DOSE.md¶

DOSE ndose {1} <dist> {0}

Dose rates are calculated for a semi-infinite slab of the material. This is the default if the keyword is not used or if ndose = 1, but if ndose = 2 then the calculations are done for a point source of 1 g of material at a distance of dist metres. dist is not used for the semi-infinite slab as the contact dose rate is always assumed. The minimum distance is 0.3 m; if a smaller value is specified then dist is set to 0.3 m and a message to this effect is printed.

An example of this keyword for a point source of 1 gram of the irradiated material at 1 metre is:

< -- Control phase -- >
...
FISPACT
* Title of the simulation
< -- Initial phase -- > 
...
DOSE 2 1.0
...
< -- Inventory phase -- > 
...

Note that the specific activity (Bq/kg), not the activity (Bq), is used to calculate dose rates, in both cases.

The surface gamma dose rate (Sv/hr), \(D\) for a semi-infinite slab is calculated as below:

\[ D=C \frac{B}{2} \sum_{i=1}^{N_{\gamma}} \frac{\mu_{a}\left(E_{i}\right)}{\mu_{m}\left(E_{i}\right)} S_{\gamma}(E_{i}) \]

where:

\(N_{\gamma}\) = number of energy groups in the \(\gamma\) spectrum histogram

\(E_{i}\) = mean energy of the \(i^{th}\) energy group

\(\mu_{a}\) = mass energy absorption coefficient (\(\mu_{en}/\rho\)) of air (m\(^{2}\) kg\(^{−1}\))

\(\mu_{m}\) = mass energy attenuation coefficient (\(\mu/\rho\)) of the material (m\(^{2}\) kg\(^{−1}\))

\(B\) = build up factor (= 2)

\(S_{\gamma}\) = rate of \(\gamma\) emission (MeV kg\(^{−1}\) s\(^{−1}\))

\(C\) = 3.6 \(\times\) 10\(^{9}|e|\) converts (MeV kg\(^{−1}\) s\(^{−1}\)) to (Sv/hr)

Whereas the dose rate (Sv/hr) from a point source in air, \(D\), is calculated as below:

\[ D=C \sum_{i=1}^{N_{\gamma}} \frac{\mu_{a}}{4 \pi r^{2}} e^{-\mu\left(E_{i}\right) r} m_{s} S_{\gamma}(E_{i}) \]

where additional terms are defined as:

\(m_{s}\) = mass of source (kg)

\(r\)= distance from source (m)

\(\mu(E_{i})\) = energy attenuation coefficient of air (m\(^{−1}\))

In both cases the emission rate, \(S_{\gamma}\), is calculated using the specific activity, \(A(t)\) (Bq/kg), as below:

\[ S_{\gamma}(E_{i}) = I_{i}A(t) \]

where \(I_{i}\) is the intensity of energy group \(i\) (MeV).

Both equations are approximations suitable for FISPACT-II calculations, but it is noted that they may not be adequate for specific health physics problems.