Neutron activation and scattering calculator
This calculator uses neutron cross sections to compute activation
on the sample given the mass in the sample and the time in the beam,
or to preform scattering calculations for the neutrons which are
not absorbed by the sample.
- Enter the sample formula in the material panel.
- 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.
- 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.
The chemical formula parser allows you to specify materials and mixtures.
Formulas are parsed with
python package (Kienzle 2008).
For FASTA sequences
use "code:sequence", where code is "aa" for amino acid sequences, "dna" for
DNA sequences, or "rna" for RNA sequences. Density is estimated automatically.
This calculation uses natural abundance of hydrogen; isotope substitution for
labile hydrogen in D2O mixtures is not supported in the online calculator,
though it is in the underlying periodictable library.
- simple formula
- A basic formula consists of elements and their quantities.
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.
all represent ikaite,
- Isotopes are represented by element[nuclide index].
can be used for 2H and 3H.
Isotopes can be mixed within a formula, such as
DHO for partially deuterated water.
- 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
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.
all give the density of D2
O as 1.11 g/cm3
- mole fractions
- Using non-integer quantities, arbitrary concentration ratios can be
78.2H2O + 21.8H2O @1n
represents water with 78.2% 16
O and 21.8% 18
- 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 Co0.552
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
O, which is the same as
- 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
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
β-casein amino acid sequence
Provide the thermal flux equivalent for the pre-sample beam configuration
for the instrument. This is only need for computing the neutron
activation from the experiment, and is not used for computing scattering
cross sections. Within the NCNR, you can access a list of
but this is not available from outside.
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 NIST atomic weights and isotope composition
database (Bölke 2005).
Calculation parameters are controlled by URL:
- isotope abundance
The NIST database can be selected for isotope abundance using:
- 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
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
indicates radioactive daughter of this nuclide in secular equilibrium
after several daughter t1/2's.
indicates transient equil via beta decay. Accumulation of that nuclide
during irradiation is separately calculated.
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
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.
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.
Time on beam
Units: h m s d w y
Time on the beam is the length of the exposure at the given flux. Activation
will be accumulated over time.
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.
Time off beam
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 time off beam 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 ago the sample was removed from the beam, you can
specify when it was removed. Times are given as
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. That is, 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.
|If you type:||This is equivalent to:|
|2 m||2 minutes ago|
|1||1 hour ago|
|2.5w||2 and a half weeks ago|
|3 y||3 years ago|
|2015-01-02 21:45:00||January 2, 2015 at 9:45 PM US/Eastern|
|2010-03||March 31, 2010 at 11:59:59 PM US/Eastern|
|2010-7-5 12:23||July 5, 2010 at 12:23:59 PM US/Eastern|
|2015-01-02 21:45:00Z||January 2, 2015 at 9:45 PM UTC|
|2015-01-02 21:45:00-0600||January 2, 2015 at 9:45 PM US/Central|
|2015-08-02 21:45:00-0500||August 2, 2015 at 9:45 PM US/Central|
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 +
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.
- Enter the density by itself, which will be interpreted as g/cm3, or
equivalently, kg/L. No units are needed. If the value is
n then it is density of the the
naturally occuring compound and the isotopic density will be computed.
O has a natural density of
and an isotopic density of
- cell volume
- Enter a number followed by A3 for Å3. 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
- 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
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.
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 which are not
accounted for in the scattering calculator. There is also a 1/v 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.
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 Kα emission line2 for
that element (Deslattes 2003).
Bölke, et al. (2005).
Isotopic Compositions of the Elements, 2001.
J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
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]
Henke, B.L.; Gullikson, E.M. and Davis, J.C. (1993).
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]
Handbook on Nuclear Activation Data.
TR 273 (International Atomic Energy Agency, Vienna, Austria).
Kienzle, P. A. (2008-2019).
Extensible periodic table (v1.5.2).
web service source]
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.
neutron cross sections]
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.
Shleien, B.; Slaback, L.A. and Birky, B.K. (1998).
Handbook of health physics and radiological health.
Williams & Wilkins, Baltimore.
- Restore support for Internet Explorer 10 and 11.
- Fix cutoff=0 handling in URL.
- Correct units on activity table: nCi becomes uCi.
Elemental carbon density changed to 2.2 to match CXRO, CRC and RSC.
- Update neutron refs with links to ILL data book and Table for Crystallography.
- Improve help system: can now scroll between sections.
- Include notes on activation calculation.
- Change default cutoff to 0.5 nCi.
- Make activation table sortable.
- 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.
- Use exponential notation for all activity levels.
- Allow decay time to be calculated from timestamp..
- Default to isotopic density.
- Support for X-ray scattering.
- Initial release.