# Answer to Question #12136 Submitted to "Ask the Experts"

*Category: Radiation Basics — Neutrons*

The following question was answered by an expert in the appropriate field:

Given a known neutron rate from an amercium-241 (^{241}Am)-beryllium (Be) source, how can I determine the neutron dose equivalence if only gamma measurements are available? For example, if I know the number of neutrons per second (n s^{-1}) being emitted from a source, can the gamma survey results in microsieverts per hour (µSv h^{-1}) be used along with an equivalency factor to calculate the neutron dose contribution? For reference, my sealed source and device registration (SSDR) states the 555 gigabecquerel (GBq) ^{241}Am-Be source is expected to emit 4.26 × 10^{7} n s^{-1}. The regulations pertaining to well logging in Texas (25 Texas Administrative Code 289.253(aa)(1)&(2)) state that surveys must take into account neutron contribution, and I want to know if there is a factor I can multiply or add to the gamma dose rate that will allow the neutron dose to be estimated. I realize that there are survey meters such as the Ludlum Model 2363 which measure both gammas and neutrons (and the two types of radiation can be measured in summation or discreetly).

Regarding the first part of your question, it is a fairly easy matter to estimate the neutron dose rate from an Am-Be source of known neutron emission rate at reasonably close distances (from about 10 centimeters [cm] to a few meters [m]) in air from the source. This is done by first calculating the expected neutron fluence rate directly from the source, assuming that the source behaves as a point isotropic source so that the fluence rate varies inversely with the square of the distance from the source and is uniform in all directions. For the general case in which a source emits S n s^{-1}, and we are concerned with the equivalent dose rate at distance r cm from the source (distance measured from the geometric center of the source), the direct neutron fluence rate, Φ, (neglecting effects of neutron scatter) is given by:

Φ = S/4πr^{2}.

For your case, S = 4.26 × 10^{7 }n s^{-1}; for an arbitrary distance of r = 100 cm, we would then obtain:

Φ = 4.26 × 10^{7} n s^{-1}/4(3.1416)(100 cm)^{2} = 3.39 × 10^{2} n cm^{-2} s^{-1}.

It turns out that the conversion factor to convert fluence rate to equivalent dose rate for the spectrum of fast neutrons emitted by ^{241}Am-Be sources, based on current U.S. Nuclear Regulatory Commission and agreement state regulations, is about 0.68 n cm^{-2} s^{-1} per µSv h^{-1}. The expected neutron equivalent dose rate, H, from the above example would then be:

H = (3.39 × 10^{2} n cm^{-2} s^{-1})(1 µSv h^{-1}/0.68 n cm^{-2 }s^{-1}) = 4.99 × 10^{2} µSv h^{-1}.

If we check the decay radiation characteristics of ^{241}Am, we would find that the only significant gamma radiation emitted by an Am-Be source with sufficient energy to escape from the source encapsulation are the 60 kiloelectronvolt (keV) photons emitted at the rate of about five gamma rays per 14 decays of ^{241}Am atoms. What is not typically shown in routine decay tables, however, is that when an alpha particle interacts with a beryllium-9 (^{9}Be) nucleus to produce a neutron, the other product produced is carbon-*12 (^{*12}C), where the asterisk (*) designates a nuclear-excited state of ^{12}C. It happens that in about 75% of the deexcitations of ^{12}C, a 4.4 megaelectronvolt (MeV) gamma ray is emitted. Thus, the expected 4.4 MeV gamma-ray emission rate from a ^{241}Am-Be source is equal to about 75% of the neutron emission rate.

The 60 keV gamma rays are attenuated to a significant extent within the source matrix and the cladding that encapsulates it. The degree of attenuation can vary appreciably with source size and construction characteristics. A "typical" 555 GBq source, as you have, might have a gamma dose rate approximately 20% of the neutron dose rate at a fixed distance in air from the source, but this can only be determined for any specific source by measurement. For purposes of an example, if we apply this 20% value to your source at the 100 cm distance, we obtain an expected 60 keV gamma equivalent dose rate of about 1 × 10^{2} µSv h^{-1}. The 4.4 MeV gamma radiation would add about 25 µSv h^{-1}. Keep in mind that these are approximations and that you should really measure the gamma dose rate at a fixed distance from the source and compare it to the calculated (or measured) neutron dose rate.

If the above example estimates were correct (i.e., 4.99 × 10^{2} µSv h^{-1} neutron dose rate and [1 × 10^{2}] + [2.5 × 10^{1}] = 1.25 × 10^{2} µSv h^{-1} gamma dose rate), we could then calculate the factor you desire to obtain the neutron dose rate from the measured gamma dose rate (i.e., 4.99 × 10^{2} µSv h^{-1}/1.25 × 10^{2} µSv h^{-1} = 3.99). Multiplying a measured gamma dose rate by this factor of 3.99 would yield the expected neutron dose rate at the same location. Naturally, such an approach assumes no major neutron or gamma attenuation or scattering are occurring that would affect the legitimacy of this ratio.

George Chabot, PhD