Nuclear Experiments - Gamma-Ray Detection and Coincidence Measurements

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Purpose

In this experiment high energy photons - gamma-rays - are detected using scintillation detectors read out by photomultipliers. The gamma-ray energy spectra of various radioactive sources is measured and the linearity of the detection apparatus is determined. The absolute activity of the source is found. The use of coincidence timing is explored in an experiment employing two scintillation detectors to record the simultaneous occurrence of two gammas from the decay of positronium.
 

Procedure

We follow the procedure in ORTEC Application Note 34:  "Experiments in Nuclear Science."    The required experiments are:
 
  • Exp. 1 Basic Identifications in Electronic Measurement Systems
  • Exp. 3 Gamma-Ray Spectroscopy Using NaI(T1)
  • Exp. 9 Time Coincidence Techniques and Absolute Activity Measurements
  • Exp. 13 Gamma-Gamma Coincidence
    • It is strongly urged that, after completing an experiment and before carrying on to the next experiment, the student perform a rudimentary analysis in order to insure that the data is good.
     

    Write-up

    Each of the four experiments should have a separate write-up. Keep them short and to the point. Each report should include: Do not include a detailed description of the experimental set-up, but rather a simple drawing of the equipment. In experiment 1 the student should observe the signal after each stage of amplification and pulse shaping and draw its shape, height (in volts), and length (in seconds).

    It is important for the student to do an error analysis with every measured number having an associated estimated error. There are many good texts which explain how to treat errors.

  • A simple introductory text is:
  • A more advanced text (which includes FORTRAN programs) is:
    • Nuclear and particle physics data almost invariably follow a Poisson probability distribution which is the Binomial distribution in the case where the number of events N is large and the probability p of any one event, small. The Poisson distribution has the particularly appealing property that the error in the mean (a = Np) is simply the square root of a.
     

    References

    Besides the ORTEC application note 34 and the various manuals describing the equipment used, we recommend the following books which can be found on the reserve shelf.

    Radioactive Sources

    Nuclear Decay Processes

    Nuclei can undergo a variety of processes which result in the emission of radiation. The three most important of these processes are: alpha decay, beta decay, and gamma emission. We briefly describe these processes below.

    1. Alpha decay: This is the emission of an alpha particle (Helium nucleus) from the nucleus: (A,A)-> (Z-2,A-4) + a The emitted alpha particles are monoenergetic, their energy in the range of a few MeV. The alpha interacts strongly and has a very short range - a few cm in air.
    2. Beta decay: This is the decay of a neutron into a proton and electron and a neutrino: n -> p + e- + n. The proton does not have enough energy to escape the nucleous but both the electron and neutrino do. The electron has a continuous energy spectrum because of the kinematics of a three body decay. A related process is the emission of a positron: p -> n + e+ + n. Neither the electron or the positron is very penetrating.
    3. Gamma emission: The nucleus has discrete energy levels, like those of the electrons in an atom. The nuclear force, however, is much stronger than the electromagnetic and hence transitions from one state to the other are characterized by the emission of photons of much larger energy - from a hundred keV to a few MeV. Such photons are called gamma-rays and are very penetrating.
    The probability that a nucleus will emit radiation is random and depends on the number of nuclei. Hence the mean number of decays as a function of time is given by the exponential:
    N(t) = N(0) e-t/t

    where N(0) is the number of nuclei at t=0. The number t is known as the mean lifetime - the time it takes the sample to decay to 1/e of its initial activity. The half-life is the time it takes the sample to decay to one-half of its initial activity.

    Handling Radioactive Sources

    The activity of a source is the number of decays which can occur in a given time. It is usually measured in Curies which are defined as:

    1 Curie = 3.7 x 1010 disintegrations/s

    This is a very large unit (originally defined as the activity of one gram of Radium). One usually deals with sources which have activities on the order of a microCurie (µCi).

    The sources we use in this experiment have low activity. For example, a 100 µCi 22Na source produces an exposure rate of 4.47 mrem/hr. For comparison, one x-ray produces a dose of 100-200 mrem. A rem is defined as an energy of 100 erg deposited in one gram of material multiplied by a quality factor for the type of radiation. For gammas the quality factor is one.

    One must be careful, however, with sources at the µCi level that one does not ingest them. Small amounts of radioactive sources in the body can be very harmful. The sources we have in this lab are normally sealed and hence ingestion is improbable. Nevertheless one should always obey the following two rules when handling radioactive sources:

    1. Never eat or smoke in the laboratory.
    2. Wash your hands after handling radioactive material.

    A Short ( click for long version ) Description of the Electronics Used in the Experiment

    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 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). The cataloging of such signals according to amplitude is accomplished by the use of 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 of time. In this experiment logic pulses are used to determine time relationships of events.

    Preamplifier - The preamp converts the pulse from the photomultiplier anode - a charge pulse - to a voltage pulse using a variable capacitance. The rise time of the pulse (important for timing measurements) is dependent upon the scintillation decay time and on the collection and transit time characteristics of the photomultiplier tube.

    Amplifier - Besides amplifying the pulse this unit shapes the pulse to obtain either optimum energy resolution of 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 stronger than after the preamp. This is done to prevent overlap (pile-up) of pulses in a high count rate experiment.

    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 "E+DE" settings (differential mode) or merely exceeding the "E" setting (Integral mode). 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.

    Overlap Coincidence Module - This unit (also called an "and-or gate") produces a logic output pulse when two or more logic input pulses "overlap" in time of arrival (coincidence mode, also called "and gate") or when they do not overlap at all (anticoincidence mode). The coincidence resolving time of this unit is limited to the sum of the widths of the overlapping pulses.

    Fast Coincidence Module - This unit also performs an overlap coincidence, but only after inspecting the input pulses to more accurately determine their time of origin.

    Linear Gate - This instrument allows the passage of a linear signal only with the simultaneous arrival at the unit of a logic signal (which "opens" the gate). The latter signal is called an enable signal. Thus, the 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).

    Multi-Channel Analyzer - This versatile instrument gives a plot of the pulse height spectrum of all of the pulses input to it. It takes each pulse, converts its pulse height into a digital number and increments the bin count that number falls within.

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