# Can I use density ratios when working out radiation shielding thickness?

This FAQ relates to photon radiation (i.e. gamma or x-rays). For a full understanding of information contained here is it worth ensuring you understand the concept of TVT (10th value thickness). You may wish to read our glossary entry “10th Value Thickness (TVT)

Basically, the TVT is the thickness of a shielding material required to reduce the pre-shielded dose rate to 1/10 of that value. To choose a TVT you need to know the radioactive material (gamma emitter) you are considering, and the shielding material available. For x-ray systems you need to know the kV of the x-ray system, and the shielding material available.

#### Where density ratios work (or might work)

Let’s first consider where density ratios generally work, and why you might want to use them. For this we will consider a 10 MV linear accelerator photon beam through concrete. In looking at these examples we will consider the TVT “as is” rather than the “1st-TVT” and “Equilibrium –TVT” as used in formal calculations. Furthermore, broad beam vs narrow beam is not considered, nor is the maths behind partial TVTs (i.e. using 10-x etc.) For the purposes of this FAQ this level of additional detail is not required (and in real shielding calculations you might want to use modelling software anyway).

The TVT for 2.35 concrete (i.e. 2.35 g cm-3), for a 10 MV photon radiation, is about 37 cm. Real life measurements have shown that using density ratios gives good practical results. For example, if you have a Barytes block with 3.3 density, then the ratio work pretty well. So, you could calculate a TVT for this Barytes block of 26.3 cm. This works in real life measurements. Or, you might only have 1.9 density concrete blocks, so a density ratio of 2.35/1.9 would indicate a new TVT of nearly 46 cm.

Let’s return to the TVT for a 10 MV photon in 2.35 concrete being 37 cm. The TVT for steel is 11 cm. Does this figure reflect density alone? Assume density of steel is say 7. Then from a density ratio perspective one would expect the TVT for steel, as related to 2.35 concrete, would be [(2.35/7)*37 cm] = 12.42 cm. Quite close, but not actually what was expected.

How about lead? The reported TVT for lead for 10 MV photons is 5.7 cm. So, let’s see how we could scale that from standard density concrete. This would be [(2.35/11)*37cm] = 7.9 cm]. It’s the same order of magnitude, but now note we are departing from a “linear” relationship. To do this calculation without using reported data would overestimate the lead requirement, based on the standard density concrete density.

In summary, for high energy Photons (e.g. x-ray / gamma rays) with concrete, scaling density by ratio for concrete works pretty well. Whilst this scaling will provide steel and lead TVT of reasonable accuracy, already our analysis shows that using specific data of energy vs. shielding material will be much more reliable. The bottom line here – don’t scale density using different types of materials (e.g. steel vs concrete), it does not work very well!

#### Ok, so far so good! How about lower energy photons?

Now what about lower energy photons? Of the order of a few 100 keV, and certainly less than 511 keV. How does density scaling then impact? In this consideration we are of course specifically looking at different material comparison (e.g. brick shielding vs. lead shielding).

So now consider 100 kV x-ray beam. Most literature will report a TVT for lead as about 0.92 mm.

Following the discussion above, let us consider density ratios alone and first try and estimate the equivalent shielding for standard 2.35 density concrete. Based on the previous discussion our concrete (100 kV, 2.35) TVT should be [(11/2.35)* 0.92 mm] = 4.3 mm. However, this figure significantly underestimates the thickness of standard concrete required to achieve a TVT. The actual TVT for 2.35 concrete for 100 kV x-rays is more like 59 mm (based on reported values in literature and Ionactive workplace measurements).

At low levels of kV, and of course keV, the same effect can be seen in other shielding materials.

Let’s try density ratios between lead and steel. Using the 0.92 mm TVT for lead with 100 kV x-rays, we might assume that the steel required is about [(11/7) * 0.92 mm] = 1.45mm steel. The actual figure is more like 6.7 mm steel. So another big underestimate!

The conclusion here is simple – never try to calculate lead equivalence, or any other material equivalence related to lead for low energy photons (i.e. typically in the range of x-rays of a few hundred KV, or gamma emitting radioisotopes of a few hundred keV) using density. It does not work! And importantly, you will underestimate the shielding requirements for materials of a lower density then lead. Drastically so. [Note that for the high energy photons discussed earlier, scaling from lower density concrete to higher density non-concrete materials actually overestimates the shielding required. So, it does err on the side of caution, but becomes excessively expensive for no good reason].

#### Why?

The point of this FAQ is not to explain the physics in any detail – we like to keep this quite practical. However, at higher energies (typically >> 1 MeV photons) the interaction with a shielding material causes ‘pair production’ - a positron / electron is created (positive electron) very near the nucleus of the shielding material. The positron almost instantly interacts with an electron causing annihilation radiation to be created (i.e. two photons with 511 keV moving in opposite directions). The incident radiation upon typical shielding at high energy is lowered below 511 keV on the first interaction. Therefore, the electron density in the shielding (which is related to physical density) leads to density ratios in different material predicating TVT pretty well (you could see this for concrete, steel and lead with 10 MV photons). At much lower energy the shielding effect is dominated by the 'photo-electric' effect and 'compton scatter' which is much more sensitive to material composition, and so density ratios for different shielding material becomes ever more significant.

Reality is merely an illusion, albeit a very persistent one

– Albert Einstein -