The S-parameter evaluation    

The Doppler Broadening Spectroscopy (DBS) of annihilation line is one of the most common techniques in the positron annihilation studies. The DBS setup consists of a positron source sandwiched between two identical samples fixed in a holder and a germanium detector (HPGe) with good energy resolution with a multichannel analyzer that collects the measured spectrum in appropriate energy channel.

HpGe detector

By use of the DBS we analyze the shape of the annihilation line, i.e., 511 keV obtained for one sample of a set of samples. The so-called S-parameter (shape parameter) defined as the ratio of counts in the central part to the total area of annihilation line, is evaluated. This parameter, with value at about 0.5 is sensitive to low momentum (free or valence) electrons. The annihilation with low momentum electrons that are also present in the open volume defects contribute to the raise of the central part of the peak thus to the increase of the value of S-parameter. The S-parameter increases when more defects are present, where positrons can be localized. This effect is clearly visible in in the presented example of copper samples with different history.

The annihilation line (S-parameter) was measured for the well annealed non-defected copper (Cu) versus copper that underwent the the compression copper sample are depicted. (Both curves are normalized in the same way.) The Cu sample after compression has siginificantly more counts in the central part due to the presence of open volume defects compared to the non-defected Cu sample.

It is also useful to use the so-called wing W-parameter (wing parameter) which is defined as the ratio of counts in the off-center fraction divided by the total area of annihilation line. The value of W-parameter increases when there are more annihilation events with core electrons, which are sensitive to the chemical surrounding of annihilation site than the S-parameter. The core electrons having higher momentum, are contributing mainly to the region of energy at (511 ± 5) keV and higher.

 S-parameter definition

The SP software program was designed for the analysis of the annihilation line. The SP program is quite versatile. It finds the S- and W-paremeters automatically subtra- cting the background. It can fit the gaussian curve to a spectrum. A location of the maximum of the gaussian curve defines the 511 keV position, which is important for finding the integration ranges for S- and W-parameters.

The SP program is a freeware, that works in working under WINDOWS XP. Download: Instal-SP-1.ZIP (2 MB), extract and run setup.exe.

The version SP-11. was prepared for WINDOWS 7 and 8; Download: setup_SP-11.rar (5 MB), extract and run setup.exe.

 Print screen from the SP program in action

The newest version (SP-16K) of the SP code was prepared for working with spectra measured using 16k channels MCA. (The earlier versions were able to accept maximum only 8k channels spectrum.) Additionally there is possibility to analyze series of spectra with the same imput parametrs, with the results saved into one batch file. The program is running under WINDOWS 7, 8 and 10.
Download: SP16K.ZIP (6MB), extract and run setup.exe.

 Print screen from the SP program in action

From the spectrum with 511 keV annihilation line one can extract also information about the triplet (three-gamma) annihilation, including ortho-Positronium (o-Ps) decay. Ps is created inside porous materials or on the entrance surface irradiated by slow positron beam. The R-parameter is useful for extracting the information about a fraction of triplet as compared to two-gamma annihilation. This parameter is defined as the ratio of the total counts area in the valley region, i.e., between the Compton edge and annihilation line (tagged between two vertical blue lines in the bottom graph in the right), devided by the total are of the annihilation line at 511 keV (two green vertical lines). The new version of the SP program can be useful for slow positron beam measurements, with not only the S-and W- parameters, but also R-parameter for monitoring of the Ps formation as the function of positron incident energy.

The program is running under WINDOWS 7, 8 and 10.
Download: SP-SE.rar (5.6 MB), extract and run setup.exe.

 Print screen from the SP program in action