Measurement of Ultra-Slow Relaxation in

TRIUMF Experiment 1111

Fitting exercise for TSI 2011 Data Analysis workshops

In the TWIST experiment at TRIUMF, an international collaboration measured the Michel parameters of µ+ decay to unprecedented precision. One of these parameters is the initial polarization of the µ+ following pion decay. We take it to be exactly 1, but if there were (for instance) a right-handed W+ intermediate vector boson with a mass of less than a few hundred GeV/c2, the absolute value of the initial µ+ polarization might be slightly less than 1.

The TWIST group was concerned that the muon might be depolarized by its environment (as we know it often is) so they measured the time dependence of the polarization using methods much more intricate than simple µSR. They also did the experiment in a silver target (which we often consider to cause no depolarization) in a longitudinal field of 2 T, which should be enough to decouple virtually any depolarization mechanism. Nevertheless, they were concerned about the first few hundred ns, which (because of systematic constraints) they could not see in their experiments.

So they proposed to use µSR to independently measure the relative µ+ relaxation function Gzz(t) in Ag and Al in a LF or 2 T, with the help of a few members of the CMMS staff and other scientists. This became TRIUMF Experiment 1111.

The Experiment

To accurately measure very slow relaxation in a 2-histogram asymmetry spectrum, one needs to know at least two systematic parameters: ALPHA = NF/NB (the empirical normalization ratio of the two opposing detectors) and BETA = AF/AB (the ratio of initial asymmetries in the two detectors). [Basically ALPHA tells you where to look for P = "zero" and BETA tells you where to look for P = 1.] There are ways of determining these parameters from wTF measurements if one is only interested in the ZF or wLF values, but in very high LF everything changes due to "curl-up" of positron tracks so that the wTF values are significantly changed. It was therefore essential to have a sample in which the muons are initially fully polarized but the µ+ polarization decays away to zero in about one muon lifetime, even in a LF of 2 T, at room temperature.

Such a material is the pyrochlore "spin glass" Gd2Ti2O7, in which the huge paramagnetic moments of Gd ions fluctuate, but not fast enough to prevent µ+ depolarization. A sample was made with Gd2Ti2O7 on one side and Al or Ag on the other side; it was then measured by LF-µSR with the µ+ beam stopping in one side, and then in the other side. The runs to be fit can be found in the archives as runs 2514 through 2519 on M20 in 2006.

The Exercise

Visit the TRIUMF µSR runs database at http://musr.ca/mud/runSel.html and search for Experiment 1111 in 2006; there aren't very many runs.

Click on the run-number button for run 2514 and investigate the run header information, especially the names and ordering of the data histograms. Select various Spectrum types and look at the entire time range with (let us say) 100 ns bins. Eventually choose Spectrum type 2 to make some nice ASY plots of both Sample and Reference spectra for runs 2514-2519.

When you have these runs selected, click Zip & Download Runs at the bottom of the Run List window to bring the selected runs into your computer; then unzip the download into the directory where you want to fit them.

If you are working on bnqrexp.triumf.ca, the zip/unzip step is not required, as all runs are directly accessible in the /data/<beamline>/<year>/ directories on that host; unfortunately this is not available on the workstations in Hennings.

Use musrgui or (on bnqrexp.triumf.ca) physica ['t0', 'bkgd' and 'early' commands] to determine the t = 0 bin, background bin range and good data bin range. Checking one run should be sufficient. Make sure you don't try to fit the data in the "hole" around t = 0. Prepare your fit-control template file, for either musrfit (.msr) or msrfit (.i), starting from another such file. There will be a single signal in each of two Spectra [S & R] and you should let each have its own amplitude and exponential (or other shapes, if you like) relaxation rate.

Note: There is no real need to fit both S and R signals at the same time, since they share no common Signal parameters and are in different Spectra; it is just a bit easier to keep track of the results this way. Fit the fast-relaxing spectrum first to determine both ALPHA and ASYM independently, then "fix" the alpha parameter and fit the slow-relaxing spectrum from the other pair of histograms. When there is such a slow relaxation, alpha and asymmetry are highly coupled parameters and cannot be fitted simultaneously, since a wide range of values can fit the data equally well.

If you are an expert, you may want to try the ADD command in your .I file to combine several runs (e.g. runs 2515 through 2519) for higher statistics in a single fit. Ask Jess if you want to use this feature.

If you get frustrated trying to compose your own .I input file for msrfit, here are some templates: 2514.IEE, 2514.I4EE and (dangerously) 2515-9.IEE or 2515-9.IGE, where the extra letters after the "I" are mnemonic indicators of the model used for fitting.

How Slow is the Relaxation?

You should get a relaxation rate of just over 1 inverse millisecond for either Al or Ag. Be sure to plot your fits to see if this ultra-slow relaxation is "visible to the naked eye".
Jess H. Brewer
Last modified: Mon Aug 15 13:33:12 PDT 2011