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Positron Research Group
Science Center 155
1520 St. Olaf Avenue
Northfield, MN 55057

Dr. Jason Engbrecht
engbrech@stolaf.edu
507-646-3849
507-646-3968 FAX

  [-web-]

Anna Legard '08
legard@stolaf.edu

Dan Endean '09
endean@stolaf.edu

David Green '09
greend@stolaf.edu

 

 

Analysis

 

One of the most important elements of the analysis is a model to fit the energy peak data. Recall the Doppler broadening phenomenon from the "crash course". We know that high energy Ps will have wide energy peaks, whereas low energy Ps will have narrow energy peaks. Hence, the increase in peak width, due to the Doppler effect, leads us to a value for the momentum carried by the Ps. Our signal consists of several components, only one of which is the desired, doppler-affected peak. In order to isolate this so-called "narrow-peak," our model must recognize the background and the wide-peak.

 

A sample energy peak from scattering data of Ps in helium gas, with accompanying fitting components. The orange curve is fit to the data, in order to extract the width of the doppler-broadened "narrow peak".

[Total fit]
[Narrow Peak]
[Background Signal]
[Wide Peak]

Background Signal:

The HPGe detector collects all radiation in the vicinity of the experiment, including small amounts of natural, incoherent radiation found on the surface of the earth. In addition to this flat background, Ps may annihilate in three gamma rays, which produces radiation between 0 and 511 keV with no definite peak. Thus, the left side of the peak is raised, as shown.

Wide Peak:

Much to our dismay, positrons will form Ps and annihilate with their respective electron only a fraction of the time. As such, there are several other outcomes that regularly occur, including slow positrons and the pickoff effect. The energy spectra from these effects combine to form a wider peak, sharing a center with the narrow peak at 511 keV.

Slow positrons are positrons that collide with the gas atoms but do not form Ps. After a certain amount of kinetic energy is lost, they are too slow to pull an electron out of its orbital and create Ps, but instead annihilate with an electron. Because the positron-electron pair gains kinetic energy from the electron’s orbital speed, the resulting peak gains a significant amount of width.

The pickoff effect refers to the case where Ps is formed, but the positron annihilates with a different electron than its original pair. Similar to the outcome of slow positrons, energy is gained by the electron’s orbital velocity and the signal peak is broadened.

 

Several analytical functions may be used to fit these components, which are controlled by parameters such as intensity (total area under the curve) and width (measured as the width of the peak at half of its full amplitude, called the "full-width half-max"). Unfortunately, the gamma-ray detector does not provide a perfect record of the incident radiation. Instead, the information is slightly altered by the resolution of the detector, by an effect called convolution. In order for the fitting parameters to keep their physical significance, we can accordingly convolve our fitting functions, once we know the nature of the detector's resolution.

Example Cs-137 energy peak
(for measure of detector resolution)

We can get a quantitative gauge for this convolution by collecting the radiation from a Cs-137 source, which sits on top of the HPGe detector for the duration of the experiment. Gamma rays from the cesium source will travel directly into the detector and will not undergo doppler-broadening. Atomic radiation of this isotope releases exactly 661.7 keV of energy per decay, so the physical distribution is a delta function at precisely this energy. Hence, any increase in peak width is due to detector resolution. (Note that the energy peak from the cesium source is easily distinguished by its decay energy. This means that we can simultaneously take gas-scattering data and resolution data, to eliminate the effects of a possible time-dependant resolution.) This information is used in the peak fitting described above. Thus, we fit the respective cesium peak to measure the magnitude of the convolution, before performing the analysis on each 511 keV energy peak.

 

A single data collection may span the course of several days. This collection is partitioned into hourly intervals, called acquisitions. Each acquisition is divided into around 20 equal parts, or "time-slices," according to the lifetimes of the Ps. This means that a 72 hour run could contain nearly 1500 distinct energy peaks, each of which needs to be individually fit. To handle these large amounts of data and automate the process, a computer program was written in a language called “OriginC,” a superset of the C programming language, made for use with the Origin software. A schematic of the flow of information is shown here.

Primary Data Analysis Schematic

 

Additional analysis will be performed on the exported peak widths (shown as the last step). This parameter is used to find the momentum of the Positronium. Acquisitions and time-slices may be as numerous as desired; the analysis program is designed to accommodate between an hour and a week’s worth of data acquisitions.

 

You guys must have some awesome results, right? --->