**Evaluation Guide FOR THE**

**INTERNATIONAL REACTOR PHYSICS EXPERIMENTS**

**EVALUATION PROJECT (IRPhEP)**

**Table of Contents**

Summary Information Guide 3

Status Sheet 5

Format Guide 8

Nuclear Constants 22

Commonly Used Symbols and Terms 25

References\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...\...27

**Summary Information**

(To be used for the report containing inventory of experiments and
linked to the first page of the evaluation)

1.  Experiment identification number

2.  Date

3.  Name of experiment

    1.  Purpose of experiment

    2.  Phenomena measured and scope

4.  Name or designation of experimental programme

5.  Description of facility

6.  Description of test or experiment

> 6.1 Experimental configuration

6.1.1 Type of assemblies

-   Zoned assembly

-   Clean benchmark assembly

-   Engineering benchmark assembly / engineering mockup core

-   Special purpose assemblies

    2.  Assembly details

        1.  Type

        2.  Fuel

        3.  Moderator

        4.  Absorbers

        5.  Critical mass

        6.  Core volume

        7.  Blanket

        8.  Reflectors

        9.  Reactivity adjustment

        10. Other

    3.  Assembly variants

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    1.  Core life cycle

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-   BOL

-   EOL

-   Other

    1.  Experimental limitations or shortcomings

6.  Phenomena measured

    1.  Description of results and analysis (values and evaluated
        uncertainties)

> 7.1.1 Reactivity control for criticality
>
> 7.1.2 Reaction rates / ratios

-   Capture

-   Fission

-   Other

> 7.1.3 Reactivity worth

-   Of samples

-   Expansion worth

-   Voided zone

-   Reflector worth

-   Other

> 7.1.4 Sample Doppler reactivity
>
> 7.1.5 Temperature coefficients
>
> 7.1.6 Control rod or rod-bank worths
>
> 7.1.7 Soluble boron worth
>
> 7.1.8 Gamma heating distributions
>
> 7.1.9 Neutron spectrum
>
> 7.1.10 Kinetic parameters
>
> 7.1.11 Reactor power distributions
>
> 7.1.12 Isotopic measurements
>
> 7.2 Special features and characteristics of experiment

1.  Moderator/fuel ratio

2.  Measured spectral indices

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2.  Measurement systems (methods) and uncertainties

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7.  Duplicate or complementary experiments / other related experiments

8.  Status of completion of the evaluation

9.  References (pointer to evaluation, archive if available, otherwise
    generic bibliographic reference)

10. Authors/ organisers

    1.  Establishment

    2.  Staff involved in experiment

    3.  Contact information

    4.  Reviewers of compiled data

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11. Material available

    1.  Data and Format

## Status of Compilation / Evaluation / Peer Review

+---------------------------+---------+----------+----------+----------+
| **Section 1**             | **Com   | **Ind    | *        | **Ap     |
|                           | piled** | ependent | *Working | proved** |
|                           |         | Review** | Group    |          |
|                           |         |          | Review** |          |
+---------------------------+---------+----------+----------+----------+
| 1.0   Detailed            |         |          |          |          |
| Description               |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.1   Description of the  |         |          |          |          |
| Critical and / or         |         |          |          |          |
|                           |         |          |          |          |
|        Subcritical        |         |          |          |          |
| Configuration             |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.2   Description of      |         |          |          |          |
| Buckling and              |         |          |          |          |
| Extrapolation             |         |          |          |          |
|         Length            |         |          |          |          |
| Measurements              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.3   Description of      |         |          |          |          |
| Spectral Characteristics  |         |          |          |          |
|         Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.4   Description of      |         |          |          |          |
| Reactivity Effects        |         |          |          |          |
|                           |         |          |          |          |
|         Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.5   Description of      |         |          |          |          |
| Reactivity Coefficient    |         |          |          |          |
|                           |         |          |          |          |
|         Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.6   Description of      |         |          |          |          |
| Kinetics Measurements     |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.7   Description of      |         |          |          |          |
| Reaction-Rate             |         |          |          |          |
| Distribution              |         |          |          |          |
|                           |         |          |          |          |
|        Measurements       |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.8   Description of      |         |          |          |          |
| Power Distribution        |         |          |          |          |
|         Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.9   Description of      |         |          |          |          |
| Isotopic Measurements     |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 1.10 Description of Other |         |          |          |          |
| Miscellaneous Types       |         |          |          |          |
|         of Measurements   |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| **Section 2**             | **Eval  | **Ind    | *        | **Ap     |
|                           | uated** | ependent | *Working | proved** |
|                           |         | Review** | Group    |          |
|                           |         |          | Review** |          |
+---------------------------+---------+----------+----------+----------+
| 2.0 Evaluation Of         |         |          |          |          |
| Experimental         Data |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.1  Evaluation of        |         |          |          |          |
| Critical and / or         |         |          |          |          |
| Subcritical               |         |          |          |          |
|         Configuration     |         |          |          |          |
| Data                      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.2  Evaluation of        |         |          |          |          |
| Buckling and              |         |          |          |          |
| Extrapolation             |         |          |          |          |
|         Length Data       |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.3   Evaluation of       |         |          |          |          |
| Spectral Characteristics  |         |          |          |          |
|                           |         |          |          |          |
|         Data              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.4   Evaluation of       |         |          |          |          |
| Reactivity Effects Data   |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.5   Evaluation of       |         |          |          |          |
| Reactivity Coefficient    |         |          |          |          |
| Data                      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.6   Evaluation of       |         |          |          |          |
| Kinetics Measurements     |         |          |          |          |
|                           |         |          |          |          |
|         Data              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.7   Evaluation of       |         |          |          |          |
| Reaction Rate             |         |          |          |          |
| Distributions             |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.8   Evaluation of Power |         |          |          |          |
| Distribution Data         |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.9   Evaluation of       |         |          |          |          |
| Isotopic Measurements     |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 2.10 Evaluation of Other  |         |          |          |          |
| Miscellaneous Types       |         |          |          |          |
|         of Measurements   |         |          |          |          |
+---------------------------+---------+----------+----------+----------+

+---------------------------+---------+----------+----------+----------+
| **Section 3**             | **Com   | **Ind    | **W      | **Ap     |
|                           | piled** | ependent | orking** | proved** |
|                           |         | Review** |          |          |
|                           |         |          | **Group  |          |
|                           |         |          | Review** |          |
+---------------------------+---------+----------+----------+----------+
| 3.0   Benchmark           |         |          |          |          |
| Specifications            |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.1   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|         Critical and / or |         |          |          |          |
| Subcritical               |         |          |          |          |
|                           |         |          |          |          |
|         Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.2   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|         Buckling and      |         |          |          |          |
| Extrapolation Length      |         |          |          |          |
|         Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.3   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|         Spectral          |         |          |          |          |
| Characteristics           |         |          |          |          |
| Measurements              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.4   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|         Reactivity        |         |          |          |          |
| Effects Measurements      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.5   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|         Reactivity        |         |          |          |          |
| Coefficient Measurements  |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.6   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|                           |         |          |          |          |
|     Kinetics Measurements |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.7   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|        Reaction-Rate      |         |          |          |          |
| Distribution Measurements |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.8   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|         Power             |         |          |          |          |
| Distribution Measurements |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.9   Benchmark-Model     |         |          |          |          |
| Specifications for        |         |          |          |          |
|                           |         |          |          |          |
|        Isotopic           |         |          |          |          |
| Measurements              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 3.10 Benchmark-Model      |         |          |          |          |
| Specifications of Other   |         |          |          |          |
|         Miscellaneous     |         |          |          |          |
| Types of Measurements     |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| **Section 4**             | **Com   | **Ind    | **W      | **Ap     |
|                           | piled** | ependent | orking** | proved** |
|                           |         | Review** |          |          |
|                           |         |          | **Group  |          |
|                           |         |          | Review** |          |
+---------------------------+---------+----------+----------+----------+
| 4.0  Results of Sample    |         |          |          |          |
|        Calculations       |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.1 Results of            |         |          |          |          |
| Calculations of the       |         |          |          |          |
| Critical or               |         |          |          |          |
|        Subcritical        |         |          |          |          |
| Configurations            |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.2 Results of Buckling   |         |          |          |          |
| and Extrapolation         |         |          |          |          |
|         Length            |         |          |          |          |
| Calculations              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.3   Results of Spectral |         |          |          |          |
| Characteristics           |         |          |          |          |
|                           |         |          |          |          |
|        Calculations       |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.4   Results of          |         |          |          |          |
| Reactivity Effect         |         |          |          |          |
| Calculations              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.5   Results of          |         |          |          |          |
| Reactivity Coefficient    |         |          |          |          |
|                           |         |          |          |          |
|         Calculations      |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.6  Results of Kinetics  |         |          |          |          |
| Parameter Calculations    |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.7  Results of           |         |          |          |          |
| Reaction-Rate             |         |          |          |          |
| Distribution              |         |          |          |          |
|                           |         |          |          |          |
|        Calculations       |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.8  Results of Power     |         |          |          |          |
| Distribution Calculations |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.9  Results of Isotopic  |         |          |          |          |
| Calculations              |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| 4.10 Results of           |         |          |          |          |
| Calculations of Other     |         |          |          |          |
|                           |         |          |          |          |
|                           |         |          |          |          |
|       Miscellaneous Types |         |          |          |          |
| of Measurements           |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| **Section 5**             | **Com   | **Ind    | *        | **Ap     |
|                           | piled** | ependent | *Working | proved** |
|                           |         | Review** | Group    |          |
|                           |         |          | Review** |          |
+---------------------------+---------+----------+----------+----------+
| 5.0 REFERENCES            |         |          |          |          |
+---------------------------+---------+----------+----------+----------+
| Appendix A: Computer      |         |          |          |          |
| Codes, Cross Sections,    |         |          |          |          |
| and Typical Input         |         |          |          |          |
| Listings                  |         |          |          |          |
+---------------------------+---------+----------+----------+----------+

##### **Evaluation Guide for the International Reactor Physics Experiments Evaluation Project (IRPhEP)**

***General Format Guidelines***

*Final formatting, in terms of the document, including text, table and
graphics, will be done by the publication staff. Evaluators are
encouraged to follow the standard formatting guidelines outlined below,
but should allow the publication staff to perform final formatting, to
ensure consistency in evaluations contained within the Handbook.
Publication templates will be used to ensure this consistency.
Evaluations containing special/individual formatting functions, such as
auto table/figure numbering, may interfere with the template styles and
capabilities. Such special formatting functions should be avoided.*

*Note: Although final formatting will be done by the publication staff,
evaluators should number tables and figures sequentially within sections
(e.g., For Section 2 tables/figures, label as Table/Figure 2.1, 2.2,
etc.). Authors of evaluations with unusually large numbers of figures
and tables may, at their discretion, use additional levels of
Table/Figure numbering (e.g., For Section 2 tables/figures, label as
Table/Figure 2.1.1, 2.1.2, etc. or Table 2.1.1.1, 2.1.1.2, etc.);
however numbering must be consistent throughout the evaluation and in no
case should more than four levels be used.*

*General presentation guidelines that evaluators should follow are given
below:*

-   *Paper size should be"A4".*

-   *Use 11-point, Times New Roman font for main text.*

-   *Main text should be left-justified.*

-   *Margins should be set as follows: top and bottom margins - .3
    inches; left-hand margins -- 1 inch; and right-hand margins - .8
    inches.*

##### **DOCUMENT FORMAT GUIDE**

**EXPERIMENT TITLE**

**IDENTIFICATION NUMBER:**

Each experiment has a unique identifier that consists of two parts. Part
1 consists of the Reactor Name, Reactor Type, Facility Type and a Three
Digit Numerical Identifier. Part 2 of the identifier begins on a
separate line and includes the Measurement Type(s). Identifiers take the
following form:

(Reactor Name)-(Reactor Type)-(Facility Type)-(Three-Digit Numerical
Identifier)

(Measurement Type(s))

+----------------+------+---------+------+--------------------+------+
| Reactor Type   |      | F       |      | Measurement Type   |      |
|                |      | ACILITY |      |                    |      |
|                |      | Type    |      |                    |      |
+----------------+------+---------+------+--------------------+------+
| Pressurized    | PWR  | Exper   | EXP  | Critical           | CRIT |
| Water Reactor  |      | imental |      | Configuration      |      |
|                |      |         |      |                    |      |
|                |      | Facili  |      |                    |      |
|                |      | ty^(1)^ |      |                    |      |
+----------------+------+---------+------+--------------------+------+
| VVER Reactors  | VVER | Power   | P    | Subcritical        | SUB  |
|                |      | Reactor | OWER | Configuration      |      |
+----------------+------+---------+------+--------------------+------+
| Boiling Water  | BWR  | R       | RESR | Buckling &         | BUCK |
| Reactor        |      | esearch |      | Extrapolation      |      |
|                |      | Reactor |      | Length             |      |
+----------------+------+---------+------+--------------------+------+
| Liquid Metal   | LMFR |         |      | Spectral           | SPEC |
| Fast Reactor   |      |         |      | Characteristics    |      |
+----------------+------+---------+------+--------------------+------+
| Gas Cooled     | GCR  |         |      | Reactivity Effects | REAC |
| (Thermal)      |      |         |      |                    |      |
|                |      |         |      |                    |      |
| Reactor        |      |         |      |                    |      |
+----------------+------+---------+------+--------------------+------+
| Gas Cooled     | GCFR |         |      | Reactivity         | COEF |
| (Fast) Reactor |      |         |      | Coefficients       |      |
+----------------+------+---------+------+--------------------+------+
| Light Water    | LWR  |         |      | Kinetics           | KIN  |
| Moderated      |      |         |      | Measurements       |      |
|                |      |         |      |                    |      |
| Reactor        |      |         |      |                    |      |
+----------------+------+---------+------+--------------------+------+
| Heavy Water    | HWR  |         |      | Reaction-Rate      | R    |
| Moderated      |      |         |      | Distributions      | RATE |
| Reactor        |      |         |      |                    |      |
+----------------+------+---------+------+--------------------+------+
| Molten Salt    | MSR  |         |      | Power              | PO   |
| Reactor        |      |         |      | Distributions      | WDIS |
+----------------+------+---------+------+--------------------+------+
| RBMK Reactor   | RBMK |         |      | Isotopic           | ISO  |
|                |      |         |      | Composition        |      |
+----------------+------+---------+------+--------------------+------+
| Fundamental    | FUND |         |      | Other              | MISC |
|                |      |         |      | Miscellaneous      |      |
|                |      |         |      | Types of           |      |
|                |      |         |      | Measurements       |      |
+----------------+------+---------+------+--------------------+------+

\(1\) Generally, experimental facilities are easily modified to
represent a wide variety of core configurations and often criticality is
achieved by a means other than control rod position (control rods are
typically fully withdrawn).  Facilities for which the primary focus is
the production of integral-experiment data that support ex-core
activities such as handling and storage of fissile material are also
categorized as experimental facilities.  

Examples of identifiers are:

ZPR-LMFR-EXP-001

CRIT-SPEC-REAC-COEF-KIN-RRATE

This identifier corresponds to the first evaluation of measurements made
on the ZPR liquid metal fast reactor experimental facility. The critical
configuration, spectral measurements, reactivity measurements and
coefficients, kinetics parameters, and reaction rates were measured and
the data are provided.

VENUS-PWR-EXP-001

BUCK-RRATE-POWDIS

This identifier corresponds to the first evaluation of measurements made
on the VENUS pressurized water reactor experimental facility. Buckling
and extrapolation length, reaction rate, and power distributions were
measured and the data are provided.

ZR6-VVER-EXP-001

CRIT-BUCK-SPEC-REAC-COEF-RRATE

This identifier corresponds to the first evaluation of measurements made
on the ZR-6 VVER experimental facility. The critical configuration,
buckling and extrapolation length, reaction rate, spectral measurements,
reactivity measurements and coefficients, and reaction rates were
measured and the data are provided.

**KEY WORDS:**

A list of words that describe key features of the experiment is
provided. Keywords include the fissile material of the reactor as well
as moderator and reflector materials (e.g., low-enriched uranium,
light-water-moderated, graphite-reflected, unreflected).

***Section 1 General Guidelines***

*A detailed description of the experiments and all relevant experimental
data are provided in the appropriate subsections within this section.
The detailed description includes the measurement methods used and the
results obtained for the parameters of interest, as well as methods used
to obtain the experimental data. Experimental data are values of
parameters that are needed to completely describe the experiment and
that have been directly measured. Examples are dimensions obtained from
tightly controlled specifications or with calibrated measuring devices,
masses obtained from weighing, and temperatures from thermometer
readings. It is recommended that only experimental data, taken directly
from the references, be included in Section 1. However, values derived
from experimental data, such as density derived from masses and
dimensions, or compositions normalized to 100 wt.%, may be included if
clearly noted as derived with the method of derivation given.*

*In order to clarify the description of the experiment and to not
prejudge the evaluation, there should be no mention of models,
calculated results, or evaluative statements in this section. Only the
physical description of the actual experiment is given.*

*Uncertainties in the data that were assigned by the experimenters,
either in published or unpublished (e.g., logbook) sources, should be
given. How the uncertainties were determined and what they represent
(e.g., standard deviation, specification tolerance, measured bounds), if
known, should be noted.*

*Any inconsistencies in the data from different sources are mentioned.
In addition to enough information that the derivation of benchmark-model
specifications in Section 3 is evident, it is recommended that more
experimental data, which might be useful for more detailed modelling or
for justification of sufficiency of the model, be provided.*

*The source of each datum should be clear. Sources of data include
published reports, logbooks, chemical-laboratory analyses, handbooks or
standards of material compositions, photographs, memos or other records
provided by experimenters, and discussions with experimenters.*

*Details of the main features of an experiment given in Section 1.1 for
the critical and / or subcritical configurations are often the same for
all other types of measurements. It is not necessary to repeat this
information in each subsequent section. However, additions and
modifications to the geometry and additional materials that are
introduced for each particular measurement type must be described in
detail in the appropriate subsections, following the recommendations
exemplified in the details given for Sections 1.1.X, below.*

*In general, modelling (idealization, simplification) of the experiment
is not discussed here. However, if the exact experimental configuration
is unknown (e.g., perhaps it was not reported because it was thought to
be too complicated to describe in detail) and an idealization was
provided by the experimenters, then the idealized experiment may be
described here. Evaluation (Sections 2 and 3.1) of an idealized
experiment includes an explanation of the assumptions used in going from
the real experimental configuration to the idealization.*

**1.0 DETAILED DESCRIPTION**

This section should start with a brief description of the scope and
objectives of the experiment carried out. A short general description of
the reactor or experimental facility is given, with a more detailed
description optionally provided in an appendix. The types of evaluated
experiments acceptable as benchmarks are summarized.

**1.1 [Description of the Critical and / or Subcritical
Configuration]{.underline}**

**1.1.1 Overview of Experiment**

The overview of the experiment should include the name of the facility,
when the experiments were performed, the organization that performed the
experiments, and perhaps the names of the experimenters if available.
The conclusions of the Evaluation of Experimental Data section,
Section 2.1, should be briefly stated. (e.g., "Twenty experiments were
evaluated, but only 12 were judged to be acceptable for use as critical
benchmark experiments.")

**1.1.2 Geometry of the Experiment Configuration and Measurement
Procedure**

This section contains the detailed description of the physical
arrangement and dimensions of the experiment. The method of determining
the critical condition and, if applicable, the measured reactivity are
stated. For ease of accurate transcription and checking, data and
uncertainties are simply copied from the references, in their original
units and to the precision that was recorded. However, if original units
are not SI, evaluators are encouraged to parenthetically provide SI
units immediately following the original units.

Subcritical measurements may require more detailed information about the
neutron source and detectors than is typically required for critical
assemblies.

**1.1.3 Material Data**

This section contains the detailed description of all materials used in
the experiment as well as significant materials in the surroundings.
Whether compositions are from physical or chemical analyses of the
materials actually used in the experiments or are from material
handbooks when only the type of material

was specified (e.g., stainless steel 304L) should be clear. Details of
the methods of analysis and uncertainties, if known, are also given.
When isotopic buildup and decay are important, relevant dates should be
provided.

**1.1.4 Temperature Data**

The temperature at which the experiments were performed should be given
and discussed in this section.

**1.1.5 Additional Information Relevant to Critical and Subcritical
Measurements**

Additional information that is relevant to critical and subcritical
measurements, such as reactivity measurements of components, is
presented in this section. Subcritical measurement description must
include the measurement technology and a discussion on the
interpretation of the measurements as well as the measured data.

**1.2 [Description of Buckling and Extrapolation Length
Measurements]{.underline}**

This section contains a detailed description of any buckling and/or
extrapolation length measurements. Uncertainties in the measurements
assigned by the experimentalists, either in published or unpublished
(e.g., logbooks) sources, should be included. Subsections 1.2.1 through
1.2.5 should contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the buckling
and extrapolation measurements. Detailed descriptions of the methods
used to obtain the data should be included in the appropriate
subsections. Values of the parameters that were directly measured should
be given, as well as other data (e.g., constants) used in the
data-reduction process. Clear distinction should be made between
measured values, derived values, and data used to process measurements
to obtain the experimental results.

**1.3 [Description of Spectral Characteristics
Measurements]{.underline}**

This section contains a detailed description of any measurements made to
determine spectral characteristics such as neutron spectra or
^238^U~c~/^235^U~f~ ratios. Uncertainties in the measurements that were
assigned by the experimentalists, either in published or unpublished
(e.g. logbooks) sources, should be included. Subsections 1.3.1 through
1.3.5 should contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the spectral
characteristics measurements. Detailed descriptions of the methods used
to obtain the data should be included in the appropriate subsections.
Values of the parameters that were directly measured should be given, as
well as other data (e.g., constants) used in the data-reduction process.
Clear distinction should be made between measured values, derived
values, and data used to process measurements to obtain the experimental
results.

**1.4 [Description of Reactivity Effects Measurements]{.underline}**

This section contains a detailed description of measurements such as
control-rod worth, void effects, small-sample worth, fuel substitution,
and xenon effects. Uncertainties in the measurements that were assigned
by the experimentalists, either in published or unpublished (e.g.,
logbooks) sources, should be included. Subsections 1.4.1 through 1.4.5
should contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the
reactivity-effect measurements. Detailed descriptions of the methods
used to obtain the data should be included in the appropriate
subsections. Values of the parameters that were directly measured should
be given, as well as other data (e.g., group constants of delayed
neutrons) used in the data-reduction process. Clear distinction should
be made between measured values, derived values, and data used to
process measurements to obtain the experimental results.

5.  **[Description of Reactivity Coefficient Measurements]{.underline}**

This section contains a detailed description of measurements such as the
temperature coefficient of reactivity, ∂ρ/∂T; the moderator-height
coefficient of reactivity, ∂ρ/∂H; and soluble boron worth, ∂ρ/∂CB.
Uncertainties in the measurements that were assigned by the
experimentalists, either in published or unpublished (e.g. logbooks)
sources, should be included. Subsections 1.5.1 through 1.5.5 should
contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the
reactivity-coefficient measurements. Detailed descriptions of the
methods used to obtain the data should be included in the appropriate
subsections. Values of the parameters that were directly measured should
be given, as well as other data (e.g., constants) used in the
data-reduction process. Clear distinction should be made between
measured values, derived values, and data used to process measurements
to obtain the experimental results.

6.  **[Description of Kinetics Measurements]{.underline}**

This section contains a detailed description of measurements such as
decay constants, β~eff~, or prompt neutron lifetime. Uncertainties in
the measurements that were assigned by the experimentalists, either in
published or unpublished (e.g., logbooks) sources, should be included.
Subsections 1.6.1 through 1.6.5 should contain, respectively, an
overview of the measurements, the configuration geometry and measurement
procedure, material data, temperature data, and additional information
relevant to the kinetics measurements. Detailed descriptions of the
methods used to obtain the data should be included in the appropriate
subsections. Values of the parameters that were directly measured should
be given, as well as other data (e.g., constants) used in the
data-reduction process. Clear distinction should be made between
measured values, derived values, and data used to process measurements
to obtain the experimental results.

7.  **[Description of Reaction-Rate Distribution
    Measurements]{.underline}**

This section contains a detailed description of reaction-rate
measurements such as flux maps, fission chamber scans, and
wire-activation fine-structure and macro-structure measurements.
Uncertainties in the measurements that were assigned by the
experimentalists, either in published or unpublished (e.g. logbooks)
sources, should be included. Subsections 1.7.1 through 1.7.5 should
contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the
reaction-rate distribution measurements. Detailed descriptions of the
methods used to obtain the data should be included in the appropriate
subsections. Values of the parameters that were directly measured should
be given, as well as other data (e.g., constants) used in the
data-reduction process. Clear distinction should be made between
measured values, derived values, and data used to process measurements
to obtain the experimental results.

8.  **[Description of Power Distribution Measurements]{.underline}**

This section contains a detailed description of power distribution
measurements. Uncertainties in the measurements that were assigned by
the experimentalists, either in published or unpublished (e.g. logbooks)
sources, should be included. Subsections 1.8.1 through 1.8.5 should
contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the power
distribution measurements. Detailed descriptions of the methods used to
obtain the data should be included in the appropriate subsections.
Values of the parameters that were directly measured should be given, as
well as other data (e.g., constants) used in the data-reduction process.
Clear distinction should be made between measured values, derived
values, and data used to process measurements to obtain the experimental
results.

**1.9 [Description of Isotopic Measurements]{.underline}**

This section contains a detailed description of isotopic measurements of
discharged fuel from particular experimental configurations.
Uncertainties in the measurements that were assigned by the
experimentalists, either in published or unpublished (e.g. logbooks)
sources, should be included. Subsections 1.9.1 through 1.9.5 should
contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the isotopic
measurements. Detailed descriptions of the methods used to obtain the
data should be included in the appropriate subsections. Values of the
parameters that were directly measured should be given, as well as other
data (e.g., constants) used in the data-reduction process. Clear
distinction should be made between measured values, derived values, and
data used to process measurements to obtain the experimental results.

**1.10 [Description of Other Miscellaneous Types of
Measurements]{.underline}**

This section contains a detailed description of other miscellaneous
types of measurements that do not fit directly into one of the other
categories, such as conversion or breeding-ratio measurements.
Uncertainties in the measurements that were assigned by the
experimentalists, either in published or unpublished (e.g. logbooks)
sources, should be included. Subsections 1.10.1 through 1.10.5 should
contain, respectively, an overview of the measurements, the
configuration geometry and measurement procedure, material data,
temperature data, and additional information relevant to the
measurements. Detailed descriptions of the methods used to obtain the
data should be included in the appropriate subsections. Values of the
parameters that were directly measured should be given, as well as other
data (e.g., constants) used in the data-reduction process. Clear
distinction should be made between measured values, derived values, and
data used to process measurements to obtain the experimental results.

***Section 2 General Guidelines***

*Missing data or weaknesses and inconsistencies in published data are
discussed and resolved in appropriate subsection of this section. The
effects of uncertainties in parameter data on the measurement results
are discussed and quantified. Codes and modelling methods used for
calculations of the effects should be specified. Use of data with large
uncertainties or data that require assumptions on the part of the
evaluator is justified.*

*Besides effects of reported uncertainties, sensitivity of the
measurement results to variation in each parameter whose uncertainty was
not reported is calculated or otherwise estimated and provided. If the
sensitivity shows that the effect of a rough but reasonable estimate of
the uncertainty is negligible, the effect may be evaluated simply as
'negligible.' (The meaning of 'negligible' should be quantified.)
Otherwise, a standard uncertainty (approximate standard deviation*[^1]*)
of the parameter is estimated based on whatever information is
obtainable, such as typical uncertainty of the parameter at the
experimental facility at the time of the experiments, information from
the manufacturer of the measuring device, and personal experience. The
basis of the uncertainty estimate should be explained.*

*Differences between code input specifications whose results are
subtracted to obtain effects, if not obvious, should be made clear. It
is not necessary to use the exact benchmark-model specifications for
sensitivity calculations, however any large discrepancies from the
benchmark model should be noted.*

*At the end of Section 2, a summary table, showing effects of the
standard uncertainties of experimental data on the parameter of
interest, is presented. It is recommended to also include sensitivities
of measurement results to the various parameters per unit measure or per
100% and with the sign (+ or -), to preserve in convenient form this
outcome of the evaluation. The table concludes with the total evaluated
uncertainty, which is defined as the individual uncertainty effects
combined with the measurement uncertainty, of the experimentally
measured value.*

**2.0 EVALUATION OF EXPERIMENTAL DATA**

The general conclusion of acceptability of data evaluated in the
following subsections is given here. If all or part of the data is found
to be unacceptable for use as benchmark data, this fact is noted, and
the reasons are summarized. \[Unacceptable data are not included in
Sections 3, 4, and Appendix A.\]

1.  **[Evaluation of Critical and / or Subcritical Configuration
    Data]{.underline}**

This section contains an evaluation of the critical and / or subcritical
configuration measurements described in Section 1.1. It concludes with
acceptance or rejection of the data for use as benchmark specifications.

2.  **[Evaluation of Buckling and Extrapolation Length
    Data]{.underline}**

This section contains an evaluation of the buckling and extrapolation
length measurements described in Section 1.2. It concludes with
acceptance or rejection of the data for use as benchmark specifications.

3.  **[Evaluation of Spectral Characteristics Data]{.underline}**

This section contains an evaluation of the spectral-characteristics
measurements described in Section 1.3. It concludes with acceptance or
rejection of the data for use as benchmark specifications.

4.  **[Evaluation of Reactivity Effects Data]{.underline}**

This section contains an evaluation of the reactivity measurements
described in Section 1.4. It concludes with acceptance or rejection of
the data for use as benchmark specifications.

5.  **[Evaluation of Reactivity Coefficient Data]{.underline}**

This section contains an evaluation of the reactivity coefficient
measurements described in Section 1.5. It concludes with acceptance or
rejection of the data for use as benchmark specifications.

6.  **[Evaluation of Kinetics Measurements Data]{.underline}**

This section contains an evaluation of the kinetic measurements
described in Section 1.6. It concludes with acceptance or rejection of
the data for use as benchmark specifications.

7.  **[Evaluation of Reaction-Rate Distributions]{.underline}**

This section contains an evaluation of the reaction-rate distribution
measurements described in Section 1.7. It concludes with acceptance or
rejection of the data for use as benchmark specifications.

**2.8 [Evaluation of Power Distribution Data]{.underline}**

This section contains an evaluation of the power distribution
measurements described in Section 1.8. It concludes with acceptance or
rejection of the data for use as benchmark specifications.

**2.9 [Evaluation of Isotopic Measurements]{.underline}**

This section contains an evaluation of the isotopic measurements
described in Section 1.9. It concludes with acceptance or rejection of
the data for use as benchmark specifications.

**2.10 [Evaluation of Other Miscellaneous Types of
Measurements]{.underline}**

This section contains an evaluation of other miscellaneous types of
measurements, as described in Section 1.10. It concludes with acceptance
or rejection of the data for use as benchmark specifications.

***Section 3 General Guidelines***

*Benchmark specifications provide the data necessary to construct
calculational models that best represent the experiment. The
benchmark-model specifications should retain as much detail as necessary
to model all important aspects of the actual experiment. When it is
necessary or desirable to simplify the representation of the experiment
for the benchmark model, the benchmark specifications must include
description of the transformations from the measured values to the
benchmark-model values and the uncertainties associated with the
transformations.*

*Data that are determined to be acceptable as benchmark-model data are
provided in Sections 3.1 through 3.10. In general, the benchmark-model
specifications include a description of simplifications (Section 3.X.1);
geometry description and dimensions (Section 3.X.2); material data
(Section 3.X.3); temperature data (Section 3.X.4); and the
benchmark-model value of the parameter of interest and its evaluated
uncertainty (Section 3.X.5).*

*Section 3.X.1 describes simplifications of the model compared to the
experiment and estimates, by calculation or measurements, the effect of
simplifications on the value of the parameter of interest. The effect is
applied as an adjustment (i.e., correction, bias) to the expected value
of the parameter to be calculated. (This expected value is called the
'benchmark-model value' of the parameter of interest.) Uncertainty of
the value of the adjustment (an estimated standard deviation) is also
given, to be combined with the total uncertainty from the end of Section
2.X to obtain the final evaluated uncertainty of the parameter of
interest in Section 3.X.5.*

*Section 3.X.2 is the complete and concise description of the
benchmark-model geometry. Schematics of the benchmark--model geometry
should always be included in Section 3.X.2.*

*Values that define the benchmark model (Sections 3.X.2, 3.X.3, and
3.X.4) are, in general, derived from experimental data without rounding
and are, thus, given with more digits than uncertainty of the
experimental data implies. This is to maintain consistency between the
benchmark model and the best values obtainable from the evaluation of
the experimental data. Uncertainties of values are given explicitly in
other sections of the evaluation, namely in Sections 1, 2, 3.X.1, and
3.X.5.*

**3.0 BENCHMARK SPECIFICATIONS**

A brief summary description of the benchmark model(s) may be given here.

**3.1 [Benchmark-Model Specifications for Critical and / or Subcritical
Measurements]{.underline}**

The subsections in this section contain benchmark specifications for the
critical or subcritical configurations described in Section 1.1.
Specifications for both detailed and simplified models are recommended
to be provided.

**3.1.1 Description of the Benchmark Model Simplifications**

Any simplifications and approximations made to geometric configurations
or material compositions are described and justified and any resulting
biases and additional uncertainties in k~eff~ are quantified. All codes
and data used for calculations of biases and their uncertainties should
be noted. If an idealized benchmark-model specification developed by the
experimenters is described here, discussion of the model includes an
explanation of the assumptions used in going from the real experimental
configuration to the benchmark-model configuration.

**3.1.2 Dimensions**

All required dimensions and information needed to completely describe
the geometry of the benchmark models are included in this section.
Specifications are derived from reported values given in previous
sections and should not be rounded, i.e., all additional digits that
result from unit conversions should be retained. Sketches, including
dimensions and labels, of the benchmark model(s) should always be
included.

**3.1.3 Material Data**

Atom densities for all materials are derived from the reported values
given in the previous sections and are concisely listed here. Lists are
broken into subheadings such as core, structural, and reflector
materials. Unique or complicated formulas for deriving atom densities
are provided. All constituents of the materials used in the experiment
description are included, or a justification for leaving them out is
provided. (Materials that are not included are, in most cases, replaced
with void; i.e., their effect is truly negligible. Substitution of other
material is discouraged because of the effect on the spectrum, thereby
changing the basic nature of the configuration to an unknown extent.)
Atom densities are listed in scientific notation with at least five
significant digits.

**3.1.4 Temperature Data**

Temperature data about the experiment and for the model are provided in
this section.

**3.1.5 Experimental and Benchmark-Model k~eff~ and / or Subcritical
Parameters**

The experimental k~eff~ and its reported uncertainty, if it is
available, are given in this section. If the experimenters simply
indicated that the system was critical, a k~eff~ of 1.0 is assumed for
the experiment.

If the experiment description is simplified (as described in Section
3.1.1) in the benchmark-model specifications, the effect on k~eff~ of
this transformation, carefully quantified either from measurements or
calculations, may result in an adjustment of the experimental k~eff~ to
obtain k~eff~ of the benchmark model. The simplifications must have only
a relatively small effect on the uncertainty in the adjusted
benchmark-model k~eff~. Generally, simplifications that have a large
effect on k~eff~ or the neutron spectrum are not made.

Uncertainty of the adjustment of k~eff~ due to simplification of the
model (from Section 3.1.1) is combined with the uncertainty of k~eff~
due to uncertainties in experimental data (from the end of Section 2.1)
to obtain the final combined uncertainty of k~eff~ of the benchmark
model.

The adjusted benchmark-model k~eff~ and its uncertainty are given. The
benchmark-model k~eff~ is the expected value of k~eff~ from a
calculation with the benchmark model, which is completely described in
Sections 3.1.2, 3.1.3 and 3.1.4.

Additional benchmark-model parameters, such as spectral ratio,
variance-to-mean, decay constant, or count-rate ratio values and their
uncertainties, are included for subcritical measurements, as well as the
interpreted benchmark-model k~eff~ values.

2.  **[Benchmark-Model Specifications for Buckling and
    Extrapolation-Length Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
buckling and extrapolation-length measurements described in Section 1.2.
Subsections 3.2.1 -- 3.2.5, analogous to the subsections of Section 3.1,
are also included.

3.  **[Benchmark-Model Specifications for Spectral Characteristics
    Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
spectral characteristics measurements described in Section 1.3.
Subsections 3.3.1 -- 3.3.5, analogous to the subsections of Section 3.1,
are also included.

4.  **[Benchmark-Model Specifications for Reactivity Effects
    Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
reactivity-effects measurements described in Section 1.4. Subsections
3.4.1 -- 3.4.5, analogous to the subsections of Section 3.1, are also
included.

5.  **[Benchmark-Model Specifications for Reactivity Coefficient
    Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
reactivity coefficient measurements described in Section 1.5.
Subsections 3.5.1 -- 3.5.5, analogous to the subsections of Section 3.1,
are also included.

6.  **[Benchmark-Model Specifications for Kinetics
    Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
kinetics measurements described in Section 1.6. Subsections 3.6.1 --
3.6.5, analogous to the subsections of Section 3.1, are also included.

**3.7 [Benchmark-Model Specifications for Reaction-Rate Distribution
Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
reaction rate distribution measurements described in Section 1.7.
Subsections 3.7.1 -- 3.7.5, analogous to the subsections of Section 3.1,
are also included.

**3.8 [Benchmark-Model Specifications for Power Distribution
Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
power distribution measurements described in Section 1.8. Subsections
3.8.1 -- 3.8.5, analogous to the subsections of Section 3.1, are also
included.

**3.9 [Benchmark-Model Specifications for Isotopic
Measurements]{.underline}**

This section contains specifications for the benchmark-model of the
isotopic measurements described in Section 1.9. Subsections 3.9.1 --
3.9.5, analogous to the subsections of Section 3.1, are also included.

**3.10 [Benchmark-Model Specifications for Other Miscellaneous Types of
Measurements]{.underline}**

This section contains specifications for the benchmark-models of any
other miscellaneous types of measurements as, described in Section 1.10.
Subsections 3.10.1 -- 3.10.5, analogous to the subsections of Section
3.1, are also included.

***Section 4 General Guidelines***

*Calculated results obtained with the benchmark-model specification data
given in Section 3 are tabulated in this section. These are regarded as
only "sample calculations" because codes often have several options
available for representing the same benchmark-model configuration, and
because details of input listings are not thoroughly reviewed. Choice of
appropriate code input to represent the benchmark model described in
Section 3 is the responsibility of the user of the evaluation.*

*Methodologies used for the sample calculations and any other
recommendations for the calculations are described.*

**4.0 RESULTS OF SAMPLE CALCULATIONS**

Calculated results obtained with the benchmark-model specification data
given in Section 3 are tabulated in this section, followed by detailed
description of and recommendations for calculational methodology. At a
minimum, results should be reported both as obtained directly from the
calculations and in the form 100(C-E)/E, where C is the calculated
result and E is the expected result from a calculation with the
benchmark model as given in Section 3. Benchmark-model uncertainties
from Section 3.X.5 should be repeated here as percentages, for
comparison purposes.

Other details about the calculations, including code versions, cross
sections, and typical input listings, are given in Appendix A (A.1
through A.10).

**4.1 [Results of Calculations of the Critical or Subcritical
Configurations]{.underline}**

Calculated k~eff~ values and methodology are presented in this section.
Additional calculated parameters, such as spectral ratio,
variance-to-mean, decay constant, or count-rate ratio values, are
included for subcritical measurements, as well as the interpreted
benchmark-model k~eff~ values.

2.  **[Results of Buckling and Extrapolation Length
    Calculations]{.underline}**

Calculated buckling and extrapolation length values and methodology are
presented in this section.

3.  **[Results of Spectral-Characteristics Calculations]{.underline}**

Calculated spectral characteristics and methodology are presented in
this section.

4.  **[Results of Reactivity-Effects Calculations]{.underline}**

Calculated reactivity effects and methodology are presented in this
section.

**4.5 [Results of Reactivity Coefficient Calculations]{.underline}**

Calculated reactivity coefficient values and methodology are presented
in this section.

**4.6 [Results of Kinetics Parameter Calculations]{.underline}**

Calculated kinetics parameters and methodology are presented in this
section.

**4.7 [Results of Reaction-Rate Distribution Calculations
]{.underline}**

Calculated reaction-rate distributions and methodology are presented in
this section.

**4.8 [Results of Power Distribution Calculations]{.underline}**

Calculated power distributions and methodology are presented in this
section.

**4.9 [Results of Isotopic Calculations]{.underline}**

Calculated isotopic concentrations and methodology are presented in this
section.

**4.10 [Results of Calculations for Other Miscellaneous Types of
Measurements]{.underline}**

Calculated results for other miscellaneous types of measurements, as
described in Section 1.10, and methodology are presented in this
section.

**5.0 REFERENCES**

All published documents referenced in the evaluation that contain
information about the experiments are listed. Internal documents such as
logbooks, memos, and internal reports should be included in footnotes.
Handbooks and computer code documentation should also be included in
footnotes. When a primary reference, internal or published, is available
in electronic form, it may be included on the CD or DVD with a hyperlink
from the point of reference.

**APPENDICES**

Supplemental information that is useful, but not essential, to the
derivation of the benchmark specification or the sample calculations is
provided in appendices. Appendices are labelled using letters (e.g.
Appendix A). Appendix A is reserved for a description of the codes,
cross section data, and typical input listings used in the sample
calculations whose results are given in Section 4. Other appendices may
be added, as needed, after Appendix A.

**APPENDIX A: Computer Codes, Cross Sections,**

**and typical input listings**

Appendix A provides a description of the codes, options, and cross
section data used in the calculations of the results given in Section 4.
Input listings for the calculations should be consistent with the
benchmark-model description in Section 3. The following information
should be included in Appendix A for each measurement type, X. The
format should be followed, but where certain information or data are
determined to be "not applicable", "not available", or "not significant"
it should be so stated.

**A.X Appropriate Measurement Type** (i.e., A.1  Critical or Subcritical
Configuration, A.2  Bucking & Extrapolation Length, etc.)

**A.X.1 Name(s) of code system(s) used.**

**A.X.2 Bibliographic references for the codes used.**

**A.X.3 Origin of cross-section data --** Nuclear data libraries that
were used in the evaluation such as ENDF/B-VI, JEF-2.2, JENDL-3.2 should
be specified. Deviations from standard libraries, (e.g. mix of different
libraries, details) should be described**.**

**A.X.4 Spectral calculations and data reduction methods used --**
Describe calculational scheme, through a figure and explanatory words
that provide essential details about assumptions made such as:

-   Resonance shielding: specify method(s), energy range(s), the
    nuclides affected (actinides, clad, fission products, oxygen), and
    which unresolved resonance treatment is used;

-   Describe how mutual shielding (overlapping of resonances) is
    handled, or not;

-   Fission spectra: specify whether only a single spectrum was used or
    a weighted mix from all fissile nuclides, explaining the procedure
    for obtaining the weighted mix;

-   Describe how the (n,2n) reaction was treated (optional);

-   Weighting spectrum for scattering matrices, e.g. corrections of the
    out-scatter and self-scatter terms considering the differences
    between the original weighting spectrum and the actual spectrum
    (optional).

**A.X.5 Number of energy groups or if continuous-energy cross sections
are used in the different phases of the calculation.**

**A.X.6 Component calculations --** The following information should be
provided for each component calculation (pin cell, assembly, etc.) as
well as full-core calculations**:**

-   Type of cell calculation (pin cell, assembly, etc.)

-   Geometry

-   Theory used (diffusion, transport)

-   Method used (finite difference, finite element, nodal, S~n~ (order),
    collision probability, Monte Carlo, J+/-, etc.)

-   Calculation characteristics (meshes, elements/assembly, meshes/pin,
    number of histories, multigroup, continuous energy, etc.).

**A.X.7 Other assumptions and characteristics.** Any differences between
the benchmark-model description (Section 3) and the model represented by
the input listing should be noted.

**A.X.8 Typical input listings for each code system type --** Typical
input listings used to obtain the results reported in Section 4.0 should
be provided. Unique and/or important features of the input may also be
discussed just prior to the input listings. Listing titles refer to the
case number and number of the table in Section 4.0 that gives the
calculated result.

**NUCLEAR CONSTANTS**

Atomic densities are based on a consistent set of basic nuclear
constants. Unless specifically stated otherwise, all nuclear constants
are taken from \"Nuclides and Isotopes,\" Fourteenth Edition, General
Electric Nuclear Energy Operations, 1989. Where atomic densities are
provided in an experimental report, and the values of Avogadro\'s Number
and the atomic weights that were used by the experimenters to determine
the atomic densities are known, reported atomic densities are adjusted
to be consistent with the nuclear constants given in this section.
Values from the consistent set that are used in the evaluations are
given below. If these values are not used, the source of the data should
be specified and values given.

Avogadro\'s Number 6.0221 x 10^23^
$\frac{\text{atoms}}{\text{gram} - \text{mole}}$

**TABLE 1. Atomic Weights.**

      **[Nuclide or Isotope]{.underline}                     [Atomic
Weight]{.underline}**

^1^H 1.0079

^2^H 2.0141

^6^Li 6.0151

Li 6.941

Be 9.0122

B 10.811

^10^B 10.0129

^11^B 11.0093

C 12.011

N 14.0067

O 15.9994

F 18.9984

Na 22.9898

Mg 24.305

Al 26.9815

Si 28.0855

P 30.9738

S 32.07

Cl 35.453

K 39.0983

Ca 40.078

Ti 47.88

V 50.9415

Cr 51.996

Mn 54.9380

Fe 55.847

Ni 58.69

Cu 63.546

Zn 65.39

**TABLE 1. Continued.**

> **   [Nuclide or Isotope]{.underline}           [Atomic
> Weight]{.underline}**
>
> Ga 69.723
>
> Sr 87.62
>
> Zr 91.224
>
> Nb 92.9064
>
> Mo 95.94
>
> ^99^Tc 98.9063[^2]
>
> Ru 101.07
>
> Rh 102.9055
>
> Ag 107.8682
>
> ^107^Ag 106.9051
>
> ^109^Ag 108.9048
>
> Cd 112.41
>
> In 114.82
>
> Sn 118.71
>
> ^129^I 128.9050^1^
>
> Cs 132.9054
>
> Ba 137.327
>
> La 138.9055
>
> Ce 140.115
>
> Nd 144.24
>
> Sm 150.36
>
> ^144^Sm 143.9120
>
> ^147^Sm 146.9149
>
> ^148^Sm 147.9148
>
> ^149^Sm 148.9172
>
> ^150^Sm 149.9173
>
> ^152^Sm 151.9197
>
> ^154^Sm 153.9222
>
> Eu 151.96
>
> ^151^Eu 150.9198
>
> ^153^Eu 152.9212
>
> Gd 157.25
>
> ^152^Gd 151.9198
>
> ^154^Gd 153.9209
>
> ^155^Gd 154.9226
>
> ^156^Gd 155.9221
>
> ^157^Gd 156.9240
>
> ^158^Gd 157.9241
>
> ^160^Gd 159.9270
>
> Dy 162.50
>
> Hf 178.49
>
> Ta 180.9479

**TABLE 1. Continued.**

**                                [Nuclide or
Isotope]{.underline}                                           [Atomic
Weight]{.underline}**

> W 183.85
>
> ^182^W 181.9482
>
> ^183^W 182.9502
>
> ^184^W 183.9509
>
> ^186^ W 185.9544
>
> Au 196.9665
>
> Pb 207.2
>
> ^232^Th 232.0381
>
> ^231^Pa 231.0359
>
> ^233^U 233.0396
>
> ^234^U 234.0409
>
> ^235^U 235.0439
>
> ^236^U 236.0456
>
> ^238^U 238.0508
>
> ^237^Np 237.0482
>
> ^238^Pu 238.0496
>
> ^239^Pu 239.0522
>
> ^240^Pu 240.0538
>
> ^241^Pu 241.0568[^3]
>
> ^242^Pu 242.0587
>
> ^241^Am 241.0568

^242m^Am 242.0596[^4]

> ^243^Am 243.0614
>
> ^242^Am 242.0588
>
> ^243^Cm 243.0614
>
> ^244^Cm 244.0627
>
> ^245^Cm 245.0655
>
> ^246^Cm 246.0672
>
> ^247^Cm 247.0704
>
> ^248^Cm 248.0723
>
> ^252^Cf 252.0816

**COMMONLY USED SYMBOLS AND TERMS**

A mass number

Af atom fraction

Aw atomic weight or mass (g/mole)

at.% atom percent

B2 buckling (cm^-^2)

β~eff~ effective fraction of fission neutrons that are delayed.

C Dancoff correction factor

D diameter (OD is outer diameter; ID is inner diameter)

∆ change in quantity \[e.g., neutron multiplication factor, ∆k;
buckling, ∆B2; tank height, ∆H; radius, ∆R; etc.\]

δ^28^ ratio of ^238^U fission to ^235^U fission

δ^25^ ratio of epithermal to thermal ^235^U fission

H height

k neutron multiplication factor - The subscripts \"eff\" and \"∞\" or
\"inf\" are used to denote the effective multiplication factor, k~eff~,
and the multiplication factor for an infinite system, k~∞~ or k~inf~.

Λ prompt neutron lifetime

m mass

M molarity (moles/l)

M neutron multiplication $M@\frac{1}{1 - k\text{eff}}$

Mw molecular weight or mass (g/mole)

NA Avogadro\'s number (atom, molecules, etc.)

Ni atomic density (atoms/barn-cm) - The subscript \"i\" is a general
descriptor used to denote either the standard elemental symbol (e.g.,
NH, NO, NPu) or the isotopic mass number (e.g., N235, N238). For
multi-elemental systems where isotopes of one element could be confused
with those of another element, both the elemental symbol and the mass
number are used (e.g., NPu238, NU238).

Na excess acid (moles/ℓ)

ν average number of neutrons per fission

R or r radius

ρ density or reactivity: $\rho º\frac{k\text{eff} - 1}{k\text{eff}}$,
sometimes denoted in units of \$ $º\frac{\rho}{\beta\text{eff}}$, where
β~eff~ is the effective fraction of fission neutrons that are delayed.

ρ^28^ the ratio of epithermal to thermal captures in ^238^U

ρ^25^ the ratio of epithermal to thermal captures in ^235^U

ρi density (g/cm3 or g/ℓ) - The subscript \"i\" is a general descriptor
used to denote the nuclide or compound for which the density is given;
e.g., ρUO~2~NO~3~, ρH~2~O, ρPu, ρHNO~3~.

s~i~ estimated standard deviation, equal to the positive square root of
the statistically estimated variance s~i~^2^

σ statistical uncertainty associated with Monte Carlo calculations or
standard deviation (the correct value has a probability of 68% of being
within ± of the quoted value, assuming a normal distribution)

σi microscopic cross section for absorption (i=a), fission (i=f),
scatter (i=s), capture (i=c), total (i=t)

**∑** macroscopic cross section or summation; e.g., Σa, Σf, Σs, Σt are
macroscopic absorption, fission, scattering, and total cross sections;
$\sum_{i\text{=1}}^{m}{}$is a summation over the range: i = 1 to i = m.

u~i~ uncertainty of a measurement result by an estimated standard
deviation, termed **standard uncertainty** and equal to the positive
square root of the estimated variance *u~i~*^2^

V volume

Vf volume fraction

Wf weight fraction

wt.% weight percent

Note: When an index \"i\" is used in conjunction with another subscript,
the two are separated by a comma (e.g., Wf,i).

**References for Uncertainty Estimations:**

-   [ICSBEP Guide to the Expression of Uncertainties -- Revision
    4,]{.underline} "International Handbook of Evaluated Criticality
    Safety Benchmark Experiments",
    [NEA/NSC/DOC(95)03/I-VIII]{.underline}, OECD-NEA, November 30, 2007.

-   "American National Standard for Expressing Uncertainty - U.S. Guide
    to the Expression of Uncertainty in Measurement," National
    Conference of Standards Laboratories, ANSI/NCSL Z540-2-1997.

-   Guide pour l\'expression de l\'incertitude de mesure - European
    Prestandard NF ENV 13005Août 1999.

-   Zoltán Szatmáry: The Effects of Technological Uncertainties on the
    Neutron Flux, IRPhE Meeting, Budapest, May 2000.

[^1]: See References for Uncertainty Estimations at the end of this
    evaluation guide.

[^2]: G. Audi, O. Bersillon, J. Blachot, A.H. Wapstra, Nuclear Physics A
    624 (1997) p. 1-124. And Updates of March 2000 at     Atomic Mass
    Data Center (A.M.D.C.).

[^3]:  \"Chart of the Nuclides,\" Thirteenth Edition, General Electric
    Company, 1984.

[^4]:  G. Audi, O. Bersillon, J. Blachot, A.H. Wapstra, Nuclear Physics
    A 624 (1997) p. 1-124. And Updates of March 2000 at     Atomic Mass
    Data Center (A.M.D.C.).