Paul Nord <paul.nord@valpo.edu>UnsubscribeTo:phys-l@phys-l.org
Wed, Oct 13 at 1:06 AM
John,
What you say is all very insightful.
I do have better hardware to do this experiment. But we simply didn’t use it for this. For the students, we hope they gain something from this very hands-on method. We’ll show them more powerful tools soon.
My concern about modeling the background is not about what the value is. Rather, I’m doubtful that the background is constant over several days. The sensitivity of the detector might also not be stable over the long time. That would show up as very much the same thing.
It’s easy to make a case for collecting more data. But my question remains: what is the best we can hope to measure from this set of data?
Paul
========================================================================Paul,I wanted to get a feel for the variation of background that you have been concerned about.
This non linear regression package of mine has problems with multi-exponential forms, no doubt. Of the five parameters of interest, I can place published values for two; the mean life time tau of the two isotopes, which gives it much less opportunity to find well fitting curves in the wrong proportions.It does have a virtue though: I can select the time-spans for fitting parameters to the data (using your first data set with the amendments for times around 3 minutes.)
I first arbitrarily chose the data around 800 minutes to slice the time series into two samples where I found a modest difference in the linear b parameter I have been using as a straight line model b*time for back ground count. I noted b1 (< 800 minutes) was 12.83 cpm and the other time slice gives b2 = 12.53 cpm.
The numbers are not terribly well-founded, but I found the difference interesting, so I varied the time for the slice, without much change;650 minutes: b1 = 12.83, b2 = 12.53 cpm200 minutes: b1 = 13.7, b2 = 12.47 cpmThe slice at 100 minutes shows a different behavior. b1 = 4.88, b2 = 12.61 opmI varied the time slices so as to locate the change if possible.150 minute slices gave the same results. 4.88 and 12.61 cpm175 minuutes ditto187 minutes ditto193 minute partitions: b1 = 12.95 cpm b2 = 12.43 cpmExcluding the very last data pair at 192.3833 minutes , the last data from the early slice, changed the linear tilt of the background parameter altogether.I deleted just this data pair pro-tem, and the b1, b2 values sprang back to b1 = 6.47 cpm for the first 192 minutes and b2 = 12.59 cpm thereafter.
This looked rather like what David Bowman called an extremization discontinuity. It marks the beginning of the longer interval data pairs.I speculated that the students may have simply subtracted their control readings of background from the first slice of data - without much evidence for the supposition. At any rate- there DOES seem to be a variation in background readings.