4.9. Understanding and using DCHAIN’s dose rate outputs¶
One of the core quantities outputted by DCHAIN is “dose” rate. That said, “dose” can mean many different things, and this section seeks to clarify the meaning of this value in DCHAIN, how it is calculated, and how one may wish to use it in their own applications.
In short, the dose rates reported by DCHAIN are determined by multiplying the activity of each nuclide by a nuclide-specific activity-to-dose coefficient. These coefficients are present for all nuclides within each decay library in DCHAIN and are ultimately derived from energy-dependent photon fluence to effective dose \(E\) (ICRP 116 [ICR10]) or fluence to ambient dose equivalent \(H^*(10)\) (ICRP 74 [IInternationalCoRProtectionInternationalCoRUnits96]) coefficients. For each nuclide, the activity-to-dose coefficient is calculated by summing the product of emission intensity \(\varepsilon\) (\(\gamma\)/decay) and \(C_{\text{ICRP}}(E)\) for every decay photon listed in a nuclide’s decay data, where \(C_{\text{ICRP}}(E)\) is the photon energy-dependent fluence to dose conversion coefficient calculated as prescribed by ICRP. Equation (4.9.1) shows this dose rate (\(\dot{E}\) or \(\dot{H}^*(10)\)) calculation for nuclide \(X\) at activity \(A_X\) with \(N_X\) photon emissions at energies \(E_i\) and emission intensities \(\varepsilon_i\). These fluence to dose coefficients \(C\) are converted from the units used within ICRP, pSv\(\cdot\)cm\(^2\), to the units used within DCHAIN, \(\frac{\mu \text{Sv} \cdot \text{m}^2}{\text{MBq} \cdot \text{hr}}\), as shown in Equation (4.9.2).
Note that ICRP assumes these coefficients will be used alongside a fluence-like or flux-like quantity, containing an areal dependence (cm\(^2\)) in the denominator, to obtain just a dose (pSv) or dose rate (pSv/s). However, in the case of decaying nuclides, the observed photon flux is entirely dependent on a number of factors, most significantly being distance and attenuation (self-shielding). Since DCHAIN is unaware of the actual dimensions and location of each region, it cannot factor in attenuation at all, so this effect is neglected. As for distance, assuming the nuclides are concentrated as a point source, one would calculate the decay photon flux \(\phi\) at a distance \(r\) from a nuclide with photon emission rate \(\dot{R}\) (where \(\dot{R}=A\cdot\varepsilon_{\text{total}}\), the product of activity and total photon emissions per decay) as \(\phi(r) = \dot{R}/(4\pi r^2)\). As the dose values reported by DCHAIN have folded within them already the activities and emission probabilities, the denominator of this equation is the only missing element to convert the values reported by DCHAIN to an actual dose rate. Thus, to assess the photon dose rate at a given distance \(\ell\), one would simply need to just divide the value reported by DCHAIN by \(4\pi\ell^2\). Of course, this math would differ if the source were assumed to be some other shape aside from a point.
The most important take-away is that to convert DCHAIN’s reported dose rates to physical dose rates, they need to be multiplied by the factor which converts the source’s photon emission rate to a photon flux at the point of observation, as demonstrated for a point source here.
One may select which ICRP conversion coefficients are used with the IDOSECF parameter, and the specific units of the reported dose rate value (dose times area per time) can be customized with the IDOSUNIT parameter. These coefficients are listed in the *_dose_rate_coeff.dat files within the <PHITS-install>/dchain-sp/data/ folder with the first portion of the filename matching the decay library selected by IDCYLIB and whose photon emission intensities and energies were used in the per-nuclide coefficient calculations.
It should be emphasized that for serious dose calculations, one should re-insert the DCHAIN-produced PHITS [Soruce] cards into a second PHITS simulation designed to tally dose instead of using solely the dose values reported by DCHAIN (unless your source happens to be a very simple object with negligible self-shielding whose only relevant emissions are photons). The values reported by DCHAIN primarily exist to provide a quick way to assess the biological significance of the produced nuclides and their activities.