Neutron Source Dose Rate Calculator

Release notes

Version 1.0  The Ionactive Neutron Source Dose Rate Calculator has two operational modes:

• Forward (Source → Dose Rate): This mode allows you to calculate neutron and gamma dose rates from a variety of radioactive based neutron sources.  
• Reverse (Dose Rate → Source): Here you may enter known, measured or assumed dose rate data (gamma, neutron or both) and infer the potential radioactivity component of the source. 

The parameters, choices and inputs will vary slightly with neutron source selection, and more significantly between the two modes selected. We first consider input choices for forward calculations. 

• Source: Select from the following neutron source types: Am-241 (AmBe), Am-241 (AmB), Cf-252, Pu-238 (PuBe), Pu-293 (PuBe). Am-241 (AmLi), Sb-124 (SbBe), Ra-226 (RaBe). Selecting a source type will bring up an information panel giving some brief facts and other relevant data (e.g. average neutron energy in MeV and the energy range).
• Strength input. Select from activity or mass of radionuclide. Each choice will bring up its own contextual sub-menu: Activity allows Si and non-Si unit choices with numerical activity input, mass allows inputs to be made in μg, mg or g (if mass is selected the activity input fields are locked).
• Output units. Select dose rates to be output in either SI or non-SI units.
• Distance. Distance from the source can be entered in SI or non-SI units. See information later below on the validity of the inverse square law (the calculator will output a warning statement if inverse square is less likely and why this is so).
• Calculate / Reset. Click calculate to display results, click reset to reset the calculator to default settings.
• Forward Results. After clicking calculate a results panel will appear giving: source activity, equivalent (or selected) mass, the distance selected, estimated neutron yield (n/s), gamma dose rate, neutron dose rate and total dose rate (in chosen output units). Some useful constant (1 GBq) based data is also provided. 

The above choices, parameters and outputs are altered for reverse calculations. The differences are as follows:

• Reverse uses. This allows the user to input a gamma or neutron dose rate, or total dose rate. Once selected, the other input options are locked. A final option is to choose all provided - this will yield three separate calculations based on the three dose rate inputs.
• Reverse results. After clicking the calculate button a results panel will appear giving: source selected, the distance from the source, the dose rate unit, the input dose rate, the inferred output activity, the equivalent mass of radionuclide, and the estimated neutron yield (n/s). 

Limitation and considerations for use

There are a number of important assumptions to be made when using this calculator. We recommend you use this calculator for basic 'what if' type of investigations,  and for education and training. We advise you to seek formal Radiation Protection Adviser (RPA) advice before working with radioactive sources (and especially neutron sources). This calculator assumes:

• The source is completely unshielded.
• The source is isotropic (treated as a point source).
• The calculation assumes that the source is not close to materials (walls / pillars, people) which could otherwise scatter / attenuate neutrons and alter the likely dose rate profile at a given distance.  This proximity effect is particularly relevant when working with neutron sources.

A consideration of neutron dose rates (from this calculator)

Try the following using our neutron dose rate calculator. Using 1 GBq at 1m, calculate the neutron dose rate and neutrons per second for Am-241Be and Ra-226Be. The results will be as follows:

Am-241Be

• Neutron dose rate 0.65 μSv/h
• Neutron yield 5.95×10⁴ n/s

Ra-226Be

• Neutron dose rate 4.46 μSv/h
• Neutron yield 4 ×10⁵ n/s

As already highlighted, there are quite a few design variables alone which might account for some of the difference between the two sets of results. However, by far the most significant aspect is the number and energy of alpha particles available to yield neutrons via this reaction:  \({}^{9}\text{Be}(\alpha ,n)^{12}\text{C}\). Let's examine by looking at AmBe and RaBe in turn. 

For the AmBe source, the neutron yield is driven by the alpha particles from Am-241 only (≈ one alpha per decay). For a sealed RaBe source that has reached secular equilibrium (which will be the case for intact RaBe), several short-lived progeny are also alpha emitters, so there will be multiple alphas per original Ra-226 decay. This will increase the number of opportunities for (α,n) reactions in beryllium, so the neutron yield per GBq could be higher. Using some basic analysis RaBe can produce approximately 6–8 × more neutrons per GBq than AmBe. How do we get this figure (?) - let's have a closer look. 

• Am-241 provides 1 GBq of alpha particles (\(E_{\alpha }\approx 5.48\text{ MeV}\) ).

By contrast the alpha particles from Ra-226 (once it has reached equilibrium) is quite extensive as noted below (somewhat simplified). 

• Ra-226: 1 GBq (\(E_{\alpha }\approx 4.78\text{ MeV}\))
• Rn-222: 1 GBq (\(E_{\alpha }\approx 5.49\text{ MeV}\))
• Po-218: 1 GBq (\(E_{\alpha }\approx 6.00\text{ MeV}\))
• Po-214: 1 GBq (\(E_{\alpha }\approx 7.69\text{ MeV}\))

So by comparison, the total alpha particle flux for Ra-226 is about 4 GBq of alpha particles per 1 GBq of Ra-226 activity, whereas for Am-241 it is 1 GBq of alpha particles per 1 GBq of the radionuclide. In addition, on average the Ra-226 et al alpha energy (particularly the 7.69 MeV from Po-214) means more neutron production efficiency, as the cross section of the  \({}^{9}\text{Be}(\alpha ,n)^{12}\text{C}\) reaction increases with alpha particle energy. You can see this by looking at the ratio of neutron yield for RaBe and AmBe given above, which is about 6.7. Actual yields depend on source construction, age/equilibrium, and capsule geometry etc which is why we gave a range of approximately 6-8.