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These notes are intended to give some information on the instruments used in this experiment and to point out features you should notice and investigate. The electronics used is all modular, designed to perform a specific function. The units are called Nuclear Instrumentation Modules (NIM for short) and must be plugged into a NIM bin to obtain power to run them. (Preamplifiers are usually separate modules which don't directly plug into bins but must be powered otherwise).
Note first of all that two distinct measurements are to be made. First, the energy of the gamma rays is to be determined; secondly, their time of occurrence (for coincidence measurements). The goal is to obtain both physical quantities with the least uncertainty (highest resolution) possible.
The two measurements are closely related to two types of electronic pulses you will observe; namely, linear pulses and logic pulses. The first is defined as those pulses in which the signal amplitude is proportional to the parameter of interest (energy in our case). Such signals may have any amplitude within a certain span, and the analysis of these amplitudes constitutes the end result of a typical application. This analysis (i.e., sorting the signals according to their amplitude) is accomplished by a multichannel pulse-height analyzer. By contrast, logic signals have a fixed shape and amplitude, and they convey information by their presence, absence, or relation to time. You will encounter the two types of standard logic pulses in common use (both require 50 Ω termination). One is a positive 5 V pulse, 0.5 μsec in width (called "slow" logic pulse); the other is a negative 16 mA (or 0.8 V across the 50 Ω termination resistor) pulse usually less than 10 nsec wide (called "fast" logic pulse). These logic pulses are used to determine time relationships of events.
Before beginning the experiment you should be familiar with the characteristics of the scintillation counter and photomultiplier tube as described in Melissinos (Chap. 5, Section 4) and Leo (Chap. 7 and 8).
Preamplifier - As the output of the photomultiplier is a charge pulse proportional to gamma-ray energy, the preamp converts this to a voltage pulse using a capacitor (V = Q/C). Pulse rise time (important for timing measurements) is dependent upon the scintillation decay time and on the collection and transit time characteristics of the photomultiplier tube. Note the rise time of the pulse.
Amplifier - Besides amplifying the pulse this unit shapes the pulse to obtain either optimum energy resolution or time resolution. Observe the effect of the different pulse shape controls (differentiation and integration switches). Note that the decay time of the pulse is much shorter than after the preamp. This is done to prevent overlap (pile-up) of pulses in a high count rate experiment. Observe the effect of count rate upon the pulse.
For the spectroscopy experiment the above instruments are all you will need. The amplifier output goes to the multichannel analyzer. This instrument places pulses into bins (channels) according to their pulse height. In our case, the voltage span of 0 to 10V is divided into 1024 bins of equal width. What you see displayed is a plot of number of pulses versus pulse height; hence the name multichannel pulse-height analyzer. Since the energies of the gamma rays are known, you can determine the energy per channel. The width of the peaks is a measure of the energy resolution of the system. Find the width of the peaks at half-maximum. You should also determine that the system is linear (i.e., pulse height linear with energy) by plotting energy versus channel number. The result should be a straight line. Finally, find the number of counts in one peak.
The gamma-gamma coincidence experiment involves time measurements. Specifically, the time coincidence of two gamma rays will be observed. Several techniques will be used to do this, and initially we will investigate these techniques. Several new modules will be used.
Single Channel Analyzer - This instrument produces a logic output pulse indicating the presence of a linear input pulse within the range determined by the "E" and "ΔE" settings (differential mode) or merely exceeding the "E" setting (integral mode). Thus one can select a range of pulse heights with this instrument. Also, the logic output pulse bears a definite time relationship to the linear pulse causing it. Thus this module converts linear signals to logic signals used in the time coincidence experiment. There is also an adjustment to delay the output pulse in time.
Coincidence Analyzer - This unit produces a logic output pulse when leading edges of all of the enabled logic inputs occur within the set resolving time. Use the delay adjustment of the single channel analyzers to observe the number of pulses coming out of the coincidence analyzer (registered on a scalar) as a function of the relative delay between the two input signals. The width of the plot of this data (called a delay curve) yields the time resolution of the device.
The above instruments indicate the time coincidence of two logic signals within the coincidence resolving time. But they do not tell which energy gamma ray is in coincidence with which other gamma ray, except if the SCA window was set on only one gamma in each case. So far we only know the presence or absence of some coincidences within the span of the SCA settings. The next techniques will allow the observation of a gamma spectrum from one detector in coincidence with one gamma ray observed in the second detector.
Linear Gate - This instrument allows the passage of a linear signal provided a logic signal arrives at the unit simultaneously to "open" the gate. The latter signal is called an "enable" signal. Thus, this unit performs a coincidence function, its resolving time being limited by the gate width (the length of time the gate is open after the arrival of the enable signal). Of course, the linear and logic signals must arrive simultaneously, so the linear signal will have to be delayed since the logic signal has passed through more electronics taking a longer time.
To obtain a coincidence spectrum, use the delayed output of one amplifier as the gate input. Use the overlap coincidence output as the enable input. Check that the signals arrive simultaneously by triggering an oscilloscope with the enable signal while observing the linear signal. The output pulses from the gate are limited to those which met the coincidence criterion (i.e., overlapped within the resolving time) in the coincidence unit. Observe the output spectrum in the multichannel analyzer. Also observe the spectrum with the detectors oriented at 90° and at 180°. The 511 keV gammas should be in true coincidence only at 180°, so any 511's seen at 90° are accidental coincidences. Obtain the number of true and accidental coincidences and their ratio. See the discussion of pages 406-07 of Melissinos.
The above data were taken with relatively poor resolving time. We can improve this by doing an overlap coincidence between the fast (negative) logic pulses given by the SCA's. This requires a new instrument.
Dual Coincidence - This is an overlap coincidence device which operates on negative input pulses, just as the previous unit did with positive pulses. The output pulses of this unit are negative also, which requires they be changed to positive to be counted by a scalar.
Gate and Delay Generator - Used here merely to change a negative pulse to a positive pulse. Can be used to change pulse width, height, and time also.
Again measure a delay curve to obtain the resolving time. Since the pulses are very narrow, very small changes in delay are required. Lengths of cable can be used for this purpose.
Next, obtain a coincidence spectrum using this fast coincidence setup. The positive output of the gate and delay generator becomes the enable signal for the linear gate, which again must be simultaneous with the linear signals. Observe gated and ungated spectra at 90° and 180°. Compare the true to accidental coincidence ratio and compare it with that obtained with the slow coincidence. Explain the difference. Since this system gives a fast time coincidence (in the coincidence unit) and a slow energy coincidence (in the linear gate), it is called a fast-slow coincidence circuit.
We next use a different system for obtaining a fast time coincidence. This new system has the advantage that it is no longer necessary to measure a delay curve to align the electronics and measure the time resolution. This utilizes the following instruments in place of the overlap coincidence units.
Time to Amplitude Converter (TAC) - This instrument utilizes the fast negative logic outputs of the SCA's as inputs. The TAC output is proportional to the time interval between the start input (from one SCA) and the stop input (from the other SCA). If these two signals are unrelated to each other, the time difference between them can take on any value and the TAC output can be any pulse height. But if the pulses bear a specific relation in time (as all real coincident events do), then the TAC output will be a specific pulse height. The important point is that this pulse height signifies all real coincident events and can be used to identify them. Also, the width of the TAC pulse-height distribution indicates the time resolution of the system. A window can be set on this TAC peak using an SCA whose output will then be the enable signal for a linear gate. The unit we use incorporates an SCA in the same housing as the TAC. The linear signal from one of the detectors is again the linear input to the gate (timed to arrive coincident with the enable signal, of course).
Obtain the same series of coincidence spectra and singles spectra at 90° and 180° as before. Find the real to accidental ratio and compare with those previously obtained.
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