Skip to content
Radiation Lab RadCalc
Sign in
Gamma dose rate validation — the constant, the coefficients and the cutoff

Validation of the gamma dose rate and shielding calculator

This calculation is a chain: a unit derivation, an interpolation, a set of emission intensities, a set of attenuation coefficients, and an exponential. Each link is checked on its own terms, and the report says plainly which link cannot be checked the way one might expect.

Subject
The calculator at /calc/gamma-shielding/, and the modules src/engine/gamma.ts and src/engine/interp.ts.
Quantity computed
Air kerma rate constant Γδ, in mGy·m²/(GBq·h), at a low-energy cutoff δ that the interface exposes.
Report date
2026-09-18
Source revision
09c0347
Archived source
10.5281/zenodo.22794265
Checks performed
654
Result
All checks pass.

Scope

This report covers the air kerma rate constant the calculator computes, the point-source dose rate it derives from it, the attenuation of that rate through a shield, and the interpolation of the coefficient tables underneath both. It does not cover buildup coefficients, which this site does not supply, nor any other calculator.

Why there is no comparison against published gamma constants

The obvious way to validate a computed gamma constant is to set it beside a published one. That comparison was attempted and abandoned, and the reason is worth more than the comparison would have been.

The published constants are a different quantity. What this tool computes is an air kerma rate constant: photons per decay, times energy, times the mass energy-absorption coefficient of air. The best-known freely available compilation, ORNL/RSIC-45, tabulates something else — the dose-equivalent rate at one metre, obtained by weighting the photon fluence with a fluence-to-dose-rate function rather than with the absorption coefficient of air. Its own equations say so. Setting the two side by side and reporting the difference as agreement or disagreement would be meaningless, and it is a mistake this field makes often enough that the three quantities involved — exposure rate constant, air kerma rate constant, and ambient dose equivalent rate constant — are worth naming separately every time.

The weighting function is inside a standard that cannot be reproduced here. Even converting between the two would require the coefficients of that function, which belong to a paid standard. This site does not reproduce such material, which is also why it supplies no buildup coefficients.

And the constant depends on a cutoff that published values often omit. Γδ counts only photons above δ. The table further down measures what that choice is worth: for americium-241 it is a factor of about eight between 10 and 20 keV. A comparison against a value whose δ is unstated is not a weak comparison; it is not a comparison.

There is a further piece of evidence, and it is the strongest of the three. The international metrology community publishes its own evaluated radionuclide table — the BIPM's Monographie-5, which is the DDEP evaluation in its formal form. That table does not contain a gamma constant of any kind. Its opening states what it recommends: half-lives, decay modes, alpha, beta, gamma, X-ray and electron emissions, and the characteristics of the transitions. Searching the whole of its first volume for the words kerma, exposure or dose rate constant returns nothing at all.

The evaluators stop at the emissions deliberately. Everything past that point — which quantity, which cutoff, which weighting function — is an application convention rather than evaluated data, and it is exactly where published gamma constants stop agreeing with each other.

So the output is not compared. Instead the derivation and the inputs are validated separately, which is what can actually be done rigorously and is what the evaluated data supports: if the formula is right, the coefficients are the published ones, and the emission intensities agree with an independent evaluation, then the constant follows. Each of those three is a section below.

Sources: ORNL/RSIC-45, page 1, equations (1) and (2) · BIPM Monographie-5, Volume 1 (2004), introduction and full text.

The unit chain, derived

The bottom link, and until this report the only one no test looked at. A factor of ten here would move every dose rate on the site by a factor of ten, and every internal consistency check would still pass.

FactorHandIn the codeDifference
The factor that carries Gy/s per Bq to mGy·m²/(GBq·h) G-U-01 · the 3.6e15 in gammaConstant and shieldedDoseRate 3.6×10¹⁵ 3.6×10¹⁵ 0
The factor that carries cm²/g to m²/kg G-U-02 · the muEn * 0.1 in gammaConstant and shieldedDoseRate 1×10⁻¹ 1×10⁻¹ 0
Collision kerma, not total kerma G-U-03 · the choice of muEn over muTr 1×10⁰ 1×10⁰ 0

G-U-01 — The factor that carries Gy/s per Bq to mGy·m²/(GBq·h)

  1. A point source of activity A emits A·yᵢ photons of energy Eᵢ per second, isotropically.
  2. At distance d the fluence rate of that line is φ̇ᵢ = A·yᵢ/(4πd²), in units of 1/(m²·s).
  3. The air kerma rate it produces is K̇ᵢ = φ̇ᵢ·Eᵢ·(µen/ρ)air.
  4. Checking the units: [1/(m²·s)]·[J]·[m²/kg] = J/(kg·s) = Gy/s. The expression is dimensionally a dose rate, which is the first thing to establish.
  5. The constant is defined as Γ = K̇·d²/A = Σ Eᵢ·yᵢ·(µen/ρ)ᵢ /(4π), in Gy·m²/(Bq·s).
  6. The interface reports mGy·m²/(GBq·h), so three conversions apply: Gy to mGy is ×10³, per becquerel to per gigabecquerel is ×10⁹, and per second to per hour is ×3600.
  7. 10³ × 10⁹ × 3600 = 3.6 × 10¹⁵ exactly.

G-U-02 — The factor that carries cm²/g to m²/kg

  1. The NIST tables give mass energy-absorption coefficients in cm²/g.
  2. 1 cm²/g = (10⁻² m)² / (10⁻³ kg) = 10⁻⁴ m² / 10⁻³ kg.
  3. = 10⁻¹ m²/kg, so the multiplier is 0.1 exactly.
  4. Getting this wrong by a factor of ten would move every dose rate on the site by the same factor, and nothing else in the chain would notice.

G-U-03 — Collision kerma, not total kerma

  1. The sum uses µen/ρ, the mass energy-absorption coefficient, not µtr/ρ, the mass energy-transfer coefficient.
  2. µen/ρ = (µtr/ρ)(1 − g), where g is the fraction of the secondary electron energy that goes to bremsstrahlung.
  3. The product therefore yields the collision kerma; total kerma is larger by 1/(1 − g).
  4. In air below a few MeV g is small, so the two are close, but this report records which of them the tool computes rather than leaving it to be assumed.
  5. This case carries no arithmetic; it is here so that the choice is stated and cannot drift unrecorded.

Exact identities

These hold whatever the attenuation coefficient is, which is what makes them identities. They test the exponential and the geometry, not the coefficients; those are the next section.

IdentityHandToolDifference
Doubling the distance quarters the dose rate G-ID-01 2.5×10⁻¹ 2.5×10⁻¹ 0
The dose rate is proportional to the activity G-ID-02 2×10⁰ 2×10⁰ 0
No shield transmits everything G-ID-03 1×10⁰ 1×10⁰ 0
Turning the shield off transmits everything G-ID-04 1×10⁰ 1×10⁰ 0
One half-value layer transmits one half G-ID-05 5×10⁻¹ 5×10⁻¹ 0
One tenth-value layer transmits one tenth G-ID-06 1×10⁻¹ 1×10⁻¹ 2.78×10⁻¹⁶
A tenth-value layer is log₂10 half-value layers G-ID-07 3.32192809489×10⁰ 3.32192809489×10⁰ 2.67×10⁻¹⁶
Buildup at zero thickness is unity G-ID-08 1×10⁰ 1×10⁰ 0
The two dose-rate code paths agree G-ID-10 1×10⁰ 1×10⁰ 2.22×10⁻¹⁶
Buildup without coefficients is unity, not zero G-ID-09 1×10⁰ 1×10⁰ 0
Derivations of the identities

G-ID-01 — Doubling the distance quarters the dose rate

  1. Ḋ = Γ·A/d², so Ḋ(2d)/Ḋ(d) = d²/(2d)² = 1/4.
  2. Exactly a quarter, for any Γ and any activity. This is the one relation a user checks in their head.

G-ID-02 — The dose rate is proportional to the activity

  1. Ḋ is linear in A, so doubling the activity doubles the rate.
  2. The ratio is exactly 2.

G-ID-03 — No shield transmits everything

  1. At x = 0 the attenuation factor is e⁰ = 1 for every line.
  2. The transmission is exactly 1, not approximately.

G-ID-04 — Turning the shield off transmits everything

  1. With the shield mode set to none the attenuation term is skipped entirely.
  2. Transmission is exactly 1, and must equal the zero-thickness case rather than merely resemble it.

G-ID-05 — One half-value layer transmits one half

  1. The half-value layer is defined by x = ln2/µ.
  2. Then µx = ln2 and the transmission is e^(−ln2) = 1/2 exactly.
  3. This holds whatever µ is, so it tests the exponential rather than the coefficient. The coefficient itself is tested separately against the NIST table.

G-ID-06 — One tenth-value layer transmits one tenth

  1. x = ln10/µ gives µx = ln10 and transmission e^(−ln10) = 1/10 exactly.

G-ID-07 — A tenth-value layer is log₂10 half-value layers

  1. TVL/HVL = (ln10/µ)/(ln2/µ) = ln10/ln2 = log₂10.
  2. = 3.321928095, independent of material and energy. The rule of thumb 'a TVL is about three and a third HVLs' is this number.

G-ID-08 — Buildup at zero thickness is unity

  1. The Berger form is B = 1 + a·µx·e^(b·µx).
  2. At µx = 0 the second term vanishes and B = 1 exactly.
  3. A buildup factor below 1 would mean the shield created a deficit of scattered photons, which is not physical.

G-ID-10 — The two dose-rate code paths agree

  1. The same physics is implemented twice in this engine: once as Γ·A/d² on a precomputed constant, and once inside the shielding routine, which rebuilds the 3.6×10¹⁵/(4π) factor for itself and sums the spectrum again.
  2. The screen uses the second one. A report that exercised only the first would be validating code the user never reaches.
  3. With the shield turned off the two must return the same number, and the ratio must be 1.
  4. They do agree, to better than one part in 10¹⁵. Nothing enforced that before this case existed, which is the reason it exists.

G-ID-09 — Buildup without coefficients is unity, not zero

  1. The coefficients for the Berger form are not supplied by this site, because the published tables are inside a standard that cannot be reproduced here.
  2. When they are absent the factor must fall back to 1, which is the narrow-beam result and an underestimate that the interface labels as such.
  3. Falling back to 0 would silently report no dose behind a shield.

The interpolation

Attenuation coefficients fall across orders of magnitude, so the tables are interpolated logarithmically in both energy and coefficient. The strongest check available is that asking for an energy that is already in the table returns the tabulated number: that fails for almost any error in the formula. It was run over every row of all 8 materials.

CaseHandToolDifference
At a tabulated energy the table value comes back unchanged G-IN-01 · air · 0.6 MeV 2.953×10⁻² 2.953×10⁻² 2.35×10⁻¹⁶
The same, for a linear attenuation coefficient in lead G-IN-02 · lead · 1 MeV 7.102×10⁻² 7.102×10⁻² 1.95×10⁻¹⁶
Between two rows, the logarithmic interpolation worked by hand G-IN-03 · air · 0.7 MeV 2.914740761×10⁻² 2.91474076053×10⁻² 1.62×10⁻¹⁰
The same in lead, where the coefficient falls faster G-IN-04 · lead · 1.1 MeV 6.549810906×10⁻² 6.54981090568×10⁻² 4.92×10⁻¹¹
Below the first row the first value is held G-IN-05 · air · 0.0005 MeV 3.606×10³ 3.606×10³ 0
Above the last row the last value is held G-IN-06 · air · 25 MeV 1.705×10⁻² 1.705×10⁻² 0
At the lead K-edge, exactly on the edge energy, the lower branch is returned G-IN-07 · lead · 0.0880045 MeV 1.91×10⁰ 1.91×10⁰ 0
One step above the edge, the upper branch G-IN-08 · lead · 0.0880046 MeV 7.68297776885×10⁰ 7.68297776885×10⁰ 0

Across all 602 tabulated values the largest disagreement is 5.764e-16. It is not exactly zero, and the reason is worth a sentence because the first version of this check demanded that it be: when the requested energy equals a tabulated one the interpolation weight is exactly 1, but log(y₀) + (log(y₁) − log(y₀)) is not exactly log(y₁) in binary floating point. The table values are therefore reproduced at the resolution of the arithmetic rather than bit for bit. The engine was left alone: a correction here would change no answer anywhere by more than one part in 10¹⁵.

How each interpolation was worked

G-IN-01 — At a tabulated energy the table value comes back unchanged

  1. The air table has a row at 0.6 MeV with µen/ρ = 0.02953 cm²/g.
  2. Asking for exactly that energy must return exactly that number: the interpolation weight is 1 and no arithmetic should intervene.
  3. This is the strongest single check on an interpolator, because it fails for almost any error in the formula.

G-IN-02 — The same, for a linear attenuation coefficient in lead

  1. The lead table has a row at 1.0 MeV with µ/ρ = 0.07102 cm²/g.
  2. It must come back unchanged.

G-IN-03 — Between two rows, the logarithmic interpolation worked by hand

  1. The bracketing rows are 0.6 MeV with 0.02953 and 0.8 MeV with 0.02882.
  2. The weight is f = (ln0.7 − ln0.6)/(ln0.8 − ln0.6) = 0.5358369345.
  3. µen/ρ = exp(ln0.02953 + f·(ln0.02882 − ln0.02953))
  4. = 0.02914740761 cm²/g.
  5. Linear interpolation would give 0.029175, which differs in the fifth digit here and by far more where the coefficient falls steeply.

G-IN-04 — The same in lead, where the coefficient falls faster

  1. Rows: 1.0 MeV with 0.07102 and 1.25 MeV with 0.05876.
  2. f = (ln1.1 − ln1.0)/(ln1.25 − ln1.0) = 0.4271249572.
  3. µ/ρ = exp(ln0.07102 + f·(ln0.05876 − ln0.07102)) = 0.06549810906 cm²/g.

G-IN-05 — Below the first row the first value is held

  1. The air table starts at 1 keV with µ/ρ = 3606 cm²/g.
  2. Below that the first value is held rather than extrapolated. Extrapolating a curve this steep would produce nonsense.
  3. No emission line in this site's data lies below 1 keV, so the clamp is a guard rather than a working path.

G-IN-06 — Above the last row the last value is held

  1. The table ends at 20 MeV with µ/ρ = 0.01705 cm²/g, and that value is held above it.
  2. The highest line in this site's data is well below 20 MeV.

G-IN-07 — At the lead K-edge, exactly on the edge energy, the lower branch is returned

  1. The NIST lead table lists 88.0045 keV twice, once with µ/ρ = 1.91 and once with 7.683: the K-shell absorption switches on there and the coefficient is discontinuous.
  2. A function of one variable cannot return two values, so a convention is forced. Asked for exactly the edge energy this implementation returns the lower branch, 1.91.
  3. One step above the edge it returns 7.683, and one step below it interpolates towards 1.91 from the row beneath. Both sides are therefore right; only the single point of discontinuity is a convention.
  4. This is recorded because the source comment claimed the opposite, and a claim that disagrees with the code is worse than no claim. The effect on any dose rate is nil: no emission line in this site's data sits on an edge energy to seven digits.

G-IN-08 — One step above the edge, the upper branch

  1. At 88.0046 keV the bracketing rows are the upper edge row (7.683) and 100 keV (5.549).
  2. The interpolation runs on the upper branch and returns 7.68297776884886, a hair below 7.683.
  3. The discontinuity is therefore resolved within one part in 10⁷ of the edge energy.

Coefficient source: Hubbell, J. H. and Seltzer, S. M., Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients, NIST Standard Reference Database 126, doi:10.18434/T4D01F. Published by NIST as a Standard Reference Database; not a public-domain work. Used here to compute, not redistributed as a dataset.

Emission intensities, derived from an independent evaluation

The nuclear data on this site come from the IAEA's Livechart interface, which serves ENSDF. The independent check is against DDEP, as in the decay report — but DDEP does not tabulate photon emission probabilities directly. It gives the transition probability Pγ+ce and the internal conversion coefficient αT, and for transitions above 1.022 MeV an internal pair creation coefficient απ. The photon intensity has to be derived: 

Pγ = Pγ+ce / (1 + αT + απ)

That derivation is itself checkable, which matters (G-EM-00): DDEP publishes the caesium-137 line intensity separately as 85.01 (0.2) %, and the derivation returns 8.501438×10¹ %, agreeing to 5.16×10⁻⁵. Without that step the formula would be an assumption that every line below inherited.

The internal pair creation term is not decoration. Left out, the 1332 keV line of cobalt-60 comes out 0.0034 % away from the value in this site's data; put back in, the two agree to the digits quoted. Both the derivation and the data had to be right for that to happen.

LineDDEP, derived This site Differenceσ
Cs-137 661.657 keV G-EM-01 8.5014383×10¹ 8.51×10¹ +0.1007% 0.37
Co-60 1332.508 keV G-EM-02 9.9982603×10¹ 9.99826×10¹ -0.0000% 0.01
Co-60 1173.24 keV G-EM-03 9.9832609×10¹ 9.985×10¹ +0.0174% 0.58
Co-60 826.1 keV G-EM-04 7.5974169×10⁻³ 7.6×10⁻³ +0.0340% 0.00
Co-60 347.14 keV G-EM-05 7.4584564×10⁻³ 7.5×10⁻³ +0.5570% 0.10
Co-60 2158.61 keV G-EM-06 1.1999406×10⁻³ 1.2×10⁻³ +0.0050% 0.00
Mn-54 834.855 keV G-EM-07 9.9975206×10¹ 9.9976×10¹ +0.0008% 2.65
Na-22 1274.577 keV G-EM-08 9.9936991×10¹ 9.994×10¹ +0.0030% 0.02
I-131 80.1854 keV G-EM-09 2.6061321×10⁰ 2.61615×10⁰ +0.3844% 0.17
I-131 163.93 keV G-EM-10 2.1106796×10⁻² 2.111×10⁻² +0.0152% 0.01
The lines as they appear in the DDEP sheets
  • Cs-137 — γ2,0(Ba) 661,657 (3) 94,57 (26) M4 αT = 1,124 (16) ×10⁻¹
  • Co-60 — γ1,0(Ni) 1332,508 (4) 99,9988 (2) E2 αT = 1,28 (5) ×10⁻⁴ απ = 3,4 (4) ×10⁻⁵
  • Co-60 — γ3,1(Ni) 1173,240 (3) 99,85 (3) E2(+M3) αT = 1,68 (4) ×10⁻⁴ απ = 0,62 (7) ×10⁻⁵
  • Co-60 — γ2,1(Ni) 826,10 (3) 0,0076 (8) M1+45%E2 αT = 3,4 (4) ×10⁻⁴
  • Co-60 — γ3,2(Ni) 347,14 (7) 0,0075 (4) [E2] αT = 55,7 (17) ×10⁻⁴
  • Co-60 — γ2,0(Ni) 2158,61 (3) 0,0012 (2) E2 αT = 0,495 (15) ×10⁻⁴
  • Mn-54 — γ1,0(Cr) 834,855 (3) 99,9997 (3) E2 αT = 2,45 (4) ×10⁻⁴
  • Na-22 — γ1,0(Ne) 1274,577 (7) 99,94 (13) E2 αT = 6,71 (9) ×10⁻⁶ απ = 2,34 (3) ×10⁻⁵
  • I-131 — γ1,0(Xe) 80,1854 (19) 6,63 (15) M1 αT = 1,544 (46) — no power-of-ten factor on this sheet
  • I-131 — γ2,0(Xe) 163,930 (8) 1,087 (21) M4 αT = 50,5 (7) — no power-of-ten factor on this sheet

The power-of-ten factor on the conversion coefficients differs from sheet to sheet — 10⁻¹ for caesium-137, 10⁻⁴ for cobalt-60, and none at all for iodine-131, whose 164 keV transition is M4 and has αT above fifty. Reading that header wrongly is a factor-of-fifty error, and the derivation catches it: taken as an absolute value the iodine line agrees with this site's data to 0.02 %, and taken as 10⁻⁴ it would be out by fifty. Agreement to the digits is itself the evidence that the sheet was read correctly.

Five nuclides, ten lines. That is a sample and the report says so rather than implying a census. Americium-241 was left out deliberately: its DDEP transition table carries approximate and blank entries, and a reference value that cannot be read without guessing is worse than none. An earlier automated reading of these sheets returned the half-life of uranium-238 as 24.10 days, which is thorium-234's, because each sheet also carries the daughter.

Source: BIPM Monographie-5, per-nuclide sheets, section 2.2.

What the cutoff does

Γδ counts photons above δ only. The interface exposes δ because the answer depends on it, and how much it depends is not a matter of opinion.

NuclideΓ(δ=10)/Γ(δ=20)What it means
Am-241 G-DL-01 7.8420957×10⁰ Nearly eight times. Almost all of the air kerma from americium-241 comes from photons between 10 and 20 keV, so the cutoff does not trim the answer — it decides it.
Ir-192 G-DL-02 1.0904852×10⁰ Nine per cent, which is larger than the agreement any published comparison would claim.
Cs-137 G-DL-03 1×10⁰ No change: the caesium X-rays lie above 30 keV, so the two cutoffs select the same lines.
Co-60 G-DL-04 1×10⁰ No change, for the same reason. A comparison built only on cobalt-60 would show none of this.
I-131 G-DL-05 1×10⁰ No change at this pair of cutoffs, although iodine-131 does move between 20 and 30 keV.

Worked cases

CaseHandToolDifference
The air kerma rate constant of caesium-137 G-W-01 · mGy·m²/(GBq·h) 7.714631742×10⁻² 7.71463174221×10⁻² 2.78×10⁻¹¹
The air kerma rate constant of cobalt-60 G-W-02 · mGy·m²/(GBq·h) 3.056472063×10⁻¹ 3.05647206254×10⁻¹ 1.50×10⁻¹⁰
37 GBq of cobalt-60 at one metre G-W-03 · mGy/h 1.130894663×10¹ 1.13089466314×10¹ 1.24×10⁻¹⁰
370 GBq of iridium-192 at two metres G-W-04 · mGy/h 1.011363917×10¹ 1.0113639167×10¹ 2.95×10⁻¹⁰
Caesium-137 through two centimetres of lead G-W-05 · (transmission) 7.874879433×10⁻² 7.87487943332×10⁻² 4.01×10⁻¹¹

G-W-01 — The air kerma rate constant of caesium-137

  1. Six lines survive the 20 keV cutoff: 661.657 keV at 85.1 %, and five X-rays between 31.8 and 37.3 keV.
  2. For the main line, µen/ρ in air interpolates to 0.02928664455 cm²/g, that is 2.928664455 × 10⁻³ m²/kg.
  3. Its contribution is E·y·(µen/ρ) = 0.661657 × 1.602176634×10⁻¹³ × 0.851 × 2.928664455×10⁻³ = 2.642059×10⁻¹⁶ J·m²/kg.
  4. The five X-rays add 5.0855×10⁻¹⁸, about 1.9 % of the total; the sum is 2.692914490×10⁻¹⁶.
  5. Γ = sum /(4π) × 3.6×10¹⁵ = 0.07714631742 mGy·m²/(GBq·h).

Why this case: The reference source of the field, and the one whose spectrum is simple enough to follow line by line.

G-W-02 — The air kerma rate constant of cobalt-60

  1. The two principal lines, 1173.228 keV at 99.85 % and 1332.492 keV at 99.9826 %, carry essentially all of it.
  2. Three weak lines and nothing below 20 keV make up the remainder.
  3. Γ = 0.3056472063 mGy·m²/(GBq·h), about four times the caesium value for twice the photon energy and twice the yield.

Why this case: Two strong lines close in energy, so the answer is dominated by a part of the attenuation curve that is nearly flat.

G-W-03 — 37 GBq of cobalt-60 at one metre

  1. Ḋ = Γ·A/d² = 0.3056472063 × 37 / 1²
  2. = 11.30894663 mGy/h of air kerma.
  3. This is air kerma, not ambient dose equivalent and not exposure: comparing it with a remembered number in R/h without converting is how the two get confused.

Why this case: One curie at one metre, the arrangement every handbook rule of thumb is quoted for.

G-W-04 — 370 GBq of iridium-192 at two metres

  1. Γ(Ir-192) = 0.1093366396 mGy·m²/(GBq·h) at the 20 keV cutoff.
  2. Ḋ = 0.1093366396 × 370 / 2² = 40.45455667 / 4
  3. = 10.11363917 mGy/h.

Why this case: An industrial radiography source at a barrier distance.

G-W-05 — Caesium-137 through two centimetres of lead

  1. For the 661.657 keV line, µ/ρ in lead interpolates to 0.1111201198 cm²/g.
  2. µ = 0.1111201198 × 11.35 g/cm³ = 1.261213360 cm⁻¹, so µx = 2.522426719 at 2 cm.
  3. e^(−2.522426719) = 0.08026459060 for that line alone.
  4. The X-rays are attenuated far more strongly, so the weighted transmission over all six lines is lower:
  5. 0.07874879433.
  6. This is narrow-beam: scattered photons are not counted, so the real rate behind the shield is higher. The interface says so, and the buildup mode exists for that reason.

Why this case: The commonest shielding sum in a radiation protection office, and the one where leaving out buildup matters most.

Required refusals

AskedWhy there is no answerReturned
A distance of zero G-R-01 The inverse-square law has a pole at the source. A point source is an idealisation and the field does not diverge in reality, but the model says nothing usable at zero and must not pretend otherwise. NaN
A negative distance G-R-02 There is no such geometry. Squaring it would hide the sign and return a plausible number. NaN

Coverage and result

CheckCountResult
Unit factors derived by hand3pass
Exact identities10pass
Interpolations worked by hand8pass
Tabulated values reproduced602within arithmetic
Emission lines against an independent evaluation10all within 3σ
Cutoff sensitivity measured5pass
Worked cases end to end5pass
Required refusals2pass

The largest disagreement anywhere in this report is 2.65σ, on the Mn-54 line at 834.855 keV, which is 0.0008 % in relative terms.

What this does not establish

Reporting a disagreement

Contact details are on the contact page. The other reports are the unit converter and the decay calculator, and the method behind the rest of RadCalc is on the methods page.