# Introduction

The neutron dose rate application in Nucleonica is based on a table of values for the Fluence Per Unit Dose Equivalent for Monoenergetic Neutrons based on NRC regulations

Quality Factors and Absorbed Dose Equivalencies NRC regulations

In the current version of the application, neutron dose rates are calculated for unshielded point sources. Shielding will be included at a later stage.

# Dose Equivalent versus Neutron Flux

For point sources which emit S neutrons/s,the neutron flux $\phi$ at a distance r is given by

$\phi(neutrons \cdot cm^{-2} \cdot s^{-1}) = \frac{S(neutrons \cdot s^{-1})}{4 \pi r^2}$

The dose equivalent for the unshielded neutron source is given by

$\dot D = f^{-1} \cdot \phi(neutrons \cdot cm^{-2} \cdot s^{-1})$

where f is the fluence per unit dose equivalent given in the table above.

## Example

Estimate the dose equivalent at 1 m for a source that emits 3x107 neutrons/s with an average energy of 5 MeV.

Solution: Using the above relations, the flux at 1m is

$\dot D = [f(neutrons \cdot cm^{-2}\cdot rem^{-1})]^{-1} \cdot \frac{3\cdot10^7(neutrons \cdot s^{-1})}{4 \pi \cdot 10^4 cm^2} = 37.4 mrem/h$

or 374 µSv/h where f is the fluence per unit dose equivalent from the above table. For 5 MeV neutrons, f = 23x106 neutrons cm-2 rem-1.

# Neutron Sources: Rules of Thumb

The neutron dose rate application has been extended to include the spectrum averaged ambient dose equivalent coefficients for common neutron sources. The relevant data (Fluence average energy, Specific source strength, Spectrum avaeraged fluence to dose equivalent conversion coefficients) have been taken from Reference neutron radiation--Part 1 This allows the user to calculate ambient dose rates for the following reference neutron sources:

- Cf-252

Californium-241 source

- Cf-252 (D2O moderated)

Heavy water sphere with a diameter of 300mm, covered with a cadmium shell of thickness approximately 1 mm. Of the source neutrons, 11.5% are moderated below the cadmium cut-off and captured in the cadmium shell.

- Am-B(α,n)

Americium-241 boron with approximately 16 neutrons per million alpha decays (specific source strength 1.6x10-5 s-1 Bq-1.)

- Am-Be(α,n)

Americium-241 beryllium with approximately 66 neutrons per million alpha decays (specific source strength 6.6x10-5 s-1 Bq-1.)

Neutron Dose Rates user interface

Cf252: Example

In the example above, the neutron dose rate for 1 g Cf-252 at 1 m is 2.65e7 µSv/h and results from a neutron source strength of 2.40e12 neutrons s-1 at the source and 1.91e7 neutrons cm-2 s-1 at 1 m distance from the source. The spectrum averaged neutron energy is 2.13 MeV corresponding to an effective quality factor, Q, of 9.35.

It is of interest to compare this result with that of a monenergetic neutron source with the same neutron source strength as in the above calculation. Selecting the "neutrons/s" from the Source drop-down menu and entering the value 2.4e12 n/s, together with an energy of 2.13 MeV, results in a neutron dose rate of 2.4e7 µSv/h. The monoenergetic neutron source results in a dose rate about 10% lower than in the case of the Cf252 with its full neutron spectrum.

Am241-Be: Example

In another example, selecting an Am241-Be neutron source, and an Am241 activity of 1GBq, the resulting neutron dose rate at 1 m is 0.739 µSv/h. The neutron source strength of 6.6e4 neutrons/s arises from (α,n) reactions on Am241 with 66 neutrons generated per million alpha decays.

Selecting "neutrons/s" from the Source drop down menu and entering the value 6.6e4 neutrons/s, together with an energy 4.13 MeV, results in a neutron dose rate of 0.773 µSv/h. The monoenergetic neutron source results in a dose rate about 5% higher than in the case of the Am241-Be full neutron spectrum.

# References

J. E. Martin, Physics for Radiation Protection, Wiley, 2000

Los Alamos Radiation Monitoring Notebook, 2001

Neutron Shielding for a 252Cf Source