NIST Center for Neutron Research
+ + +
+
+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). +
+-
+
- 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. +
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.
++CaCO3represents 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 6H2Oand +CaCO3(H2O)6all represent ikaite, + CaCO3·6H2O +
+
+
- isotopes +
- Isotopes are represented by element[nuclide index].
+Special symbols Dand +T+can be used for 2H and 3H. +Isotopes can be mixed within a formula, such as +DHOfor partially deuterated water. +UseH[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@1.29nrepresents 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 Co0.552Ti0.448+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+- biomolecules
+- + 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 1H for labile hydrogen, with substitution + by H in natural abundance and pure D when computing contrast match point. +
+β-casein amino acid sequence+aa:RELEELNVPGEIVESLSSSEESITRINKKIEKFQSEEQQQTEDELQDKIHPFAQTQSLVYPFPGPIPNSLPQNIPPLTQTPVVVPPFLQPEVMGVSKVKEAMAPKHKEMPFPKYPVEPFTESQSLTLTDVENLHLPLPLLQSWMHQPHQPLPPTVMFPPQSVLSLSQSKVLPVPQKAVPYPQRDMPIQAFLLYQEPVLGPVRGPFPIIV++ +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. +
+ ++
+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 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@1nor +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 + nthen it is density of the the + naturally occuring compound and the isotopic density will be computed. +D2O has a natural density of ++1nand an isotopic density of +1.11
+
- 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 ++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 Kα emission line2 for + that element (Deslattes 2003). +
+++ +References
+-
+
- + CIAAW. Isotopic compositions of the elements 2021. Available online + at www.ciaaw.org + Bölke, et al. (2005). + [atomic weights, + isotopic abundance] + +
- + 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). + 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] + +
- + IAEA (1987). + Handbook on Nuclear Activation Data. + TR 273 (International Atomic Energy Agency, Vienna, Austria). + [tech report] + + +
- + Kienzle, P. A. (2008). + Extensible periodic table + [Computer Software]. + https://periodictable.readthedocs.io. + [calculator source, + web service source] + +
- + 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] +
- + 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] + +
- + 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] + +
- + Shleien, B.; Slaback, L.A. and Birky, B.K. (1998). + Handbook of health physics and radiological health. + Williams & Wilkins, Baltimore. + [activation data] + +
++ + + +History
+-
+
- 2025-04-23 v2.0.0 +
- Fix sort by half-life with units of ky, My, Gy. +
- 2025-02-28 v2.0.0 +
- Use standard year as 365 rather than 365.2425 days when reporting decay time. + +
- 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 bc when computing + σc = 4π |bc|2/100 and + σi = σs - σc. +
+ - 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. +