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Investigating the 14.4 kev peak with an SCA
Investigating the 14.4 kev peak with an SCA
Ascertaining the optimal window around the 14.4 kev peak is very important because the resulting count rates can greatly improve (or decrease) the amount of data that can be taken. Because of reflections, obtaining the true value of the number of events per second in the 14.4 kev peak from the Ortec 994 Counter can be next to impossible. Using the scanning SCA described below, we can view the peak more clearly. Here is some further discussion of this process.
Converting an SCA into an MCA-like Device
An Ortec 550 single-channel analyzer (SCA) has several additional features located on its back panel, including a toggle switch between internal and external. When 'EXT' is selected, the lower-limit threshold voltage is taken from an externally-applied voltage (which connects to the 'LL Ref' input on back panel). Because of this feature, it is possible to use the SCA in a way that emulates an MCA (multi-channel analyzer). See the setup page for a detailed explanation of SCA settings.
When the back-panel toggle switch is in the 'Int' or internal mode, all window or threshold voltages are controlled by the front-panel dials. However, when the toggle switch is set to 'Ext' or external, the 'LOWER LEVEL' dial becomes defunct the lower level threshhold voltage is set to the (absolute value of the) voltage applied to the 'LL Ref' input. The 'LL Ref' input accepts voltages between 0 and -10 V. The voltage range included in the window then begins at the lower level threshold and ends at a voltage equal to the LL plus the window width.
In order to best emulate an MCA with the SCA, the SCA should be set to 'WINDOW' mode on the front panel toggle switch, and a relatively narrow window can be selected. A LabVIEW program that uses the BNC-2110 box and 6036E card can be used to scan a preset voltage range in a given number of steps and for a given amount of time spent at each step. This makes the SCA work like a somewhat inefficient MCA that looks at multiple channels, but only one at a time.
The LabVIEW code for the scanning SCA:
https://sites.google.com/a/umn.edu/mxptest/home/mxp-ii-labs/mossbauereffectlab/mossbauerpeak/Programmable_SCA_6036E_V2c.vi?attredirects=0&d=1: LabVIEW code for SCA to MCA
The Ortec 550(A) spec sheet:
550A.pdf : Ortec 550A Spec Sheet
Determining the Correct Window Width
An MCA breaks its range down into a number of bins (2048, say) with neither space nor overlap between bins. All events encountered by an MCA (within its range) will be counted into one and only one bin. Since the range, number of bins, and bin widths (window widths) are manually determined by the user for an SCA, care must be taken to select appropriate values. The number of bins equals the selected voltage range divided by the number of steps. Clearly, the greater the number of steps, the smaller the step size for a given voltage range. When the window width exceeds the step size, events in overlapping regions of the spectrum will be counted in more than one bin. If the window width is smaller than the step size, there will be some regions of the spectrum that don't contribute to any bin. Either way, the area under the peak may not be accurate because you either didn't count the activity in all regions of the peak, or you counted some regions multiple times. Furthermore, if the window is too wide, you will lose information about the true peak width and position, and the signal-to-noise ratio will be worse.
We will be considering two window widths: first, we will look at the effects of using varying window widths while the SCA is in its MCA configuration. Second, we will extract the "final" window widths that we would like to use for the Mossbauer setup.
SCA/MCA CONFIGURATION: When using a window width that is too wide (wider than the actual peak), the resulting peak gets spread out to about the width of the window, with an amplitude about equal to the full amplitude of the true peak. When using a window that is too narrow (narrower than the step size), the amplitude of the resulting peak will be smaller than the full amplitude of the true peak, because events in the 'gaps' aren't counted at all. These effects are shown in the graph below, where a 0.1 step size has been used each time:
Clearly, as the window width approaches the step size of 0.1 V, the peak becomes more resolved. It is not as wide as the 0.5 V window width data runs would suggest. A plateaued or rectangular peak occurs with overly wide window widths such as 0.5 V, because the data points taken at 3.7 to 4.3 V all contain the true peak within their window. (Note also that the 0.25 V window width data results in a peak half as wide as the 0.5 V window width, for exactly the same reason.) The 0.15 and 0.10 V window widths give a much more accurate view of the peak shape and location, which appears to be between roughly 4.0 and 4.4 V.
The y-values should be interpreted very carefully, however! They do not mean counts/sec. The y-values are clearly dependent on the SCA window width (0.1, 0.25, 0.5 V or whatever). They are actually measurements of counts/sec*dx, where dx indicates the window width. If you divide all the y-values by the window width, the resulting values are in units of counts/sec, and they can be thought of as the average count rate that occured within each window. This process introduces a phase shift because now you are reporting an average count rate for an interval at the very beginning of each interval. If you instead want to report the average count rates in the center of the intervals over which they occurred, you should shift the x-values to the right by one-half of the interval length (step size).
DETERMINING THE MOSSBAUER WINDOW WIDTH: The areas to the right and left (and under!) of the peak contain very constant levels of noise. The optimal window width is one the contains the entire peak out to the point on either tail where the signal-to-noise ratio is 1. Going further away from the peak center would then give a signal-to-noise ratio of <1, and thus include more non-events than real ones. To determine where the signal-to-noise ratio becomes equal to 1, data should be taken using the scanning SCA technique with 0.1 V step size and window width, from about 3.5 to 5 V. Next, this data should be uploaded into Origin, and fit to a Gaussian or Lorentzian distribution (Gaussian is used here because Lorentzian did not converge). The fitting algorithm will provide the user with a constant background term, y0. All that remains is then finding the point on either tail where the true signal equals y0, as shown below. This can be accomplished by using the provided peak formula (minus y0) and all the calculated fit parameters to tabulate expected count rates in small increments (0.005 V or so), and then finding where this equals y0.
For a Gaussian peak fit, the peak center was found to be at 4.1735 V, with a width of 0.1411 V. The y0 offset (noise) was found to be 1.39057 cps/V*dx. Because the background has the same dependancy on dx as the signal does, we don't need to correct for dx right away. By using the given fit parameters to calculate an expected count rate in small increments, the points at which the signal-to-noise ratio is 1 were found to occur at 4.013 V and 4.335 V. Therefore, for this source geometry, with the PX2T gain of 3.5 and using a 1 mm steel foil, these should be the optimal SCA UL- and LL- threshold values.
Using this method, the signal-to-noise ratio can be found for the entire SCA window region. Integrating the peak (including the noise) from 4.013 V to 4.335 V gives 8.328. Then true, non-background events are calculated by the following:
8.323 - 1.39057*(4.335 - 4.013) = 7.880, or about 94% of the events under the peak are non-background events. After dividing by a dx = 0.1 V, about 79 cps are real evens.
This leaves background events:
1.39057*(4.335 - 4.013) = 0.44478, or about 6% of events under the peak are background events, as expected. Dividing by dx = 0.1 V gives a background count rate of about 13.9 cps.
The signal-to-noise ratio within the SCA window is then 0.4478/0.056 = 0.056. Widening the window any further would cause this value to decrease. Finally, the total number of counts that occur within the range (the count rates that should be observed by the ideal counter) can be found by dividing each data point by the window width setting of the scanning SCA (in this case, 0.1 V), and then integrating over the final window region (the 4.013 V to 4.335 V). In this case, this gives a total count rate of around 82 cps. The data must be divided by the scanning SCA window width because each data point represents a count rate as a function of that width - the wider the scanning SCA window width, the more counts would be recorded in each point.
The origin spreadsheet can be viewed here:
https://sites.google.com/a/umn.edu/mxptest/home/mxp-ii-labs/mossbauereffectlab/mossbauerpeak/SCAwindow.opj?attredirects=0&d=1: Origin Fit for SCA window calibration
The Original Data folder shows the window LL (column A), the data as reported by LabVIEW (column B), and the reported data after being divided by the window width of 0.1 V (column C). (The Modeled Peak uses the fit parameters generated from the original data to plot the 14.4 keV peak in its predicted form, and then integrates that peak over the window width.) The integration of the original data (divided by the window width) is shown below:
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