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# Neutron Activation Calculator - HELP

(last updated 4 Mar 2024)

Contents:

## Introduction

This calculator determines radioactive activation products of elements and nuclides exposed to neutron radiation, presenting the results in numerical and chart form.
In addition, the calculator also performs the inverse operation, that is, potential origin nuclides can be determined for given activation products.

Depending on the elements and nuclides contained in the matter, neutron interaction can cause various types of reaction, many of which leading to the formation of radioactive activation products. Thus, matter irradiated by neutrons becomes radioactive and remains, at least for some time, radioactive even after the neutron source is shut off.

The measurement of activation products in accidentally irradiated matter allows to determine the strength of the neutron exposure.
On the other hand, in case of a known neutron exposure of a sample, the same method can be used to determine concentrations of any (including non-radioactive) nuclides in the sample (Neutron Activation Analysis - NAA).

In the nuclear power industry, neutron activation is a matter of concern in reactors and in spent fuel management.
In the nuclear fuel industry, it can inadvertently occur in case of criticality accidents.

In addition, neutron activation can be used to produce artificial radionuclides for a number of purposes.

The calculator offers two modes of operation:

• In the Forward mode, initial masses of up to 52 elements or nuclides can be entered in the Nuclide Input table. In case of entry of an element rather than a nuclide, the natural isotope abundance of the element is used for the analysis.
The nuclides entered may be stable or radioactive.
Possible neutron capture activation products are determined for each nuclide of the origin material, plus any decay products growing in from the activation products.
The neutron capture reactions covered are:
• (n,γ) - thermal neutron capture results in release of gamma radiation
• (n,2n) - fast neutron capture results in release of 2 neutrons
• (n,3n) - fast neutron capture results in release of 3 neutrons
• (n,p) - fast neutron capture results in release of a proton
• (n,t) - fast neutron capture results in release of a triton
• (n,α) - fast neutron capture results in release of an alpha particle
Note: Activities of the activation products and their decay products are calculated for thermal neutrons only.
For thermal neutrons, the calculator moreover assesses the radiation hazard from the activation products by calculating the air kerma (kinetic energy released per unit mass: the kinetic energy of charged particles liberated by photon and neutron interactions per unit mass), whereby the irradiated target is treated as a point source.

• In the Reverse mode, the names of up to 5 activation and/or decay products can be entered in the Nuclide Input table. All possible origin nuclides are determined which may result in the listed activation and decay products.
Note: In this mode, no masses are calculated; however, calculated origin nuclides of interest can be entered in the Forward mode to perform quantitative calculations (for thermal neutrons).

The decay and air kerma database contains a total of 1252 radionuclides.
The cross section database contains the thermal neutron activation cross sections of 597 nuclides.

The calculator performs a complete decay analysis for the activation products and all their decay products, according to [Bateman 1910]; minor nuclides are listed at the end.

Notes:

• The calculator takes depletion of origin nuclides only from decay and from activation by thermal neutrons into account.
• The calculator does not consider any decay products growing in from radioactive origin nuclides.
• The calculator only determines radioactive end products of neutron capture, and only those listed in its decay database.
• The calculator does not determine metastable activation products (isomers).
• The calculator does not take into account any reduction of the irradiation efficiency from effects such as self shielding in the target, among others.
• The calculator does not consider further neutron activation of activation products or of decay products growing in from activation products.
• The calculator does not consider any fission products or their decay products.
• The calculated point source air kerma does not necessarily cover all radiations released from the irradiated target and does not consider any self-shielding within the irradiated target.

The results are presented in numerical form in the Results table for the irradiation period and the post-irradiation delay time specified. The remaining amount/activity of the origin nuclide (due to depletion from (n,γ) reactions and decay) is preceded by "=>", activation products by "->", and decay products of the activation products by "~>".
The mechanisms taken into account for target depletion are indicated as follows: "λ" for decay of radioactive target nuclides, and "γ" for thermal neutron activation.
Note: The contents of the numerical result field can be marked and copied to the clipboard for further use.

In addition, the results are optionally presented in an Output Chart showing the total series activities for each series specified, or individual nuclide activities, vs. time. The output chart type can be chosen as a line chart, a stacked area chart, or an animated bar chart.
Note: Please be aware that in line charts, a nuclide may hide one or more others. Clicking on a nuclide name in the legend toggles the corresponding curve on/off. If charts are enabled, computing time may increase.

The contents of the database for any element or nuclide can be checked with the "Query nuclide database" button. It shows, where available, the following data:

• for elements: name, acronym, atomic number, isotopic abundance, list of radionuclides in database,
• for radionuclides: half-life, specific activity, possible parent nuclides, decay products with branching ratios and decay type.
Note that only alpha and beta decays are listed: in addition, each decay emits gamma radiation.
• for any nuclides: thermal neutron activation cross sections (1 barn = 10-24 cm2).

More properties of radionuclides can be looked up with the Nuclear Data Viewer.

This JavaScript calculator is suitable for offline use.

## Search Mode

Select appropriate mode before any other data entry (this selection resets the complete calculator):

• Forward (Search activation products for given origin material)
• Reverse (Search original nuclides for given activation products)

## Nuclide Input

### Forward Mode

Enter initial masses for up to 52 elements or nuclides, or select one of the pre-defined nuclide mixes from the sample data pick list.

Data import: Longer lists of input data can be imported by pasting the data to the Import field first (next to the "IMPORT" button), then clicking the "IMPORT" button. For this purpose, the data must be delimited by space, comma, tab, or new lines. So, direct import from applications such as Excel is possible by copying and pasting, if the data is organized in two columns for name and mass value.
Note: make sure that you get decimal points (not commas!) from your spreadsheet software!
Note: Don't forget to select the appropriate mass unit!

Original Element / Nuclide
Enter element acronym (e.g. Fe) or nuclide name (e.g. Na-23).
The name is checked with the database immediately on entry. If the element or nuclide is not found, the available nuclides resp. elements are listed.
Note: Element acronyms can be looked up with the "Query nuclide database" button.

Mass
Select unit from pick list for all mass entries in this table, and enter mass values.
If no mass value is entered for an Element/Nuclide entry, only a qualitative analysis is performed.

### Reverse Mode

Enter names of up to 5 radioactive nuclides resulting from neutron activation
Activated Nuclide
Enter name of radioactive nuclide (e.g. Na-24).
The name is checked with the database immediately on entry. If the nuclide is not found, the available nuclides resp. elements are listed.
Note: Element acronyms can be looked up with the "Query nuclide database" button.

## Output Parameters

Neutron flux [per cm2s], or
Point source neutron emission rate [per s] and
Target distance from neutron point source [m] (Forward mode only)
Enter either neutron flux, or emission rate of a point source and distance.
(Note: if a neutron flux is entered, then it supersedes any point source input)

Typical neutron flux values:
Neutron SourceNeutron Flux
[per cm2s]
Cosmic radiation at sea level in Germany0.0122
Alpha (Pb-210, Po-210, Ra-226, Th-228, Pu-239, or Am-241) or Gamma (Sb-124) emitters, with beryllium powder104 - 107
Cyclotron-accelerated Deuterons on H-2, H-3, or Be-9108 - 1010
Uranium reactor108 - 1016
Ohio State University reactor, Columbus, OH, USA2.7 x 1013
ANSTO OPAL reactor, Lucas Heights, NSW, Australia1.1 x 1014
FRM-II reactor Garching (TU München), Germany8 x 1014

Neutron emission rates:
 The total number of fissions which occured during the 1999 JCO Co. criticality accident was approx. 2.5·1018. Each fission releases 2-3 neutrons, so the total number of neutrons released was approx. 6·1018. Since the criticality persisted for 20 hours, the average neutron emission rate would have been 8·1013 per s. In fact, however, a first strong peak of a few minutes was followed by a longer phase of decline.

thermal neutron activation   (n,γ)
fast neutron activation   (n,2n)   (n,3n)   (n,p)   (n,t)   (n,α)
Select neutron types of interest
Note: Quantitative analysis and chart output are only available for thermal neutrons in forward mode.

 "The thermal neutron component consists of low-energy neutrons (energies below 0.5 eV) in thermal equilibrium with atoms in the reactor's moderator. At room temperature, the energy spectrum of thermal neutrons is best described by a Maxwell-Boltzmann distribution with a mean energy of 0.025 eV and a most probable velocity of 2200 m/s. In most reactor irradiation positions, 90-95% of the neutrons that bombard a sample are thermal neutrons. In general, a one-megawatt reactor has a peak thermal neutron flux of approximately 1E13 neutrons per square centimeter per second. The epithermal neutron component consists of neutrons (energies from 0.5 eV to about 0.5 MeV) which have been only partially moderated. A cadmium foil 1 mm thick absorbs all thermal neutrons but will allow epithermal and fast neutrons above 0.5 eV in energy to pass through. In a typical unshielded reactor irradiation position, the epithermal neutron flux represents about 2% the total neutron flux. Both thermal and epithermal neutrons induce (n,γ) reactions on target nuclei. [...] The fast neutron component of the neutron spectrum (energies above 0.5 MeV) consists of the primary fission neutrons which still have much of their original energy following fission. Fast neutrons contribute very little to the (n,γ) reaction, but instead induce nuclear reactions where the ejection of one or more nuclear particles - (n,p), (n,n'), and (n,2n) - are prevalent. In a typical reactor irradiation position, about 5% of the total flux consists of fast neutrons. [...]" [Glascock 2001]

Duration of irradiation (Forward mode only)
Enter time (and appropriate unit from pick list) during which the sample was subject to neutron irradiation

use IAEA 2003 cross sections, where available
If checked, the cross sections are taken from the report [IAEA 2003], where available. If unchecked, or for nuclides not listed in this report, the data is extracted from [BNL 2001].
The value and origin of the cross section data actually used for a particular nuclide can be identified with the Query nuclide database button.

Time delay since end of irradiation (Forward mode only)
Enter time (and appropriate unit from pick list) passed between termination of neutron irradiation and analysis of the activation-induced activities

Max. half-life for consideration of progeny [years]
Enter an appropriate value, if the Results window is cluttered with non-relevant decay products of activated nuclides. Leave open otherwise.

Product Unit (Forward mode only)
Select appropriate mass or activity unit for the activation and decay products

Show depletion of stable target nuclides (Forward mode only)
May be of interest in case of long irradiation periods at high neutron flux
Note: applies for Activation Product Unit "g" only.

Distance from target for air kerma [m] (Forward mode only)
Distance from the activated target, for which the air kerma is to be determined
Note: the target is treated as a point source

Point source air kerma unit (Forward mode only)
Select kerma rate unit

Naturally occuring nuclides only for origin (Reverse mode only)
Check to eliminate all artificial nuclides as origin

## Chart Parameters

(Forward mode only)
Time
Enter numbers for Start, End time and select appropriate time unit.
Note: The numerical results displayed in the Results field are for the irradiation and delay times specified under Output Parameters, while the charts cover the whole time period between Start and End time, counting from the beginning of the irradiation.
Note: In case of a linear time axis, the Start time 0 is used, independent of the entry made.

Chart Type
Select option.

Chart Data
Select option.
Note: The units are the same as for the numerical output.

Chart Detail
Select options.
If "skip minor nuclides" is selected, then the chart legend shows only those nuclides that are visible in the chart. The number of minor nuclides can further be reduced by reducing the "Decades on log. Y axis" value, if "log. Y axis" is chosen for line charts.

Chart Axes
Select options.

## Calculation Details

Basically, the calculator uses the following equation from [Cember 1988] to determine the activity (λ · N) of an activation product resulting from the exposure of a target to thermal neutrons:

λ · N   =   Φ · σ · n · (1 - e - λ · t)

where:
Φ = neutron flux [neutrons per cm2 per sec]
σ = activation cross section of the target nuclide [cm2]
λ = transformation constant of the induced activity [per sec]
N = number of induced radioactive atoms
n = number of target atoms

To simplify calculation, the neutron flux is treated as a virtual parent nuclide for the activation product. The build-up of the activation product and the depletion of the origin nuclides thus actually is computed as part of the decay chain calculation.
The decay analysis for the activation products and all their decay products is performed according to [Bateman 1910].
For the air kerma calculations, the air kerma coefficient Kair,δ for a hypothetical point source from [ICRP 2008] is used. It does not necessarily cover all radiations from a real source.

## Bibliography

[Bateman 1910] Harry Bateman: Solution of a system of differential equations occurring in the theory of radioactive transformations , in: Proceedings of the Cambridge Philosophical Society, Mathematical and physical sciences. Cambridge [etc.] Cambridge Philosophical Society. v. 15 (1908-10): Pages 423-427

[BNL 2001] PCNuDat data base at BNL (no longer online).

[Cember 1988] Introduction to Health Physics, Second Edition, by Herman Cember, 1988

[Glascock 2001] An Overview of Neutron Activation Analysis , by Michael D. Glascock, Missouri University Research Reactor, 2001

[IAEA 2003] Thermal Neutron Capture Cross Sections, Resonance Integrals and g-Factors , International Atomic Energy Agency - International Nuclear Data Committee, IAEA INDC(NDS)-440, February 2003.

[ICRP 2008] ICRP Publication 107: Nuclear Decay Data for Dosimetric Calculations , by A. Endo and K.F. Eckerman, 2008

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