Neutron activation and scattering calculator

This calculator uses neutron cross sections to compute activation of the sample given the mass in the sample and the time in the beam, and to perform absorption and scattering calculations for samples on slow neutron beamlines (energy below 325 meV, wavelength above 0.05 nm).

1. Enter the sample formula in the material panel.
2. To perform activation calculations, fill in the thermal flux, the mass, the time on and off the beam, then press the calculate button in the neutron activation panel.
3. To perform scattering calculations, fill in the wavelength of the neutron and/or xrays, the thickness and the density (if not given in the formula), then press the calculate button in the absorption and scattering panel.

Chemical formula

The chemical formula parser allows you to specify materials and mixtures. Formulas are parsed with periodictable python package (Kienzle 2008).

simple formula

A basic formula consists of elements and their quantities.

CaCO3

represents the chemical CaCO₃

multi-part formula

Formulas can be built from parts by separating them with "+" or space, with a number before the part representing repeats. Using parentheses, a formula is treated as if it were a single unit.

CaCO3+6H20

,

CaCO3 6H2O

and

CaCO3(H2O)6

all represent ikaite, CaCO₃·6H₂O

isotopes

Isotopes are represented by element[nuclide index]. Special symbols

D

and

T

can be used for ²H and ³H. Isotopes can be mixed within a formula, such as

DHO

for partially deuterated water. Use

H[1]

in formula for labile hydrogen. These will be substituded with H and D in proportion with the D₂O fraction when computing the contrast match point of the sample.

O[18]

represents the ¹⁸O

C3H4H[1]NO@1.29n

represents alanine with one labile hydrogen.

density

Mass density is needed to compute scattering factors for the material. The density can be entered in the density field, or it can be given in the formula by adding @value to the end. Densities for the pure elements are already known.

H2O@1

indicates that water has a density of 1 g/cm³

isotopic density

If the formula uses a mixture of isotopes, you can still use the density of the material assuming natural abundance, but add an "n" to the value to scale it to the isotope specific density. If you already know the isotopic density, use the value by itself and it will not be scaled.

D2O@1n

,

D2O@1.11

, and

D2O@1.11i

all give the density of D₂O as 1.11 g/cm³

mole fractions

Using non-integer quantities, arbitrary concentration ratios can be be constructed.

78.2H2O[16] + 21.8H2O[18] @1n

represents water with 78.2% ¹⁶O and 21.8% ¹⁸O

mass fractions

Formulas can be mixed by mass, with each part starting with a percentage followed by formula followed by "//". The first part must use "%wt" to indicate that it is a mass fraction. The final part is the base, and it does not need a percentage since it makes up the rest of the material.

50%wt Co // Ti

is more descriptive than Co_0.552Ti_0.448

33%wt Co // 33% Fe // Ti

builds a 1:1:1 mixture by mass of cobalt-iron-titanium

volume fractions

Volume fractions are like mass fractions, but they use "%vol" instead. Each component of the volume fraction must specify the density.

20%vol (10%wt NaCl@2.16 // H2O@1) // D2O@1n

is a 10% saline solution by weight mixed 20:80 by volume with D₂O, which is the same as

NaCl(H2O)29.1966(D2O)122.794@1.10i

mass and volume mixtures

Specific amounts of materials can be mixed, with each part giving the quantity of material followed by "//". Quantities can be masses (kg, g, mg, ug, or ng) or they can be volumes (L, mL, uL, nL). Density is required for materials given by volume. For scattering calculations density is required for the materials given by mass as well.

5g NaCl // 50mL H2O@1

is more descriptive than

NaCl(H2O)32.4407

5g NaCl@2.16 // 50mL H2O@1

computes the density as 1.05 g/cm³. Not useful in this case since 9%wt brine has a density of 1.0633 at ambient temperature.

50 mL (45 mL H2O@1 // 5 g NaCl)@1.0707 // 20 mL D2O@1n

uses the appropriate density for a 10%wt brine in the mixture.

layer thickness

Multilayer samples can specified as layer thickness and material separated by "//". Thicknesses are in length units (cm, mm, um, nm). The resulting material will compute activation for 1 cm² of material. Density is required for each layer.

1 cm Si // 5 nm Cr // 10 nm Au

Thermal flux

Units: n/cm²/s

Provide the thermal flux equivalent for the pre-sample beam configuration for the instrument. Because neutron capture cross sections are linear above 0.5 Å for most isotopes, simply scale the flux by λ/1.798 Å, where λ is the average wavelength at the sample weighted by spectral intensity. For non-linear isotopes activation may be underestimated (¹⁷⁶Lu < 1.8 Å; ¹⁵¹Eu < 0.8 Å) or overestimated (³³S < 11 Å; ²⁰⁴Hg < 20 Å).

The neutron activation calculation follows (Shleien 1998). Activation is a function of isotope, not element. When an element is used in a formula, the natural abundance of the individual isotopes is used to determine the total activation. By default, the activation calculator uses values from the IAEA handbook (IAEA 1987), and the scattering calculator uses the IUPAC 2021 atomic weights and isotope composition database (CIAAW 2021).

For very high fluences, e.g., more than 10¹⁶ n/cm2, the activation equations give erroneous results because of the precision limitations. If there is doubt simply do the calculation at a lower flux and proportion the result. This will not work for the cascade reactions, i.e., two neutron additions.

Reaction = b : This is the beta produced daughter of an activated parent. This is calculated only for the cases where the daughter is long lived relative to the parent. The calculated activity is through the end of exposure only. Contributions from the added decay of the parent after the end of irradiation are left for the user to determine, but are usually negligible for irradiations that are long relative to the parent halflife.

Calculation parameters are controlled by URL:

isotope abundance

Use the following to select IUPAC 2021 isotopic abundance data rather than the IAEA 1987 data: index.html?abundance=IUPAC

activation cutoff

The cutoff values for displaying activation data are set to 0.0005 μCi by default. The full activation levels can be displayed using: index.html?cutoff=0

decay cutoff

The activation calculator determines the amount of time for the activation to decay to the cutoff level, or to 0.0005 μCi if cutoff is 0. This can be set to a value such as 0.1 μCi using: index.html?decay=0.1

Notes on calculation:

• For some numerical combinations with very large half-lives the numerical precision is inadequate and you get negative results. This can be corrected by reformulation or approximations but has not been done. Remember, the X in EXP(X) is limited to |X|<709
• Simplifications have been made as indicated in the comments column in data table
• Typically, for a decay chain where the daughter is also produced (isomers) the s of the parent has been added to that of the daughter when the daughter t1/2 is much longer (true for most cases) and the parent t1/2 is relatively short, e.g. less than 1 day, so that all the daughter will be made relatively promptly.
• In cases where the above condition is not met an * is put next to the nuclide name to warn that the daughter production has not been accounted for. In most cases the daughter is in a simple decay equilibrium.
• Where the decay product is a new nuclide a line has been added to the database to account for this. This production mode is indicated in the reaction column by 'b'. Where both m and g state contribute to daughter production it is simplified to a single parent, that with the greater cross-section or that with the longer half-life together with the sum of the cross-sections.
• In a few cases where the parent nuclide t1/2 is very short all production is assigned to the daughter and no entry is made for the parent, as noted in the comments column.
• No correction for neutron burn up has been made.
• Most cross-section data is from IAEA 273.
• Fast neutron data from NBSIR 85-3151, Compendium of Benchmark Neutron Fields is for reaction above the Cd cutooff, .4eV. Noted in comment column.
• Fast neutron reaction data from IAEA 273 has been weighted by a unit fluence fast maxwellian spectrum as described in NBSIR 85-3151, but no further weighting for a 1/v or thermal component has been made. Only selected reactions have been included.
• Reaction = b indicates production via decay from an activation produced parent.
• Notation on reaction product name:

  m, m1, m2

  indicate metastable states. Decay may be the ground state or another nuclide.

  +

  indicates radioactive daughter production already included in daughter listing several parent t1/2's required to acheive calculated daughter activity. All activations are assigned at end of irradiation. In most cases the added activity to the daughter is small.

  *

  indicates radioactive daughter production NOT calculated, approx secular equilibrium.

  s

  indicates radioactive daughter of this nuclide in secular equilibrium after several daughter t1/2's.

  t

  indicates transient equilibrium via beta decay. Accumulation of that nuclide during irradiation is separately calculated.

Cadmium ratio

Units: none

Samples in the rabbit tubes can be shielded with cadmium to reduce the thermal flux while leaving the epithermal flux mostly unchanged. The cadmium ratio determines the degree of reduction in the scattering cross sections, corresponding to the reduced flux. This value is unitless. Use a value of 0 for beamline experiments.

Thermal/fast ratio

Units: none

When performing neutron activation analysis in a rabbit tube, the additional fast neutron activations need to be determined. The thermal/fast ratio is used to determine the fast neutron flux from the thermal flux equivalent for the given rabbit tube. The resulting fast flux is (thermal flux)/(thermal/fast ratio). This value is unitless. Use a value of 0 for beamline experiments.

Material mass

Units: g, kg, mg or ug

The total neutron activation depends on the mass of the individual isotopes in the sample and the total time in the beam. All activation calculations assume a thin plate sample, with all parts of the sample exposed to full flux during activation, and no self-shielding when estimating the activation level outside the beam.

Exposure

Units: h m s d w y

Exposure is the duration of the exposure at the given flux. Activation will be accumulated over that time, with decay beginning the moment the sample is activated. Time defaults to hours, but can be set to hours, minutes, seconds, days, weeks or years by adding h, m, s, d, w, or y to the value respectively.

Decay

Units: h m s d w y OR yyyy-mm-dd hh:mm:ss

The sample begins to decay immediately, even while it is being activated. The decay field allows you to specify how long since the sample was removed from the beam. The default is hours, but can be set to hours, minutes, seconds, days, weeks or years by adding h, m, s, d, w, or y to the value respectively. We always compute the activation level when the sample is removed from the beam, and at 1 hour, 1 day and 15 days post activation.

Instead of saying how long the sample activation has decayed, you can use the time that the sample was removed from the beam. Times are given as year-month-day hour:minute:second. Approximate times are allowed, such as 2010-03 for March, 2010. This is equivalent to 2010-03-31 23:59:59, which is the end of March so that the activation estimate will be conservative. This is the most activation consistent with the sample being on the beam sometime in March, 2010. Times are specified in US/Eastern. Add "Z" after the time of day to indicate universal coordinated time (UTC), or add a timezone offset such as "+01" for +1 hours in France in winter, when daylight savings time is not in effect.

Examples

Mass density

Units: g/cm³ or A3

Density is used to compute absorption, transmission and scattering.

from formula

Leave the density field blank and add

@

+ density to the end of the formula, where density is in g/cm³. For compounds with specific isotopes, you can use the density of the naturally occurring compound as

@

+ density +

n

and the isotope specific density will be computed. Density defaults to 1 g/cm³, or for pure elements, the natural density given in the periodic table is used.

D2O@1n

or

D2O@1.11

g/cm³

Enter the density by itself, which will be interpreted as g/cm³, or equivalently, kg/L. No units are needed. If the value is density +

n

then it is density of the the naturally occuring compound and the isotopic density will be computed.

D₂O has a natural density of

1n

and an isotopic density of

1.11

cell volume

Enter a number followed by A3 for ų. Be sure that your formula contains the correct number of atoms for the unit cell, possibly by using n(formula), where n is 6 for hexagonal close packed, 4 for face centered cells, 2 for body centered and base centered cells, or 1 for simple cells.

4NaCl has a cell volume of

179.4 A3

crystal lattice parameters

Enter lattice parameters "a:n b:n c:n alpha:n beta:n gamma:n" where a, b, c are in Å and α, β, γ are in degrees. If not specified, b and c default to a. Ratios can also be used, so that "b/a:n" gives b=n*a, and "c/a:n" gives c=n*a. Angles α, β, and γ default to 90°. Be sure that the formula contains the correct number of atoms for the unit cell.

4NaCl has a cubic lattice with

a:5.6402

Thickness

Units: cm

The material thickness in cm is used to determine sample transmission, or how much beam will be absorbed by the sample or scattered incoherently. Leave it at 1 cm if you do not need this information.

Source neutrons

Units: Ang, meV or m/s

The energy of the source neutrons will affect the absorption cross section and hence the penetration depth and sample attenuation. Energy can be expressed as wavelength in Å, as energy in meV, or as neutron velocity in m/s. Neutron cross sections are tabulated at 1.798 Å = 25.3 meV = 2200 m/s, with an assumed 1/v dependence for the absorption cross section (Rauch 2003, Sears 2006).

For heavier isotopes (Cd, Hf, rare earths) and/or shorter wavelengths (below 1 Å) there are neutron resonances in the thermal range. For common rare-earth isotopes the energy-dependent coherent and absorption cross sections tabulated in Lynn and Seeger 1992 are used. Incoherent scattering will be understimated for these elements. Resonances for ¹¹³Cd and ¹⁸⁰Ta are ignored.

There is also a wavelength dependence for single phonon interactions which gives rise to significant inelastic scattering for lighter isotopes (H, D) and/or longer wavelengths (above 5 Å). This factor is both temperature and material dependent and will not be included in the scattering calculations. In particular, penetration length and transmitted flux are going to be significantly overestimated.

Source X-rays

Units: Ang, keV or Ka

X-ray absorption and scattering are computed from the energy dependent atomic scattering factors (Henke 1993). Energy can be expressed as wavelength in Å, as energy in keV, or using an element name for the K_α emission line² for that element (Deslattes 2003).

References

1. CIAAW. Isotopic compositions of the elements 2021. Available online at www.ciaaw.org Bölke, et al. (2005). [atomic weights, isotopic abundance]
2. Deslattes, R.D.; Kessler, Jr., E.G.; Indelicato, P.; de Billy, L.; Lindroth, E. and Anton, J. (2003). Rev. Mod. Phys. 75, 35-99. [xray emission lines]
3. Henke, B.L.; Gullikson, E.M. and Davis, J.C. (1993). X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92, Atomic Data and Nuclear Data Tables Vol. 54 (no.2), 181-342. [xray cross sections]
4. IAEA (1987). Handbook on Nuclear Activation Data. TR 273 (International Atomic Energy Agency, Vienna, Austria). [tech report]
5. Kienzle, P. A. (2008). Extensible periodic table [Computer Software]. https://periodictable.readthedocs.io. [calculator source, web service source]
6. Lynn, J.E. and Seeger, P.A. (1990). Resonance effects in neutron scattering lengths of rare-earth nuclides. Atomic Data and Nuclear Data Tables 44, 191-207. doi:10.1016/0092-640X(90)90013-A [rare earth scattering lengths]
7. Rauch, H. and Waschkowski, W. (2003). Neutron Scattering Lengths in ILL Neutron Data Booklet (second edition), A.-J. Dianoux, G. Lander, Eds. Old City Publishing, Philidelphia, PA. pp 1.1-1 to 1.1-17. [booklet, neutron cross sections]
8. Sears, V. F. (2006). "Scattering lengths for neutrons" In Prince, E. Ed. International Tables for Crystallography Volume C: Mathematical, Physical and Chemical Tables" Kluwer Academic Publishers, pp 444-454. doi:10.1107/97809553602060000103 [scattering calculations]
9. Shleien, B.; Slaback, L.A. and Birky, B.K. (1998). Handbook of health physics and radiological health. Williams & Wilkins, Baltimore. [activation data]

History

2024-12-03 v2.0.0

Update mass and abundance tables, and physical constant values
neutron cross section updates for H, He, C, O, Zn, Kr, Sn, Xe, Sm, Eu, Ir, Pb, Bi
X-ray cross section updates for Pt, Cr, Nb, Y, Er
208Pb activation scaled by 0.001 (value was reported in mbarns but added as barns)

2024-03-22 v1.7.0

Mixture formulas allow wt% and vol%.
Formulas allow unicode subscripts such as H₂O.
FASTA sequences (aa: rna: dna:) allowed as mixture components.
FASTA calculations updated.
Use correct halflife for Tm-171, Ho-163 and W-188 activation products.
Improve numerical precision of activation calculations.

2021-04-21 v1.6.0

Support energy-dependent rare earth elements.
Use complex scattering length b_c when computing σ_c = 4π |b_c|²/100 and σ_i = σ_s - σ_c.

2020-10-29 v1.5.3

Change field labels from 'time on/off beam' to 'exposure/decay duration'.

2020-01-22

Restore support for Internet Explorer 10 and 11.

2019-12-02

Fix cutoff=0 handling in URL.

2019-11-14 v1.5.2

Correct units on activity table: nCi becomes uCi.
Elemental carbon density changed to 2.2 to match CXRO, CRC and RSC.

2019-11-04

Update neutron refs with links to ILL data book and Table for Crystallography.

2019-09-16

Improve help system: can now scroll between sections.

2019-09-11 v1.5.1

Include notes on activation calculation.

2019-08-27

Change default cutoff to 0.5 nCi.

2018-01-12

Make activation table sortable.

2017-05-11 v1.5.0

Improved support for printing tables.
Support for biomolecules with labile hydrogen (FASTA format).
Mixture by mass and volume, e.g., 5 g NaCl // 50 mL H2O@1
Multi-layer materials, e.g., 5 um Si // 3 nm Cr // 8 nm Au
Compute incoherent cross section from coherent and total.

2016-12-07

Use exponential notation for all activity levels.

2015-10-20

Allow decay time to be calculated from timestamp..

2014-03-20 v1.4.1

Default to isotopic density.

2013-11-05

Support for X-ray scattering.

2013-04-17 v1.3.8

Initial release.