Nuclear Experiments - Gamma-Ray Detection and Coincidence Measurements

IMPORTANT NOTE:  Before coming to the first lab meeting for this experiment, read the relevant chapters in Leo (see listing), which is on reserve in the Physics Library. There may be a quiz on this material!

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 a 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.

Tasks

We (loosely) follow the procedure in ORTEC Application Note 34 "Experiments in Nuclear Science."   Note that we are using different instruments than the ones referenced in the Ortec manual and so you will need to ignore the instrument specific instructions and instead use them as a guide.   Refer to the equipment manuals for operating details.

IMPORTANT NOTE:  After completing an experiment and before moving on to the next, perform a rudimentary analysis in order to ensure that the data are good and discuss the results with the instructor.

The required experiments are:

• 1.1 Observing the direct and attenuated outputs of the pulser
  Exercise c, d
• 1.2 Using the pulser as the linear input to a typical counting system
  Exercise a, b
• 1.3 Using a single-channel analyzer
  Exercise c, d, e

• 3.1 Energy calibration
  Note: Use ²²Na as well as ⁶⁰Co and ¹³⁷Cs for the energy calibration
  Exercise a, b
• 3.3 Spectrum analysis of ⁶⁰Co and ¹³⁷Cs
  Exercise a, b (Make sure that you recognize what parts of the spectrum are due to the source and what parts are due to the detection mechanism and that you make it clear in your write-up which is which)
• 3.4 Energy resolution
  Exercise
• 3.6 Activity of a gamma emitter (absolute method)
• 3.7 Mass absorption coefficient
  Exercise a

• 9.1 Simple fast coincidence experiment
  Exercise a, b, c

• 13.1 Overlap coincidence method for measuring gamma-gamma coincidence of ²²Na
  Exercise
• 13.2 Linear gate method for measuring gamma-gamma coincidence of ²²Na
  Exercise

Write-up

Each of the four experiments should have a separate section. Keep them short and to the point. Each section should include:

• a description of the experimental setup including a schematic and simple drawing of the apparatus
• the raw data (photocopied from your notebook, if necessary)
• plots of the gamma ray spectra recorded by the multichannel analyzer using appropriate units [e.g., "Counts per bin" vs. "keV"]
• any other plots you are asked to make. MAKE SURE THAT YOU USE APPROPRIATE UNITS!
• answers to the exercises
• relevant commentary, including a discussion of the function of any new piece of equipment (e.g., Single Channel Analyzer) or technique used

It is important for you 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 good introductory text (and one you are likely to own) is:

A more advanced text is:

Chapter 4 of Leo (see references below) also has a good, concise discussion of errors as well as curve fitting.

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 (μ = Np) is simply the square root of μ.

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:

This recent, well-written book fills a long-standing need for a practical introduction to the techniques of experimental nuclear and particle physics. It does so admirably.

Another excellent text, albeit more advanced than Leo.

A classic text, although dated. Skip over the description of the electronics - the remainder is well done.

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: (Z,A) --> (Z-2,A-4) + α 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^- + ν. The proton does not have enough energy to escape the nucleus 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⁺ + ν. 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:

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:

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 capacitor. 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 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.

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+ΔE" 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.