Re: Radiation Detection Question

Gregory L. Hansen wrote:
> In article <ZvBnf.37650$Y7.35469@trnddc02>, Matt <zeusmta@xxxxxxxxxxx> wrote:
> >Regarding radiation a radiation detection system for gamma rays, following
> >is a quote from a paper I read:
> >
> >"Halving the distance between source and detector would increase the
> >sensitivity by a factor of four; quadrupling the counting time would
> >increase the sensitivity by a factor of two."
> >
> >I understand the first part -- i.e. source strength goes as the inverse
> >square of the distance, therefore half distance implies four times
> >sensitivity. I also understand the geometrical reasons for this.
> >
> >I don't understand why quadrupling counting time only increases the
> >sensitivity by 2. In my ignorance, I cannot imagine why quadrupling the
> >counting time would not result in four times the sensitivity or detection
> >capability. Can someone please enlighten me on this? Perhaps someone could
> >point me to an Internet source that explains this phenomenon.
>
> I don't understand the first part.
>
> Radioactive decay is statistically distributed-- Poisson, or something
> like that. If "sensitivity" means precision in a measurement of average
> number of counts per unit time, the uncertainty associated with N counts
> is sqrt(N), and the relative uncertainty is then sqrt(N)/N=1/sqrt(N). If
> you quadruple the number of counts, you halve the uncertainty. It doesn't
> matter whether that quadrupling is done by moving the source closer or by
> counting for a longer time.

Not quite. If you are trying to distinguish a signal from a background,
then moving the source closer will mean you have a larger signal.
So, if sensitivity is defined as "the smallest size radioactive source
that could be distinguished from background" then this clearly
depends on how close to the source the detector is, and not just
by the number of counts.

So, if you are 1 meter away, you can see 1E6 Bq, for example, but
at 2 meters away you can only see 4E6 Bq. Assuming that moving
your detector does not change the background. In each case, this
assumes the same counting time.

> Socks mentioned distinguishing a signal from background. That's really
> best done by changing the signal periodically, e.g. by moving the source
> back and forth, back and forth. Or by opening and closing a shutter.
> Even a very small periodic signal can be distinguished from the background
> if you average over enough periods. A complication is that radiation can
> bounce around every which way inside the apparatus, and the amount of
> backscattered radiation entering the detector will change when you change
> the location of the source, so that must be simulated or measured so a
> correction can be made.

The problem with doing the periodic thing you mention is that it does
not
produce a periodic signal. What it produces is periodicity in the
probability
of getting a count. The number of counts will then be some statistical
thing that follows whatever distribution is happening.

So, even doing this, you get some kind of statistical thing happening.
It's more complicated than for a source sitting still, and I have not
tried to work out the details. But I'd expect (without having made the
slightest effort to justify it) that there would still be some kind of
1/root(N) involved.

But basically, it's just a variation on the usual method. You put the
source very far away, such as in a shieled container, and do your
background count. Then you bring the source closer, and do your
count again. The difference is the signal, plus or minus the
statistical
fluctuation estimates.
Socks

.

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