2*pi vs 4*pi

[glhansen]

Took me a while to get my head around it because those are solid angles to me. I understand that 4*pi efficiency is in dpm, as in decays don't have a direction, and the decay products can go anywhere, and the question is, if you put your detector over a sample on the table, how much is there? (And self-absorption and backscattering is just not addressed, which probably doesn't matter for gamma, but could for particles.)

And 2*pi, in cpm, answers the question, of all the radiation that goes through your probe, how much of it is detected? (So it doesn't directly relate to amount of sample, but detector efficiency.)

How do people decide which one they want, and how do they actually use it in practice? Do they often just measure it themselves with dummies and rod sources or something?

[Sesselmann]

Greg,

Good question...., as you already understand, a point source will radiate in all directions so if your detector is placed at a distance r the energy reaching the probe is proportional to 1/4πr^2

If however you have a large source like a big rock and you place your detector in contact with the source the amount of energy absorbed by the detector is closer to 1/2πr^2, however it can become complicated with self absorbtion and things like that.

The simple way to calibrate for exposure is always with a calibrated source of known activity, preferably with the same energy peaks.

There are also formulas for calculating counts based on crystal size housing thickness, distance etc, but it involves many factors. I recall an earlier discussion about this.

Steven

[GigaBecquerel]

Hello glhansen,

There are two "different" detector efficiencies, and I think you might be mixing them up a bit here.
One is the 2pi / 4pi you're talking about, which just says how much of the sphere is covered by your detector.
The other one is your detectors "response spectrum", which says which particle at what energy has what detection probability. That can then further be divided for spectroscopic devices into counting efficiency (gives a count) and full energy peak efficiency (gives a count at its full energy in the spectrum).

The first one is simple geometry, and can easily be changed by eg. changeing the distance between your source and detector.
The second one is defined by your detector, its material, size, housing material etc and cannot really be changed.

Both of these determine how you measure something, together with the activity of your source, your detectors max. count rate, your background rate etc.
The geometric efficiency can easily be calculated, especially if you assume your source to be a point source, which is often a good approximation. With a regular cylindrical detector this cannot be higher than 2pi.
If your source has a finite volume the calculations get a lot more complicated, but you can get higher efficiencies, eg. with marinelli beakers.
The intrinsic detector efficiency is harder to determine, and can often only be guesstimated unless you do eg. monte carlo simulation. This is often just calibrated with a source of the same nuclide, or similar energies.
Due to this (in)efficiency a detector can never truly detect every single decay.
The simplest and most common way is to recreate the source with something of known activity, and then compare the counting rates between the standard and your sample. This also takes self absorption and other effects into account, if done correctly.
I hope this answers your question, but to be honst I'm not sure what exactly your question is, lol.

Steven, I think you mixed something up here. The bigger the source is compared to your detector the lower the overall efficiency is, unless you insert your detector into the source.
Think of the source as a light bulb and your detector as something blocking the light, eg. your hand. If the light bulb is small you can easly cover the whole thing with your hand and stop all of the light, but if it is bigger than your hand you can only stop a fraction of the light.

Lukas

[Sesselmann]

Steven, I think you mixed something up here. The bigger the source is compared to your detector the lower the overall efficiency is, unless you insert your detector into the source.
Think of the source as a light bulb and your detector as something blocking the light, eg. your hand. If the light bulb is small you can easly cover the whole thing with your hand and stop all of the light, but if it is bigger than your hand you can only stop a fraction of the light.

Lukas is right, if the source is significantly larger than the detector diameter, then I suppose the efficiency goes the other way again. I'm trying to imagine how the count rate would change if one approaced a radioactive asteroid form a large distance, initially the counts would follow the 1/r^2 rule, but how would this change as you approached the surface?

Steven

[GigaBecquerel]

Yes, exactly, every source can be approximated as a point source and therefore follows the r² law if it's small enough, and / or far enough away.
A good rule of thumb is to be more than 10 times the sources diameter away from the source, at this point your errors due to the finite volume will be absolutely negible.
If you get too close the maths become very hard, and it is more common to produce a geometry standard that replicates your source than to actually calculate anything.

Here is an example taken from Knoll (4th edition)

[Peter-1]

The same formula can also be found in Fünfer-Neunert "Counting tubes and scintillation counters" 1945.

[Ousmane90]

This link will be helpful I hope.
https://seintl.com/articles/instrument- ... ncy-2-vs-4

[glhansen]

Dangit. Sorry, I didn't mean to ignore this nice discussion. I had a little trouble figuring out how to make a post stick. The main thing I get is that it's very application-dependent. An efficiency gives you a reference, I suppose, since the energy dependence is supposedly known, but the rest is up to you.

1/r^2 is a standard part of the ALARA training at work. It works even for the smallest distances, they say. Having a degree in science, I think happy thoughts and keep my peace when that comes up. Not that 1/r^2 is ever wrong, but it could be that you don't move every part of your body as far away from every part of the source as you think you do. But distance is always relevant to ALARA, and it's industrial safety, not scientific measurement, so fine details like that probably don't matter.