, an individual detector may be declared suspect and

given reduced weight or discarded. However, in this case the justification and procedure used

must be documented.

2.4 Ex-vessel Dosimetry

As-built in-vessel surveillance capsule dosimetry cannot easily be updated. Furthermore,

the dosimetry irradiated with metallurgical specimens is only available at infrequent intervals. 

However, additional and upgraded dosimetry is important for understanding and following vessel
28

exposures, especially for low-leakage core modifications. The ex-vessel cavity may be used as an

alternative site for installing additional improved dosimetry. Recent pressure vessel benchmark

experiments (Refs. 7, 67, 94) have demonstrated that the ex-vessel dosimetry can provide useful

exposure information within the pressure vessel wall (Refs. 72, 81). When placed at appropriate

circumferential locations, this dosimetry is a good monitor of the effectiveness of low-leakage

core strategies.

3. REPORTING

When fluence determinations are required by the regulations, the licensee's documentation

describing the determination of pressure vessel fluence must provide a complete description of the

methods used to calculate and measure the neutron fluences. In applying the methodology of this

guide, the details of the application and the results should be reported as described in this section. 

A topical report providing the details of the fluence methodology, as outlined in Regulatory

Positions 1 and 2, should be satisfactory for compliance with this guide. Plant-specific

measurements and data should be reported in the pressure vessel surveillance reports. 

The specific regulatory positions on reporting are given in this section and are summarized

in Table 1, ìSummary of Regulatory Positions on Calculation and Dosimetry.î

3.1 Fluence Methods

The methods used to calculate the integral and multigroup fluences and fluence rates and

associated methods qualification should be reported. The calculational uncertainty analysis,

benchmark comparisons, and the determination of the overall fluence uncertainty should be

described in detail. If the calculated fluence is adjusted, the fluence adjustment and associated

uncertainty together with justification must be reported. A discussion of any deviations from the

procedures provided in this regulatory guide should be included. The source of the cross-section

data, the numerical methods (e.g., quadrature, mesh, and convergence criteria), and the treatment

of special effects (e.g., fuel burnup, axial effects, and pin-power distributions) should be described

in detail.

3.2 Multigroup Fluences

The calculated absolute multigroup neutron fluences and fluence rates at the peak wall (or

other limiting) location, surveillance locations, and T/4 and 3T/4 positions within the pressure

vessel should be reported. The multigroup energy boundaries should be included. 

3.3 Integral Fluences

The calculated E > 1 MeV integral fluences and fluence rates at the vessel inner wall

locations (determined as described in Regulatory Position 1.4.3), together with the uncertainties,

should be reported.
29

3.4 Comparisons of Calculation and Measurement

If the qualification of the calculation methods is performed using fluence comparisons, the

measured and calculated E > 1 MeV integral neutron fluences should be reported. If the methods

qualification is performed using reaction rate comparisons (or other responses as described in

Regulatory Position 2.3), the calculated and measured reaction rates (or reaction probabilities)

should be reported. The spectrum-averaged reaction cross-section used to relate the fluence and

reaction rate and the method for its determination should also be provided. In either case, the

M/C ratios and the measurement uncertainty should be reported for the average fluence and for

each detector at each measurement location. If these measurements are used to adjust the

calculation, the adjustment should be described and the M/C ratios before and after adjustment

should be reported.

3.5 Specific Activities and Average Reaction Rates

The specific activities at the end of irradiation and the measured average reaction rates

should be reported, together with the associated uncertainty tables and the power-time history. 

For each dosimeter, provide the reaction type, dosimeter material and form (wire, foil, etc.),

weight-percent and isotopic-percent of the target material, fission yields, and half-lives. The

corrections for the detector response perturbations, interfering reactions, and photofission should

also be described. The results of the measurement validation should also be described. If

thermal-neutron fluence rate measurements have been performed, these should be reported

together with the uncertainty and the dosimeter thermal-neutron shield material.

D. IMPLEMENTATION

The purpose of this section is to provide information to applicants and licensees regarding

the NRC staffís plans for using this regulatory guide.

Except in those cases in which an applicant or licensee proposes an acceptable alternative

method for complying with the specified portions of the NRCís regulations, the methods 

described in this guide will be used in the evaluation of applications for new licenses and for

evaluating compliance with 10 CFR 50.61 and Appendix G to 10 CFR Part 50, which is imposed

by 10 CFR 50.60.
30

TABLE 1. SUMMARY OF REGULATORY POSITIONS ON 

CALCULATION AND DOSIMETRY

FLUENCE CALCULATION METHODS Regulatory

Position

Fluence Determination. Absolute fluence calculations, rather than extrapolated

fluence measurements, must be used for the fluence determination.

1.3

Modeling Data. The calculation modeling (geometry, materials, etc.) should be

based on documented and verified plant-specific data.

1.1.1

Nuclear Data. The latest version of the Evaluated Nuclear Data File (ENDF/B)

should be used for determining nuclear cross-sections. Cross-section sets based on

earlier or equivalent nuclear-data sets that have been thoroughly benchmarked are

also acceptable. When the recommended cross-section data change, the effect of

these changes on the licensee-specific methodology must be evaluated and the

fluence estimates updated when the effects are significant.

1.1.2

Cross-Section Angular Representation. In discrete ordinates transport

calculations, a P3 angular decomposition of the scattering cross-sections (at a

minimum) must be employed.

1.1.2

Cross-Section Group Collapsing. The adequacy of the collapsed job library must

be demonstrated by comparing calculations for a representative configuration

performed with both the master library and the job library.

1.1.2

Neutron Source. The core neutron source should account for local fuel isotopics

and, where appropriate, the effects of moderator density. The neutron source

normalization and energy dependence must account for the fuel exposure

dependence of the fission spectra, the number of neutrons produced per fission, and

the energy released per fission.

1.2

End-of-Life Predictions. Predictions of the vessel end-of-life fluence should be

made with a best-estimate or conservative generic power distribution. If a best

estimate is used, the power distribution must be updated if changes in core loadings,

surveillance measurements, or other information indicate a significant change in

projected fluence values.

1.2

Spatial Representation. Discrete ordinates neutron transport calculations should

incorporate a detailed radial- and azimuthal-spatial mesh of ~2 intervals per inch

radially. The discrete ordinates calculations must employ (at a minimum) an S8

quadrature and (at least) 40 intervals per octant.

1.3.1
Regulatory

Position 

31

Multiple Transport Calculations. If the calculation is performed using two or

more "bootstrap" calculations, the adequacy of the overlap regions must be

demonstrated.

1.3.1

Point Estimates. If the dimensions of the tally region or the definition of the

average-flux region introduce a bias in the tally edit, the Monte Carlo prediction

should be adjusted to eliminate the calculational bias. The average-flux region

surrounding the point location should not include material boundaries or be located

near reflecting, periodic, or white boundaries.

1.3.2

Statistical Tests. The Monte Carlo estimated mean and relative error should be

tested and satisfy all statistical criteria.

1.3.2

Variance Reduction. All variance reduction methods should be qualified by

comparison with calculations performed without variance reduction.

1.3.2

Capsule Modeling. The capsule fluence is extremely sensitive to the geometrical

representation of the capsule geometry and internal water region, and the adequacy

of the capsule representation and mesh must be demonstrated.

1.3.3

Spectral Effects on RTNDT. In order to account for the neutron spectrum

dependence of RTNDT, when it is extrapolated from the inside surface of the pressure

vessel to the T/4 and 3T/4 vessel locations using the E > 1-MeV fluence, a spectral

lead factor must be applied to the fluence for the calculation of ∆RTNDT.

1.3.3

Cavity Calculations. In discrete ordinates transport calculations, the adequacy of

the S8 angular quadrature used in cavity transport calculations must be

demonstrated.

1.3.5

Methods Qualification. The calculational methodology must be qualified by both

(1) comparisons to measurement and calculational benchmarks and (2) an analytic

uncertainty analysis. The methods used to calculate the benchmarks must be

consistent (to the extent possible) with the methods used to calculate the vessel

fluence. The overall calculational bias and uncertainty must be determined by an

appropriate combination of the analytic uncertainty analysis and the uncertainty

analysis based on the comparisons to the benchmarks.

1.4.1,

1.4.2,

1.4.3

Fluence Calculational Uncertainty. The vessel fluence (1 sigma) calculational

uncertainty must be demonstrated to be 20% for RTPTS and RTNDT determination. 

In these applications, if the benchmark comparisons indicate differences greater

than 20%, the calculational model must be adjusted or a correction must be applied

to reduce the difference between the fluence prediction and the upper 1-sigma limit

to within 20%. For other applications, the accuracy should be determined using the

approach described in Regulatory Position 1.4, and an uncertainty allowance should

be included in the fluence estimate as appropriate in the specific application.

1,

1.4.3
Regulatory

Position 

32

FLUENCE MEASUREMENT METHODS

Spectrum Coverage. The set of dosimeters should provide adequate spectrum

coverage.

2.1.1

Dosimeter Nuclear and Material Properties. Use of dosimeter materials should

address melting, oxidation, material purity, total and isotopic mass assay,

perturbations by encapsulations and thermal shields, and accurate dosimeter

positioning. Dosimeter half-life and photon yield and interference should also be

evaluated.

2.1.1

Corrections. Dosimeter-response measurements should account for fluence rate

variations, isotopic burnup effects, detector perturbations, self shielding, reaction

interferences, and photofission.

2.1.2

Response Uncertainty. An uncertainty analysis must be performed for the

response of each dosimeter. 

2.1.3

Validation. Detector-response calibrations must be carried out periodically in a

standard neutron field.

2.2

Fast-Neutron Fluence. The E > 1 MeV fast-neutron fluence for each

measurement location must be determined using calculated spectrum-averaged

cross-sections and individual detector measurements. As an alternative, the

detector responses may be used to determine reaction probabilities or average

reaction rates.

2.3

Measurement-to-Calculation Ratios. The M/C ratios, the standard deviation and

bias between calculation and measurement, must be determined.

2.3

REPORTING PROVISIONS

Neutron Fluence and Uncertainties

Details of the absolute fluence calculations, associated methods qualification and

fluence adjustments (if any) should be reported. Justification and a description of

any deviations from the provisions of this guide should be provided.

3.1

Calculated multigroup neutron fluences and fluence rates should be reported. 3.2

The value and basis of any bias or model adjustment made to improve the

measurement-to-calculation agreement must be reported.

3.2
Regulatory

Position 

33

Calculated integral fluences and fluence rates for E > 1 MeV and their uncertainties

should be reported.

3.3

Measured and calculated integral E > 1 MeV fluences or reaction rates and

uncertainties for each measurement location should be reported. The M/C ratios

and the spectrum averaged cross-section should also be reported.

3.4

The results of the standard field validation of the measurement method should be

reported.

3.5

Specific Activities and Average Reaction Rates

The specific activities at the end of irradiation and measured average reaction rates

with uncertainties should be reported.

3.5

All corrections and adjustments to the measured quantities and their justification

should be reported.

3.5
34

TABLE 2. THRESHOLD DETECTORS RECOMMENDED FOR 

PRESSURE VESSEL DOSIMETRY

Nominal

Threshold (MeV)

Applicable

ASTM Standards

237Np(n,f)FP* 0.69 E 705 (Ref. 83)

93Nb(n,ní)93mNb 0.97 E 1297 (Ref. 84)

238U(n,f)FP 1.45 E 704 (Ref. 85)

58Ni(n,p)58Co 2.05 E 264 (Ref. 86)

54Fe(n,p)54Mn 2.32 E 263 (Ref. 87)

46Ti(n,p)46Sc 3.76 E 526 (Ref. 88)

63Cu(n,α)60Co 4.65 E 523 (Ref. 89)

* FP indicates fission product.
35
36

Figure 2. Monte Carlo Calculation Methodology

Cycle-Dependent

Assembly/Pin

Powers &

Exposures

Multi-Group

Library

(Optional)

Component

Material

Compositions

Macroscopic

CrossSections Isotopic Fission Spectra MCNP* Source

Core/Internals/

Vessel 

Geometry

MCNP

Fluence

3-D Vessel

Fluence

Estimate

(1.2)Ü (1.1.1) (1.1.2.2)

(1.3.2)

(1.1.1)

Ü Relevant Regulatory Positions are 

* The MCNP code is used as an exa
Calculation Bias Based on Analytic

(Benchmark) Uncertainty Analysis

σ Estimated Calculation Uncertainty 

C (BC) 

Calculational Uncertainty Based onAnalytic (Benchmark) UncertaintyAnalysis

Figure 3. Calculation Methodology Qualification Procedure

Fluence Calculation

Methods

σCa (σCb) BCa (BCb) 

Sensitivity

Analysis

(Φ/X)

Uncertainty

Determination

(Φ/X)ï∆X

Plant

Model Input

Estimated

Calculation

Uncertainties

& Biases

(∆X)

Combine

Analytic & 

Benchmark

Estimates

Calculation

Methods Revision

(When Necessary)

AgreementAcceptable

Plant

Model

Input

Calculation of 

Operating

Reactor

Measurements

Simulator

Model Input

Calculation

of Simulator

Benchmarks

CalculationalBenchmarkModel Input

Calculatio

of Benchma

Problem

Capsule/

Cavity

Measurement

Data

Simulator

Measurement

Data

Benchmark

Solution

Compariso

of Results

Comparison

of Results

Comparison

of Results

Combine

Benchmark

Uncertainty/

Bias 

Estimates

(1.4)*

Analytic

Uncertainty

Analysis

Benchmark

Uncertainty

Analysis (1.4.2)

(1.4.1)

* Relevant Regulatory Positions are indicated.

(1.4.2.1) (1.4.2.2) (1.4.2.3)

(1.4.3)

σCa , BCa

σC, BC

σCb, BCb

Resolution 

Difference
38

Φ = Φ [Equation (6)]

Figure 4. Uncertainty-Dependent Fluence Determination

*

Relevant Regulatory Position
Fluence

Measurement

Methods

Dosimeter 

Uncertainty

Analysis

Periodic Validationin Standard and/orReference Fields

Combine

Uncertainty &

Bias Estimates

Dosimeter

Measurement

Uncertainties

& Biases

Ce

Spe

MeasuremBased on AUncertainty 

MeasuremAnalytic (VAnalysis

Estimated Uncertaint

* Relevant Regulatory Positions are indicated.

(2.1.3)* (2.2)

Figure 5. Measurement Qualification Procedure

σMv , BM σ v Ma , BMa

σM, BM

σMa , (σMv ) -BMa , (BMv ) -

σM, (BM ) -
1

 Available from the American Society for Testing and Materials, 1916 Race Street, Philadelphia, PA 19103-1187.

2

 Copies are available for inspection or copying for a fee from the NRC Public Document Room at 11555 Rockville Pike,

Rockville, MD; the PDR's mailing address is USNRC PDR, Washington, DC 20555; telephone (301)415-4737; fax (301)415-

3548. 

3

 Copies may be purchased at current rates from the U.S. Government Printing Office, Post Office Box 37082, Washington, DC

20013-7082 (telephone (202)512-2249 or (202)512-2171); or from the National Technical Information Service by writing NTIS

at 5285 Port Royal Road, Springfield, VA 22161. Copies are available for inspection or copying for a fee from the

NRC Public Document Room at 11555 Rockville Pike, Rockville, MD; the PDR's mailing address is USNRC PDR,

Washington, DC 20555; telephone (301)415-4737; fax (301)415-3548. 

4 Available from the Radiation Safety Information Computational Center, Oak Ridge National Laboratory, Post Office Box 2008,

Oak Ridge, TN 37831-6362.

40

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Dosimetry, ASTM STP 1398 (J.G. Williams et al., Eds.), ASTM, West Conshohoken, PA.

2000.1

79. A. Haghighat, H. Ait Abderrahim, and G.E. Sjoden, ìAccuracy and Performance of

PENTRANTM Using the VENUS-3 Benchmark Experiment,î Reactor Dosimetry, ASTM STP

1398 (J.G. Williams et al., Eds.), ASTM, West Conshohoken, PA. 2000.1

80. R.E. Maerker and B.A. Worley, "Activity and Fluence Calculations for the Startup and TwoYear Irradiation Experiments Performed at the Poolside Facility," NUREG/CR-3886 (Prepared

for NRC by Oak Ridge National Laboratory, ORNL/TM-4265), October 1984.2

81. W.N. McElroy, "LWR Pressure Vessel Surveillance Dosimetry Improvement Program. PSF

Experiments Summary and Blind Test Results," NUREG/CR-3320, Vols. 1-4 USNRC,

(Prepared for the NRC by Hanford Engineering Development Laboratory), July 1986 through

July 1992.2

82. G. L. Guthrie, E. P. Lippincott, E. D. McGarry, îLight Water Reactor Pressure Vessel

Surveillance Dosimetry Improvement Program: PSF Blind Test Workshop Minutes,î

Westinghouse Hanford Company, April 1994.1

83. "Standard Test Method for Measuring Reaction Rates by Radioactivation of Neptunium-237,"

ASTM E 705-90, ASTM, Philadelphia, 1991.1

84. "Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of

Niobium," ASTM E1297-89, ASTM, Philadelphia, 1989.1

85. "Standard Test Method for Measuring Reaction Rates by Radioactivation of Uranium-238,"

ASTM E 704-90, ASTM, Philadelphia, 1991.1

86. "Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of

Nickel," ASTM E 264-87, ASTM, Philadelphia, 1987.1

87. "Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Iron,"

ASTM E 263-88, ASTM, Philadelphia, 1988.1

88. "Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of

Titanium," ASTM E 526-87, American Society for Testing and Materials, Philadelphia, 1987.1

89. "Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of

Copper," ASTM E 523-87, ASTM, Philadelphia, 1987.1

90. "Standard Guide for Sensor Design and Irradiation for Reactor Surveillance, E 706 (IIC),"

ASTM E 844-86, ASTM, Philadelphia, 1986.1
8

Available from the National Institute of Standards and Technology, NIST Publication Productions, Room A635, Gaithersburg,

MD 20899.

48

91. "Standard Test Method for Application and Analysis of Radiometric Monitors for Reactor

Vessel Surveillance, E 706 (IIIA)," ASTM E 1005-84, ASTM, Philadelphia, 1984.1

92. "Standard General Methods for Detector Calibration and Analysis of Radionuclides," ASTM E

181-82, ASTM, Philadelphia, 1983.1

93. R. Gold et al., "Neutron Dosimetry with Solid-State Track Recorders in the Three-Mile Island

Unit-2 Reactor Cavity," Nuclear Tracks, Vol. 103, p. 447, 1985.

94. F.H. Ruddy et al., "Solid-State Track Recorder Neutron Dosimetry in Light-Water Reactor

Pressure Vessel Surveillance Mockups in Reactor Dosimetry,"Proceedings of the 5th ASTMEURATOM Symposium on Reactor Dosimetry, Geesthacht, Federal Republic of Germany, Sept.

24-28, 1984, EUR 9869, Commission of the European Communities, D. Reidel Publishing Co.,

1985.1

95. "Standard Test Method for Application and Analysis of Solid State Track Recorder (SSTR)

Monitors for Reactor Surveillance, E 706 (IIIB)," ASTM E 854-90, ASTM, Philadelphia, 1990.1

96. "Standard Test Method for Application and Analysis of Helium Accumulation Fluence Monitors

for Reactor Vessel Surveillance, E 706(IIIC)," ASTM E 910 95, ASTM, Philadelphia, 1995.1

97. J.A. Grundl and C.M. Eisenhauer, Compendium of Benchmark Neutron Fields for Reactor

Dosimetry, NBSIR 85-3151, National Bureau of Standards, Gaithersburg, MD, January 1986.8

98. A. Hawari et al., "Materials Dosimetry Reference Facility," Proceedings of the Eighth ASTMEuratom Symposium on Reactor Dosimetry, Vail, Colorado, August 1993.1

99. "Standard Guide for Benchmark Testing of Light Water Reactor Caalculations,î ASTM E2006-

99, ASTM, Philadelphia, 1999.1

100. "Standard Practice for Determining Neutron Fluence, Fluence Rate and Spectra by

Radioactivation Techniques,î ASTM E261-98, ASTM, Philadelphia, 1998.1
49

REGULATORY ANALYSIS

1. STATEMENT OF THE PROBLEM

The U.S. Nuclear Regulatory Commission (NRC) has promulgated regulations to ensure the

structural integrity of the reactor pressure vessel for light water power reactors. Specific fracture

toughness requirements for normal operation and for anticipated operational occurrences for power

reactors are set forth in Appendix G, "Fracture Toughness Requirements," to 10 CFR Part 50,

"Domestic Licensing of Production and Utilization Facilities." These requirements are imposed

through 10 CFR 50.60. Additionally, in response to concerns over potential pressurized thermal

shock (PTS) events in pressurized water reactors (PWRs), the NRC issued 10 CFR 50.61,

"Fracture Toughness Requirements for Protection Against Pressurized Thermal Shock Events."

To satisfy the requirements of Appendix G; 10 CFR 50.61; Criterion 14, ìReactor Coolant

Pressure Boundary,î Criterion 30, ìQuality of Reactor Coolant Pressure Boundary,î and Criterion

31, ìFracture Prevention of Reactor Coolant Pressure Boundary,î of Apppendix A, ìGeneral

Design Criteria for Nuclear Power Plants,î to 10 CFR Part 50, methods for determining the fast

neutron fluence (E > MeV) are necessary to estimate the fracture toughness of the pressure vessel

materials. Appendix H, "Reactor Vessel Material Surveillance Program Requirements," to 10 CFR

Part 50 requires the installation of surveillance capsules, including material test specimens and flux

dosimeters, to provide data on material damage correlations as a function of fluence.

The neutron fluence is attenuated by several decades between the core and vessel. This

attenuation results in a strong sensitivity of the calculated vessel fluence to the physical description

of the core and vessel internals and the numerical calculation of the neutron transport, and it makes

an accurate determination of the pressure vessel fluence difficult. As a result, a wide range of

methods of varying reliability and accuracy have been used to determine the reactor vessel fluence. 

Consequently, comparisons of measured and calculated fluences have shown varying degrees of

agreement, and in some cases conservatisms have been required in licensing analyses to

accommodate the observed measurement-to-calculation differences.

Over the past decade, substantial improvements have been made in both the calculation and

measurement of the pressure vessel fluence. These improvements have stemmed from both NRC

and industry programs. These include the development and improvement of computer codes,

calculational models, measurement techniques and basic cross-section data, and the systematic

qualification of the fluence methods by comparison to NRC-sponsored benchmark experiments.

These calculation and measurement improvements provide increased accuracy in the fluence

determinations that are an essential part of meeting the requirements of Appendices G to 10 CFR

Part 50 and 10 CFR 50.61. This is especially important for plants seeking to renew their operating

licenses. 

The wide variation in fluence calculation methods has resulted in lengthy plant-specific

reviews and made it difficult to confirm, during the review process, that the actual fluence is

adequately bounded by the various calculational methods used. This calculation and dosimetry
50

guide would provide standardized methods and procedures that would allow these reviews to be

greatly simplified, and would improve confidence in the calculated fluence values.

2. OBJECTIVE

The objective of this guide is to provide state-of-the-art calculation and measurement

procedures that are acceptable to the NRC staff for determining pressure vessel fluence. These

procedures would yield a more accurate and reliable vessel fluence determination than the

procedures that have been used in the past. The improved accuracy and realistic assessment of the

uncertainty in the calculation would provide assurance that the fluence value is appropriate for use

in evaluating compliance with the regulations. 

3. ALTERNATIVES

The alternatives to issuing the vessel fluence calculation and dosimetry regulatory guide are

as follows:

3.1 Branch Technical Position

The pressure vessel fluence methods provided by the regulatory guide could be included in a

branch technical position. However, this is not considered an acceptable alternative since the

branch position does not provide the same high level of input and participation, especially public,

industry, and the ACRS input, that the vessel fluence analysis requires.

3.2 NUREG-Series Report

The vessel fluence procedures could be published in a NUREG-series report. However,

these reports also do not receive the required input and participation from the public, industry, and

the ACRS and they are not appropriate for providing regulatory guidance.

3.3 Discussions with Licensees

The detailed fluence calculational and measurement methods that are considered acceptable

to the NRC staff could be provided to the licensees through individual reviews and discussions on

a case-by-case basis. This alternative is basically the same as the current practice and is equivalent

to taking no action. Individual licensee discussions are extremely time-consuming for both the

NRC staff and the licensee, they lead to highly individual analyses and reviews, and they do not

result in an established standard.

4. COSTS AND BENEFITS

4.1 Benefits

The methods described in this guide may be used for all fluence determinations used in

vessel fracture toughness evaluations, including the determination of the fluence used in

calculating the pressure vessel material values of RTNDT specified in Appendix G to 10 CFR Part

50 imposed by 10 CFR 50.60, and the values of RTPTS specified in 10 CFR 50.61. The regulatory
51

guide would improve the accuracy and reliability of these evaluations and provide consistent and

reliable uncertainty estimates by incorporating state-of-the-art methods and procedures for

determining the fluence and the fluence uncertainty. The guide would also ensure the

completeness of licensee vessel fluence submittals and improve the efficiency of staff reviews.

The improved fluence determination will provide fluence and uncertainty estimates that are

more reliable and understandable. Thus, it will provide more reliable and accurate information for

the PTS screening criteria of 10 CFR 50.61 and improve application of this rule. In this regard it is

noted that, for a pressure vessel near the PTS screening criteria of 10 CFR 50.61, a 25% reduction

in calculated end-of-license fluence, which is typical of existing uncertainties, will reduce the

calculated vessel failure frequency by approximately a factor of three.

4.2 NRC Costs

The NRC costs for reviewing fluence-related submittals would be reduced substantially by

the issuance of this guide. For estimating the costs, it is assumed that of the ~60 PWRs, half have

a RTPTS within ~40F of the PTS screening criterion (or other temperature limit) at the end of

license and will require a detailed review. Assuming each submittal requires a staff week and only

half of the PWR owners submit revised fluence analyses, the total NRC cost is approximately 15

staff weeks. If the licensees used the methods given in the guide, this cost could be reduced to

approximately 2 staff weeks.

4.3 Licensee Costs

Increased costs to the licensee would result from changes in the fluence calculation and

measurement procedures. The calculational costs would be one-time costs and have been

estimated in Table RA-1. The licensee costs resulting from the changes in the measurement

procedures have been estimated in Table RA-2.

5. DECISION RATIONALE

It is recommended that the proposed regulatory guide be issued because (1) a high level of

participation of the NRC, ACRS, industry, and the public is reflected in the guide, (2) a

methodology standard would be established, and (3) inefficient use of NRC staff and licensee

resources during the review process would be eliminated.

The alternatives identified above for providing acceptable fluence methods to the licensees

do not provide the advantages listed above associated with issuance of this regulatory guide. In

particular, while these alternative approaches may result in the same or slightly increased cost to

licensees, they result in a highly inefficient use of the NRC staff resources. The alternatives to a

regulatory guide are therefore judged to be unacceptable.
* This estimate reflects the reduced licensee costs from not attending meetings with the NRC staff and responding to questions as

a result of following the procedures in the regulatory guide.

52

TABLE RA-1. ADDITIONAL LICENSEE CALCULATION COSTS

Calculation Tasks Staff Weeks

(a) Modifications to calculational models + 2

(b) Additional calculation benchmarking and

qualification

+ 8

(c) Calculation uncertainty analysis + 3

(d) Calculation documentation and reporting + 2

(e) Reduced Licensing Activities* - 4

Total Additional Licensee Cost +11 staff weeks

TABLE RA-2. ADDITIONAL LICENSEE MEASUREMENT COSTS

Measurement Task Staff Weeks

(a) Additional Quality Control + 1

(b) Dosimeter Response Corrections + 1

(c) Periodic Detector Calibration + 2

(d) Response Uncertainty Analysis + 2

(e) Additional Measurement

Documentation and Reporting

+ 1

Total Additional Licensee Cost + 7 staff weeks
BACKFIT ANALYSIS

The regulatory guide does not require a backfit analysis as described in 10 CFR 50.109(c)

because it does not impose a new or amended provision in the Commission rules or a regulatory

staff position interpreting the Commission rules that is either new or different from a previous

applicable staff position. In addition, this regulatory guide does not require the modification or

addition to systems, structures, components, or design of a facility or the procedures or

organization required to design, construct, or operate a facility. Rather a licensee or applicant can

select a preferred method for achieving compliance with license or the rules or the orders of the

Commission as described in 10 CFR 50.109(a)(7). The regulatory guide provides the opportunity

to use the methods described in the guide for all fluence determinations used in vessel fracture

toughness evaluations, including the determination of the fluence used in calculating the pressure

vessel materials' values of RTNDT for use in 10 CFR Part 50, Appendix G (imposed by 10 CFR

50.60), and the values of RTPTS in accordance with 10 CFR 50.61.