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Re: [Phys-L] Half-Life measurement



Addendum to previous message:
Here is what the fits look like:
https://www.av8n.com/copper-decay/img48/rate-v-short-time-1.png
https://www.av8n.com/copper-decay/img48/rate-v-long-time-1.png
or equivalently
https://www.av8n.com/copper-decay/pdf/rate-v-short-time-1.pdf
https://www.av8n.com/copper-decay/pdf/rate-v-long-time-1.pdf

This is pretty much what you expect to see when fitting to
noisy data.

==============================
Change topic slightly:

On 10/13/21 12:03 PM, I wrote:

1) The data is imperfect, so we have to ask:
How could we improve the experiment?

2) Is the data analysis method robust enough
to handle imperfect data?

These are two perfectly reasonable questions. In particular,
there is some pedagogical advantage to /not/ improving the
technique too much. It is good for students to get experience
dealing with less-than-ideal data.

Taking the questions in reverse order:

2) I would expect the least-limp fitting routine to be robust and
pretty close to optimal. No assumptions, no decisions required,
other than:
-- Assume Poisson physics.
-- Settle for max likelihood rather than max a posteriori,
at least for the moment.

Well, maybe it is slightly more complicated than that; the key
decision is deciding not to make any approximations except as
noted above. The first step is realizing that's possible. Then
you have to do the calculus to make sure you are plugging the
proper numbers into the standard Poisson formulas. Once you
decide to go down the no-approximations take-no-prisoners road,
there are no other decisions to make. There is work to be done
but no decisions, no options of any consequence.

For details, see previous message.



1a) Running out the baseline another day or two would probably
help quite a bit. Uncertainty in the baseline messes up the
other parameters.

1b) More generally: More observations would help.

-- Measure the fast component once every 30 seconds for the
first half hour (not just the first 15 or 20 minutes). Every
20 seconds would be even better. Consider using a camera to
take a literal snapshot of the timer and counter so that the
there is no skew (no time parallax) between the readings.

-- If at all possible, measure the slow component once every
hour during the workday, out to 72 hours or so.

There is no advantage in hanging around for two minutes to
take a second observation. The point is to minimize the
/maximum/ time between observations. Minimax. That is to say,
if you are going to take two readings per hour, 30/30/30/30
is better than 58/2/58/2. The 2s don't help much, unless
there are a lot of them. (A huge number of 2s would be great.)

1c) A higher-rate source would help a lot. Is it possible to
get a physically larger piece of copper? It doesn't have
to be thick, so long as it is big in the other directions.

A copper tube that slips around the Geiger tube would optimize
the geometry.

A higher neutron flux would be great, but I assume that's
not easily achievable.

If you are worried about the purity: The copper used for
electrical work is usually quite pure. It is easy to buy
copper foil that is 99.9% pure. With a little more work
you can find stuff that is 99.99% pure, although I doubt
that is worth the trouble.

Copper used for other purposes may not be super-pure. The
pre-1982 pennies were 95% Cu and 5% Zn. I don't know what
they use for copper plumbing, but I know it's not hard to
get 99.9% pure copper tubing.

If you want the really good stuff, shop for OFHC copper. That
stands for oxygen-free high-conductivity. That's really nifty
if you want high conductivity at low temperature (liquid
nitrogen or below). The low temperature gets rid of resistivity
due to thermal scattering, and getting rid of the impurity
scattering means the resistivity goes up and up and up as the
temperature goes down. Oxygen is worst-case from the impurity
scattering point of view, because it's magnetic.

1d) A layer of copper-sulfide tarnish is not your friend. My
guess is that tarnish or krud at all is moderately unhelpful.
It might make an amusing side-experiment to measure a heavily
tarnished sample, then clean it and measure it again. Maybe
there will be no significant difference; that would be nice
to know.