Beta shielding, Aluminium thickness and bremsstrahlung (braking radiation)

On another thread ( here ) we sort of got to discussing the thickness of Aluminium for shielding beta but I didn't want to divert that thread too much so started a new thread on this subject here.

I had quoted, roughly in all honesty, that 5mm aluminium would do well for beta shielding and was met with this reply:

FSM19 wrote:

For a beta shield you need 3mm of aluminium, foil isn't thick enough, UK Civil Defence geiger counters and ionisation instruments, such as the Meter Doserate Portable No 1 Trainer, Meter Doserate Portable No 1 and the Meter Survey Radiac No 2 had diecast bodies about 1/8" thick to act as a beta shield - the latter two could be used to detect beta by removing the bottom of the case. For a few more details see my site https://tocsin-bang.000webhostapp.com/radiac.html .

So which is it? 3mm or 5mm? Turns out neither and both are true from what I can work out.

I have done a some research on beta shielding for an up coming project and I must say that I find trying to work out what would be the ideal thickness for using aluminium quite confusing. I have read on various sites, papers and opinions (whether educated or not) the thickness should be anywhere between 0.5mm and 15mm! I have a Meter Survey Radiac No 2 and just popped the bottom off to have a look. The internal aluminium shield is 3.2mm but there is also the outer cover (also aluminium) that is 2.4mm, making a total thickness of 5.6mm. It is my understanding that whilst the inner shield may be used or not for shielding of beta the outer cover must always be in place as this offers humidity protection for the ion chamber inside. So when using the Meter Survey Radiac No 2 you would always have a minimum of 2.4mm with an additional 3.2mm shield depending on what you were surveying.

In all honesty the 5mm I quoted on this post is a rough semi-educated guesstimation that would stop most beta from passing. So I did a little more research. It turns out that the density of the material is the key factor and the following basic equation can be used to calculate the thickness of aluminium for shielding:


That is, provided you know the range of the beta particles, in which case you need to know the energy for the particular beta particles. There is something known as Feather's Rule where:
Betas with a maximum energy above 0.6 MeV: Range(g/cm2) = 0.542 E -0.133 and
Betas with a maximum energy below 0.8 MeV: Range(g/cm2) = 0.407 E^1.38

So it is looking like the thickness of aluminium shielding is directly relative to the energy level of the beta particle. But it gets more confusing than that as there is bremsstrahlung (braking radiation) that causes electromagnetic radiation from the slowing or deflection of the beta particles. However bremsstrahlung can pretty much be ignored in energies below 1MeV.

Here are some of the web sites I have used for reference:
https://www.nuclear-power.net/nuclear-power/reactor-physics/atomic-nuclear-physics/radiation/shielding-of-ionizing-radiation/shielding-beta-radiation/
https://www.nuclear-power.net/nuclear-power/reactor-physics/atomic-nuclear-physics/fundamental-particles/beta-particle/bremsstrahlung-2/
https://www.nasa.gov/sites/default/files/files/SMIII_Problem25.pdf
https://www.nrc.gov/docs/ML1122/ML11229A721.pdf

I know, my brain hurts too..... Anyway I'd like to open this for discussion and try to work out the optimum for beta shielding a GM tube to pretty much omit beta from background counts and that in an event. Your input would be very much appreciated.

I forgot to include the density of aluminium. From this page: https://www.thyssenkrupp-materials.co.uk/density-of-aluminium.html

The density of aluminium is about 2,710kg/m3. The density of the alloys of aluminium does not vary widely from this figure ranging between 2,640kg/m3 and 2,810kg/m3.

It seems strange to me that a panel would be left off when out in the field. I cannot however find any information regarding the bottom panel on that meter so I'll take your word for it as you have past experience with that meter and I just have a dead one! (batteries left in a corroded). I do have a copy of the instructions for that meter though but it says very little about the beta shield and absolutely nothing regarding the bottom panel. I would have attached but the PDF is 225Mb so here is a link to view/download: https://archive.org/details/OperatorsHandbookForMeterSurveyRadiacNo.2