Research Update – Timing Resolutions

I haven’t posted much about my research in quite a while since it’s hard to make calibrating electronics exciting in writing.  But I thought I would give a summary of the overall goals and results of this calibration phase were, since I just finished this stage of the project a couple of days ago.

In case anyone forgot – the overarching goal of my research is to measure the lifetimes of positrons in various materials.  Basically, positrons wander around a material until encountering their anti-matter counterpart (electrons).  When the two meet they annihilate, emitting radiation.  Before I can time how long the positron was able to wander I need to determine how precisely the instruments I am using can measure lifetime, so that I can account for this error later on.  The degree of precision I can attain from the electronics is called the timing resolution.

For my first measurements of the timing resolution I looked at Cobalt 60 (60Co).  In this source, any positrons created by radioactive decay annihilate immediately – so theoretically there should be 0 nanoseconds (ns) between the detection of a positron being born and annihilated.  But when we take a timing spectra, our data shows up as a Gaussian, like the one shown below.  This tells us that there is some error introduced by the electronics, and to quantify that error as timing resolution we measure the width of a Gaussian that fits the data at half it’s height (FWHM).

In this case there are two Gaussians making up the timing resolution.  After changing many settings on the timing electronics, the best (smallest) FWHM of the main contributor to the timing resolution (the red curve) I measured was 0.29 ns (a nanosecond is 10^-9 s).

When we take the timing spectra of a source whose positrons do not immediately annihilate, we should find that the lifetimes fall off as a decreasing exponential.  However, it is standard to plot on semi-log axes (take the log of the vertical axis), so we actually  observe a decreasing linear function.  We also have to take into account the timing resolution, which is in the form of a Gaussian.  When you combine these (really a convolution) you get a function like the one in red in the picture below.

The red function is what our lifetime spectra will actually look like.  The timing resolution for a source that actually has a lifetime component will be a bit bigger than that from a source where positrons immediately annihilate.  I therefore needed to measure the timing resolution again, using a source that also has a lifetime component (I used Bismuth).  The idea is to isolate the Gaussian part of the red function above, and measure it’s FWHM like we did previously with Co60.  Bismuth is a good source to use because it only has 1 lifetime, whose length is already well documented.  To pull out the resolution function I used PATFIT- a program developed in the 1980s and originally written in Fortran.  (Luckily my research advisor has adapted it to work with Labview to be a little more user friendly.)  This program allowed me to guess how many Gaussians made up the resolution function and the FWHM of each.  I initially tried a single Gaussian, and then two Gaussians with the FWHM’s I found using 60C0.  The best fit I found used 3 Gaussians – the main one makes up 80% of the total resolution function, and the other two contribute 10% each.


The timing spectra of Bismuth (blue) fitted with a timing resolution function (red).



The graph above shows the spectrum of Bismuth (blue) with the fitted resolution function in red.   Unlike in previous posts, the vertical axis here is the number of times it took X ns for a positron to annihilate.  So in this plot you can see that most of the positrons annihilated at 0 ns (this does not actually mean they annihilated instantaneously, the data has just been shifted).  The timing resolution here was indeed bigger than 60Co, coming in at 0.5129 ns.

Armed with a resolution function for sources with lifetime components, I now take a spectra of a new source, 22Na.  Unlike Bismuth, I do not know the lifetimes of positrons in 22Na, so I will use PATFIT and my resolution function to pull out information about the lifetime part of the data.   Like before, I make some initial guesses until I get a good fit like the one shown below.


Positron lifetimes in a sodium 22 button source (blue) fitted with a resolution function and lifetime curve.



I find that there are two different lifetimes in 22Na.  Sometimes the positrons get lucky and live for as long as 1.75 ns, and some only live for 0.28ns (depending on the kind of positron).   These results are in pretty good agreement with the accepted lifetime values for positrons in such a source, but I will still try to minimize the timing resolution with a few additional adjustments.  Once I make those final changes and then I will be ready to measure lifetimes of positrons in a variety of new materials.


November 23, 2009. Tags: , . Physics, Positronium Research.

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