External Radiation Dose Calculator - HELP
(Virtual Geiger Counter)

(last updated 19 Mar 2013)

Contents:

• Introduction · Input Data · Calculation Details · Bibliography

Introduction

The External Radiation Dose Calculator determines the radiation dose from a shielded gamma source. The source can be a point source, or a cylindrical volume source with an evenly distributed concentration of radionuclides. The shield may consist of consecutive layers, each of which may also contain additional radionuclides.
For source and each shield layer, a number of common materials and compositions of natural radionuclides can be selected, or a custom mix of elements and radionuclides can be entered.
The receptor location can be varied in two dimensions.

Typical situations covered by the calculator:

The Calculator does take into account:

• Nuclide-specific Gamma radiation for a selection of important natural and a few artificial radionuclides.
• in case of a volume source, the Gamma radiation emitted from the top of the cylinder.
• Dose contributions from the source, plus from radionuclides contained in the shield material(s), if applicable
• Self-shielding within a volume source, and within shield layers containing radioactive materials.
  Note: Self-shielding can also be taken into account for sources otherwise treated as point sources, if sufficient material properties are known (density and attenuation coefficients); in this case, the effective radiation emitted from the top of a cylinder with height equaling diameter is used as the activity of the point source, and the source is labeled "Effective Point Source".
• Attenuation of Gamma radiation through a selection of common shield materials, also when arranged in multiple layers. The calculator uses the point-kernel method with buildup factors (see Calculation Details).
• Gamma attenuation in air
• Cosmic ionizing radiation, if required (calculated according to UNSCEAR 2000)

The Calculator does not take into account:

• Alpha or Beta radiation, nor secondary X-Rays (Bremsstrahlung) from shielding of Beta radiation, nor neutron radiation
• Radiation from the side walls of the cylinder (volume source, or shields containing radionuclides)
• Radiation from radionuclides other than those for which decay energies are contained in its database
• Gamma attenuation from shield materials not contained in its database, nor composed of elements for which shielding properties are stored.
• Alteration of the given radionuclide compositions with time due to decay
• Cosmic neutron radiation

With these properties, the calculator is suitable for a rough assessment of the following situations, for example:

• Gamma radiation on a bare or covered uranium mill tailings pile, also with multi-layer covers (Volume Source mode)
• Gamma radiation near transport containers carrying uranium ore, U₃O₈, UF₆, or the like (Volume Source mode)
• Gamma radiation near transport containers containing heels after unloading UF₆ (Point Source mode)
• Gamma radiation from DU penetrator lying on the ground, or buried in the ground (Point, or Volume Source mode)

References to other calculators:

• For internal exposure from ingestion or inhalation of uranium and decay products, use the Uranium Individual Dose Calculator.
• For a residential exposure scenario, the radiation dose and risk for an individual living on soil contaminated from uranium and/or in a home built from such contaminated material can be determined with the Uranium in Soil and Building Material Individual Dose Calculator. It not only covers external exposure, but also the following pathways: ingestion of soil, inhalation of fugitive dusts, ingestion of produce grown in the soil, ingestion of contaminated groundwater, and inhalation of radon.
• Determine the radon flux from a bare and/or water-covered uranium mill tailings pile: Uranium Mill Tailings Radon Flux Calculator
• Determine the radon flux through a multi-layer soil cover of an uranium mill tailings pile and/or optimize the cover for a given flux: Uranium Mill Tailings Cover Calculator

The geometry of the situation and the properties of the materials involved are defined in the Input Data table.

With Java enabled, a section of the geometry of the situation is shown in a Graph.

Upon execution of the calculation, the graph shows the Gamma dose rate at the selected receptor location. The receptor can easily be moved to other locations by mouse clicking.

In addition, the gamma dose can be visualized in a color map, if the Show color map box is checked.
Note 1: Each square in the color dose map represents the dose value in its center, not the value averaged over the square. Due to the sharp dose increase near point sources, the color scheme may change considerably with a decrease of the raster width, therefore.
Note 2: In logarithmic mode, the color of the square with the highest dose value is red. The span given by the selected number of decades is represented by the rainbow colors red - yellow - green - cyan - blue - violet. If the range of values is not covered by the number of decades selected, the remaining (too low) values are displayed in a linear fade-out of violet.

Computing time increases considerably with number of shields, number of elements and radionuclides per layer, and in particular with color map enabled. The example parameter sets take a few seconds to compute on current machines.

Output graph (with linear color map): Click image to view animation !

Also upon the calculation, the layer colors change according to the following color scheme, allowing for a simple overview and for easy detection of data problems:

Layer Color Scheme
Point Source	Effective Point Source	Volume Source	Shield	Meaning
dark red	n.a.	red	pink	layer contains radionuclides, no attenuation data defined
n.a.	yellow	yellow	yellow	attenuation data is defined for this layer, no radionuclides contained
n.a.	dark orange	orange	light orange	layer contains radionuclides, plus attenuation data is defined for this layer
white	n.a.	white	white	no, or insufficient information defined for this layer

indicates problem with missing data
n.a. = not applicable

The Result field repeats some important input data, reports any warnings about missing input data, and shows the calculation results for the current receptor location. The contributions from the source and from each layer containing radionuclides are shown separately and in summary.
The contents of the Result field can be highlighted and copied for further use.
Note: The figures are for the current geometry - so, if the effect of a shield is to be compared to the open source, disable the shield (select Layer OFF) and compare the results manually.

The contents of the database of the calculator (decay energies of radionuclides, gamma attenuation and energy absorption coefficients) can be viewed with the Query Database button.

See instructions for offline use of this calculator.

Input Data

Mode · Point/Volume Source Material · Shield #n Material · Cosmic Radiation · Geometry · Output · Element and Radionuclide Compositions and Series

Mode

Number of Shield layers

Point / Volume Source

Example data sets

These data sets preset the whole calculator for certain typical cases of interest. A first calculation result can then be obtained by just clicking the Calculate button. After selection, the example data can also be modified as required, to study the effect of parameter variations.
Note: set Number of Shield layers=1 and select appropriate source mode first, before choosing an example data set!

Ex. 1: Shielding in free air (for Point Source Mode)

Study the impacts of distance, shield thickness, and shield material. With the highest Result Detail setting, the factors affecting attenuation can be checked for each single energy emitted by the radiation source.
Note: when entering individual source radionuclides, make sure that the calculator's database actually contains the gamma energy data for these nuclides (Query Database button): for space considerations, the calculator contains energy data for a few selected nuclides only.

Ex. 2: 48Y Cylinder with Heels (for Point Source Mode)

After unloading of an uranium hexafluoride (UF₆) cylinder by heating in an autoclave, the decay products of the uranium remain in the cylinder as so-called Heels. See, how an "empty" cylinder emits much more gamma radiation than a full one.

Ex. 3: DU bullet buried in soil (for Point Source Mode)

Depleted uranium bullets buried in soil are difficult to locate by their gamma radiation emission.

Ex. 4: Uranium mill tailings cover (for Volume Source Mode)

Gamma radiation from uranium mill tailings can be reduced by soil covers, often applied in several layers. Check the effects of layer material, cover thickness and of residual radioactivity contained in the cover material.

Ex. 5: 48Y Cylinder with UF_{6 nat} (for Volume Source Mode)

Determine the gamma dose rate outside the top of a typical transport cylinder for natural uranium hexafluoride.
Note: In addition, the cylinder emits neutron radiation which is not covered by this calculator.

Point/Volume Source Material Composition

Layer usage selector

This drop down list allows to easily disable parts or all of the properties of the source layer for test purposes:

NORMAL	the layer is fully operational
RAD. ONLY	the attenuation properties of the layer are disabled
ATTEN. ONLY	any radiation emission from the layer is disabled
Layer EMPTY	attenuation and radiation properties are disabled; the layer is filled with air
Layer OFF	the layer is completely removed

Total amount / Individual amounts below (Point Source only)

Choose, whether the composition of the source material is to be entered as total mass plus activity or mass concentrations, or as individual activities and masses.

Total amount: Mass figure (Point Source only)

Enter number

Total amount: Mass Unit (Point Source only)

Select unit from pick list

Source Material

Material data for the radiation source
Select sample material from the pick list (and modify any entries, if required), or enter new data in the table.
The pick list contains elemental compositions, as well as radionuclide compositions and radionuclide series.
Note: The decay energy and attenuation data can be viewed with the "Query database" button.

Consider self-shielding of point source with: rho_so - Source density [g/cm³] (Point Source only)

Check box and enter density value to take self-shielding within the point source into account: if attenuation coefficients are available for the source material, then the activity of the point source is taken as the activity at the top surface of an upright cylinder with diameter equalling height, and the source is labeled "Effective Point Source".

rho_so - Source density [g/cm³] (Volume Source only)

Value must be larger than zero.

Element / Nuclide

Enter short names of elements (e.g. Th) or radionuclides (e.g. U-238) and associated concentrations in weight-percent, or, for radionuclides, alternatively the activity concentration in Bq per gram of source material. For point sources, there is also the possibility to enter individual masses in grams and activities in Bq directly, if the box "Individual amounts below" is checked.
In addition, the short names of a number of pre-defined radionuclide compositions (e.g. U_nat) and radionuclide series (e.g. U-238++) can be entered.
Note 1: For elements, the natural isotopic abundance of the element is assumed, if there is one defined (check with the "Query database" button) - otherwise enter individual nuclides.
Note 2: For radionuclides, check the availability of the associated decay data with the "Query database" button.
Note 3: Mass and activity concentrations entered for a radionuclide composition refer to the total mass/activity of all nuclides of the nominal element contained (e.g. U-238, U-234, and U-235 for U_nat++), while those entered for a radionuclide series refer to the mass/activity of the nominal nuclide only (e.g. U-238 for U-238++).

Data import: Longer lists of input data can be imported by pasting the data to the "Results" field first, then clicking the "Import" button. For this purpose, the data must be delimited by space, comma, tab, or new lines, and "wt_%" must be encoded as 0, "Bq/g" as 1. So, direct import from spreadsheet applications such as Excel is possible by copying and pasting, if the data is organized in three columns for name, value, and unit.
Note: make sure that you get decimal points (not decimal commas!) from your spreadsheet software!

Shield #n Material Composition

Layer usage selector

This drop down list allows to easily disable parts or all of the properties of each shield layer for test purposes:

NORMAL	the layer is fully operational
RAD. ONLY	the attenuation properties of the layer are disabled
ATTEN. ONLY	any radiation emission from the layer is disabled
Layer EMPTY	attenuation and radiation properties are disabled; the layer is filled with air
Layer OFF	the layer is completely removed

Shield Material

Material data for each shield
Select sample material from the pick list (and modify any entries, if required), or enter new data in the table.
The pick list contains some elements, as well as elemental compositions and radionuclide compositions.
Note: The attenuation data and/or decay energy data can be viewed with the "Query database" button.

rho_shn - Shield density [g/cm³]

Value must be larger than zero, for the shield to be effective.
Note: If no value, or zero, is entered, this layer is treated as vacuum.

Element / Nuclide [wt_% / Bq/g]

Enter short names of elements (e.g. Pb) or radionuclides (e.g. U-238) and associated abundance in weight-percent, or, for radionuclides, alternatively the activity concentration in Bq per gram of source material. In addition, the short names of a number of pre-defined radionuclide compositions (e.g. U_dep) and radionuclide series (e.g. U-238++) can be entered.
Note 1: For elements, the natural isotopic abundance of the element is assumed, if there is one defined (check with the "Query database" button) - otherwise enter individual nuclides.
Note 2: For radionuclides, check the availability of the associated decay data with the "Query database" button.
Note 3: Mass and activity concentrations entered for a radionuclide composition refer to the total mass/activity of all nuclides of the nominal element contained (e.g. U-238, U-234, and U-235 for U_nat++), while those entered for a radionuclide series refer to the mass/activity of the nominal nuclide only (e.g. U-238 for U-238++).

Data import: Longer lists of input data can be imported by pasting the data to the "Results" field first, then clicking the "Import" button. For this purpose, the data must be delimited by space, comma, tab, or new lines, and "wt_%" must be encoded as 0, "Bq/g" as 1. So, direct import from spreadsheet applications such as Excel is possible by copying and pasting, if the data is organized in three columns for name, value, and unit.
Note: make sure that you get decimal points (not commas!) from your spreadsheet software!

Cosmic Radiation Parameters

Layer usage selector

This drop down list allows to enable/disable the inclusion of cosmic radiation to the dose calculations:

NORMAL	cosmic radiation is considered
Layer OFF	cosmic radiation is neglected

Altitude [m above sea level]

Cosmic radiation increases with altitude.
(Note: for terrestrial use only)

Latitude [°]

Cosmic radiation is slightly lower at latitudes below 30°.

Outdoor/Indoor

The ceiling of a building provides some shielding from cosmic radiation.

Indoor: Shielding factor

Dimensionless ratio of indoor to outdoor radiation level from ionizing cosmic radiation.

Geometry Parameters

Point Source Geometry: (2 shield layers)

Volume Source Geometry: (2 shield layers)

The geometry parameters can be initialized with 5 predefined data set examples, corresponding to the example buttons in the Mode section.
Note: While the buttons in the Mode section initialize all parameters, here only the geometry is affected.

• Ex. 1: Shielding in free air (for Point Source Mode)
• Ex. 2: 48Y Cylinder (for Point Source Mode)
• Ex. 3: Source buried in soil (for Point Source Mode)
• Ex. 4: Tailings cover (for Volume Source Mode)
• Ex. 5: 48Y Cylinder (for Volume Source Mode)

a - Distance of source from shield front surface [cm] (Point Source only)

If no value is entered, zero is assumed.
If a negative value is entered, the point source is located inside the shield (Shield #1 only).

x - Horizontal displacement of receptor [cm]

If no value is entered, zero is assumed. For volume sources or shields containing radionuclides, the horizontal displacement is limited to the source or shield radius, respectively.

y - Distance of receptor from x-axis [cm] - or -
b - Distance of receptor from shield rear surface [cm]

Enter either y or b. The value must be larger than zero.
Upon entry of y, b is erased, and vice versa.
Note: The x-axis runs through the point source, the top of the effective point source, or the top of the volume source, respectively.

d - Source depth [cm] (Volume Source only)

Value must be larger than zero.

dsn - Shield #n thickness [cm]

If no value is entered, zero is assumed.

r - Source radius [cm] - or -
sa - Source surface area [m²] (Volume Source only)

Enter either r or sa. The value must be larger than zero.
Upon entry of r, sa is calculated automatically, and vice versa.

rs - Shield radius [cm] - or -
sas - Shield surface area [m²]

Enter either rs or sas. The value must be equal or larger than the source radius.
Upon entry of rs, sas is calculated automatically, and vice versa.
(In the case of a point source, this parameter is only required if the shield contains radionuclides)

integration step width [cm]

Maximum horizontal size of the section of the volume elements used for the point-kernel method.
Note: smaller sizes improve the precision, but increase computing times and memory requirements considerably
(In the case of a point source, this parameter is only required if the shield contains radionuclides)

integration step height [cm]

Maximum vertical size of the section of the volume elements used for the point-kernel method.
Note: smaller sizes improve the precision, but increase computing times and memory requirements considerably
(In the case of a point source, this parameter is only required if the shield contains radionuclides)

Output Parameters

Dose Options: Dose Rate Unit

Select from pick list
Note: The primary unit calculated is Gy/h. All other units are derived from this one.

Dose Options: Exposure for annual dose rates

Select occupancy form pick list

Dose Options: Receptor Material

Select from pick list
Note: The absorbed gamma energy dose usually is calculated for air, and any further dose figures are derived from this value.

Dose Options: Terrestrial gamma dose coeff. in air [Sv/Gy]

Conversion coefficient from absorbed dose in air to effective dose equivalent for terrestrial gamma rays.
UNSCEAR (2000) recommends 0.7 Sv/Gy for adults, 0.8 for children, and 0.9 for infants.
Note 1: this coefficient is used energy-independently
Note 2: this coefficient is only used for receptor air, otherwise unity is used
Note 3: the coefficient used for the contribution from cosmic ionizing radiation is unity

Dose Options: Use buildup factors for:

Check to enable computing of buildup factors to compensate for the non-ideal geometry of the situation.
Note: although the use of buildup factors increases computing time, unchecking is not advisable, except for test purposes.
For each layer, the material to be used for the buildup factor calculations can be selected manually from the respective drop-down list, or "auto select" can be chosen.
Note: For "auto select", the buildup data for the layer material is used, if available; otherwise the buildup data for an estimated effective atomic number of the layer material is used.

Graph Detail: Show integration grid

Check to show the grid defined by the integration step width/height entered under Geometry Parameters

Graph Detail: Show dose color map

Check to calculate dose values for the following raster of x and y positions and show the result as a coloured map.
Note: If this checkbox is checked, computing time increases considerably, in particular for volume sources and/or shields containing radionuclides!

Graph Detail: Raster width [pixel]

Raster width in pixels for calculation of dose values in color map
Min. value: 10 pixel
If no value, or zero, is entered, the minimum raster width is used.
Note: Reduction of the number increases computing time considerably!

Graph Detail: Logarithmic color scale

Check for logarithmic color scale, otherwise a linear scale is used

Graph Detail: Decades

Number of decades to be covered by color map in logarithmic mode.
If no value, or zero, is entered, an appropriate scale is selected automatically.
Note: If, for logarithmic scale, the range of values is too large for the number of decades selected, the remaining (too low) values are displayed in a linear fade-out of violet.

Result Detail: Dose from each layer

Select desired level of detail for the dose summary in the Result field.
(The selections "by Radiations" are available in Point Source mode only and affect the contributions from the point source itself only)

Element and Radionuclide Compositions and Series

Element Compositions
Name	Description
Air	Air, Dry (Near Sea Level)
Water	Water, Liquid
Brick_cs	Bricks, Common Silica
Concr_ord	Concrete, Ordinary
Concr_BA	Concrete, Barite (Type BA)
Wood_SP	Wood, Southern Pine
Glass_Pb	Glass, Lead
Glass_BS	Glass, Borosilicate ("Pyrex")
Glass_plt	Glass, Plate
Glass_acr	Glass, Acrylic ("Lucite")
Tiss_sft	Tissue, Soft (ICRU-44)
St_304	Stainless Steel (Type 304)
Soil_US	U.S. Soil
Soil_05	U.S. Soil with Ra-226 @ 5 pCi/g = 0.185 Bq/g (U-series in equil.) a)
Soil_15	U.S. Soil with Ra-226 @ 15 pCi/g = 0.555 Bq/g (U-series in equil.) a)
Rock_cru	Rock, Crustal
Salt_rck	Salt, Rock
Asph_05	Asphalt mixture (5% bitumen, 95% crustal rock)
Uore_dgo	Uranium ore 0.33 wt-% U, Durango, Colorado, USA c)
Utail_dgo	Uranium mill tailings, Durango, Colorado, USA
Uore_01	Uranium ore 0.1 wt-% U b)
Utail_01	Uranium mill tailings from 0.1 wt-% U ore, extraction = 90% b)
Uore_nor	Uranium ore 0.066 wt-% U, Nordic Lake, Elliot Lake, Ontario, Canada b)
Utail_nor	Uranium mill tailings, Nordic Lake, Elliot Lake, Ontario, Canada
UF6_nat+	Uranium hexafluoride, natural, solid, with short-lived progeny (Th-234, Pa-234m, Th-231)
UF6_rec+	Uranium hexafluoride, recycled uranium, solid, init. enr. 3.5 wt-%, burnup 39 GWd/tHM, 5 y delay, with progeny
UF6_enr+	Uranium hexafluoride, enriched to 3.5 wt-% U-235, solid, from natural uranium, with short-lived progeny (Th-234, Pa-234m, Th-231)
UF6_ere+	Uranium hexafluoride, enriched to 3.5 wt-% U-235 equiv., solid, from recycled U (3.5 wt-% init.enr. 39 GWd/tHM, 5 y), with short-lived progeny (Th-228, Ra-224, Pb-212, Bi-212, Tl-208, Th-231, Th-234, Pa-234m)
UF6_dep+	Uranium hexafluoride, depleted to 0.2 wt-% U-235, solid, from natural uranium, with short-lived progeny (Th-234, Pa-234m, Th-231)
UF6_dre+	Uranium hexafluoride, depleted to 0.2 wt-% U-235, solid, from recycled U (3.5 wt-% init.enr. 39 GWd/tHM, 5 y), with short-lived progeny (Th-231, Th-234, Pa-234m)
U3O8_nat+	U3O8, natural, with short-lived progeny (Th-234, Pa-234m, Th-231)
U3O8_rec+	U3O8, recycled uranium, init. enr. 3.5 wt-%, burnup 39 GWd/tHM, 5 y delay, with progeny
U3O8_dep+	U3O8, depleted to 0.2 wt-% U-235, from natural uranium, with short-lived progeny (Th-234, Pa-234m, Th-231)
UO2_enr+	UO2, enriched to 3.5 wt-% U-235, from natural uranium, with short-lived progeny (Th-231, Th-234, Pa-234m)
UO2_ere+	UO2, enriched to 3.5 wt-% U-235 equiv., from recycled U (3.5 wt-% init.enr. 39 GWd/tHM, 5 y), with short-lived progeny (Th-228, Ra-224, Pb-212, Bi-212, Tl-208, Th-231, Th-234, Pa-234m)
Heels_nat	Heels from sublimation of natural uranium hexafluoride, radionuclides only (Th-234, Pa-234m, Th-231)

^a) based on Soil_US, density and/or radionuclides modified
^b) based on Utail_nor, density and/or radionuclides modified
^b) based on Utail_dgo, density and/or radionuclides modified
Note 1: Mass and activity concentrations entered for an element composition refer to the total mass/activity of all nuclides contained, except for those only contained in the decay series indicated by "+".

Radionuclide Compositions
Name	Description
U_nat	Natural Uranium, without progeny
U_nat+	Natural Uranium, with short-lived progeny (Th-234, Pa-234m, Th-231)
U_nat++	Natural Uranium, with all major progeny in sec. equilibrium
U_tailx90++	Uranium in mill tailings, extraction = 90%, with all major progeny
U_rec	Recycled Uranium, init. enr. 3.5 wt-% U-235, burnup 39 GWd/tHM, 5 y delay
U_rec+	Recycled Uranium, init. enr. 3.5 wt-% U-235, burnup 39 GWd/tHM, 5 y delay, with progeny
U_dep	Depleted Uranium, 0.2 wt-% U-235, without progeny
U_dep+	Depleted Uranium, 0.2 wt-% U-235, with short-lived progeny (Th-234, Pa-234m, Th-231)
U_dre	Depleted Recycled Uranium, 0.2 wt-% U-235, init. enr. 3.5 wt-% U-235, burnup 39 GWd/tHM, 5 y delay
U_dre+	Depleted Recycled Uranium, 0.2 wt-% U-235, init. enr. 3.5 wt-% U-235, burnup 39 GWd/tHM, 5 y delay, with short-lived progeny (Th-231, Th-234, Pa-234m)
U_enr	Enriched Uranium, 3.5 wt-% U-235, without progeny
U_enr+	Enriched Uranium, 3.5 wt-% U-235, with short-lived progeny (Th-234, Pa-234m, Th-231)
U_ere	Enriched Recycled Uranium, 3.5 wt-% U-235 equiv., init. enr. 3.5 wt-% U-235, burnup 39 GWd/tHM, 5 y delay, without progeny
U_ere+	Enriched Recycled Uranium, 3.5 wt-% U-235 equiv., init. enr. 3.5 wt-% U-235, burnup 39 GWd/tHM, 5 y delay, with short-lived progeny (Th-228, Ra-224, Pb-212, Bi-212, Tl-208, Th-231, Th-234, Pa-234m)

Note 1: Mass and activity concentrations entered for a radionuclide composition refer to the total activity of all nuclides of the nominal element contained (e.g. U-238, U-234, and U-235 for U_nat++).
Note 2: Radionuclide compositions are calculated with the material properties of the nominal element.

Radionuclide Series
Name	Description
Thorium-232 series
Th-232++	Thorium-232, with all major progeny in sec. equilibrium
Ra-228+	Radium-228, with short-lived progeny (Ac-228)
Ra-228++	Radium-228, with all major progeny in sec. equilibrium
Th-228++	Thorium-228, with all major progeny in sec. equilibrium
Uranium-238 series
U-238+	Uranium-238, with short-lived progeny (Th-234, Pa-234m)
U-238++	Uranium-238, with all major progeny in sec. equilibrium
Th-230++	Thorium-230, with all major progeny in sec. equilibrium
Ra-226+	Radium-226, with short-lived progeny (Rn-222, Po-218, Pb-214, Bi-214, Po-214)
Ra-226++	Radium-226, with all major progeny in sec. equilibrium
Pb-210++	Lead-210, with all major progeny in sec. equilibrium
Uranium-235 series
U-235+	Uranium-235, with short-lived progeny (Th-231)
U-235++	Uranium-235, with all major progeny in sec. equilibrium
Pa-231++	Protactinium-231, with all major progeny in sec. equilibrium
Ac-227++	Actinium-227, with all major progeny in sec. equilibrium
Neptunium-237 series
Np-237+	Neptunium-237, with short-lived progeny (Pa-233)
Np-237++	Neptunium-237, with all major progeny in sec. equilibrium
Th-229++	Thorium-229, with all major progeny in sec. equilibrium
Other
U-232++	Uranium-232, with all major progeny in sec. equilibrium
Cs-137+	Cesium-137, with progeny

Note 1: Mass and activity concentrations entered for a radionuclide series refer to the activity of the nominal nuclide only (e.g. U-238 for U-238++).
Note 2: Radionuclide series are calculated with the material properties of the nominal nuclide.

With these Radionuclide Series, the decay series can be composed as follows, for example:

Name	Complete Series
Thorium Isotopes
Th-232	Th-232++ Th-232   Ra-228++ Th-232   Ra-228+   Th-228++
Th-231	Th-231   Pa-231++ Th-231   Pa-231   Ac-227++
Th-230	Th-230++ Th-230   Ra-226++ Th-230   Ra-226+   Pb-210++
Th-229	Th-229++
Th-228	Th-228++
Uranium Isotopes
U-239	U-239   Np-239   Pu-239   U-235++ U-239   Np-239   Pu-239   U-235+   Pa-231++ U-239   Np-239   Pu-239   U-235+   Pa-231   Ac-227++
U-238	U-238++ U-238+   U-234   Th-230++ U-238+   U-234   Th-230   Ra-226++ U-238+   U-234   Th-230   Ra-226+   Pb-210++
U-237	U-237   Np-237++ U-237   Np-237+   U-233   Th-229++
U-236	U-236   Th-232++ U-236   Th-232   Ra-228++ U-236   Th-232   Ra-228+   Th-228++
U-235	U-235++ U-235+   Pa-231++ U-235+   Pa-231   Ac-227++
U-234	U-234   Th-230++ U-234   Th-230   Ra-226++ U-234   Th-230   Ra-226+   Pb-210++
U-233	U-233   Th-229++
U-232	U-232++ U-232   Th-228++
Plutonium Isotopes
Pu-239	Pu-239   U-235++ Pu-239   U-235+   Pa-231++ Pu-239   U-235+   Pa-231   Ac-227++
Neptunium Isotopes
Np-237	Np-237++ Np-237+   U-233   Th-229++

Calculation Details

The calculator uses the point-kernel method with buildup factors.

• For point sources, the attenuation of a radiation beam is calculated, as it passes through the shield (which may be composed of consecutive shield layers). For each decay energy of each radionuclide in the source, the energy-specific attenuation on the beam's path through the shield is taken into account. For sections of the path outside of the shield, attenuation by air is assumed.
  If no attenuation data is stored for a shield layer material, it is calculated from the layer's elemental composition, if given, and if attenuation data is stored for the relevant elements.
  Shields containing radionuclides are treated as additional volume sources (see below).

  To compensate for the non-ideal geometry of the situation, buildup-factors are used for the shield layers. In case the material of a shield layer consists of more than one element, and buildup factors for the material are not available, an energy-specific effective atomic number (Z_eff) is calculated for the layer material according to [Singh 2003], which is then used to determine the buildup factors. In case the buildup factors for a layer element (real or effective) are not available, the buildup factors are interpolated between those known for the elements with the nearest atomic numbers. For multi-layer shields, buildup factors are calculated according to the empirical formula provided in [Broder 1963].
  
  

• For volume sources, the cylindrical source is divided into small volume elements in the form of rings with a rectangular section. This allows to handle the three-dimensional problem in two dimensions to save computing time. For each volume element, the attenuation of a radiation beam is calculated, as it passes through the rest of the source and through the shield (which may be composed of consecutive shield layers). For each decay energy of each radionuclide in the source, the energy-specific attenuation on the beam's path is taken into account. For sections of the path above the shield, attenuation by air is assumed.
  If no attenuation data is stored for a layer material, it is calculated from the layer's elemental composition, if given, and if attenuation data is stored for the relevant elements.
  If the receptor is horizontally displaced away from the common axis of the source and shield cylinders, the volume rings follow the displacement, and only their intersections with the source/shield cylinders are taken into account.
  Shields containing radionuclides are treated as additional volume sources.

  To compensate for the non-ideal geometry of the situation, buildup-factors are used for each layer. In case the material of a source or shield layer consists of more than one element, and buildup factors for the material are not available, an energy-specific effective atomic number (Z_eff) is calculated for the layer material according to [Singh 2003], which is then used to determine the buildup factors. In case the buildup factors for a layer element (real or effective) are not available, the buildup factors are interpolated between those known for the elements with the nearest atomic numbers. For multi-layer situations (i.e. source plus at least one shield), buildup factors are calculated according to the empirical formula provided in [Broder 1963].
  
  

Bibliography and Resources

• [Broder 1963] The transmission of gamma-radiation through heterogeneous media, by D. L. Broder, Yu. P. Kayurin, A. A. Kutuzov, in: Problems in reactor shielding physics, Collection of articles , D. L. Broder, et al., Editors, Gosatomizdat, Moscow, 1963, NASA Technical Translation TT F-411, Washington, D.C., June 1967 (26.3 MB PDF), p. 287-299

• [Parks 1988] Assessment of shielding analysis methods, codes, and data for spent fuel transport/storage applications , by C. V. Parks, B. L. Broadhead, O. W. Hermann, et al., Oak Ridge National Laboratory, ORNL/CSD/TM-246, July 1988

• [Singh 2003] ZnO-PbO-B₂O₃ glasses as gamma-ray shielding materials, by H. Singh, K. Singh, L. Gerward, et al., in: Nuclear Instruments and Methods in Physics Research B, Vol. 207 (2003), p. 257–262

• [UNSCEAR 2000] Sources and Effects of Ionizing Radiation, UNSCEAR 2000 Report to the General Assembly, with Scientific Annexes, United Nations Scientific Committee on the Effects of Atomic Radiation, United Nations, New York, 2000
  > Download full text: Vol. I: Sources · Vol. II: Effects

• Source for the decay data:
  Oak Ridge National Laboratory (ORNL): ICRP38 program

• Source for the photon mass attenuation and mass energy-absorption coefficients:
  • Z = 1 - 92: NIST Physical Reference Data
  • Z > 92: NIST: XCOM program

• Source for the Buildup Factors:
  New gamma-ray buildup factor data for point kernel calculations: ANS-6.4.3 standard reference data , by D. K. Trubey, NUREG/CR-5740, U.S. Nuclear Regulatory Commission, ORNL/RSIC-49, Oak Ridge National Laboratory, September 1988 (3.1MB PDF)

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