Nuclear Spectroscopy

There is a very nice manual provided by PASCO, which both explains the physiscs and guides the students through exercises. Unfortunately, it is not available online, so each student will receive a xerox copy. (The copies are ready and should be picked up from the Intermediate Lab.)

This time we will only do the experiments 1 through 5. The main goal is to introduce the equipment, and basic concepts such as calibration, resolution, and recognition of spectra based on the known spectral shapes.

Task #1: calibrate the detector. Use three-point calibration with Na-22 and Cs-137. The center of each peak is obtained from the centroid of the ROI distribution.

NOTE: in the plot of gamma ray energy vs channel number, include the errors on the mean channel number of each peak. Obviously, this error is completely systematic. So what is it? All systematic errors common for all peaks are taken out by the calibration itself. What remains are the effect that can bias each peak individually. The dominant systematics thus comes from the very fact that we use the mean of the ROI, since:

it includes background, which can be sloped (the higher the slope, the larger the systematic bias)

the centroid depends on the fact that ROI is symmetic around the peak, and the human eye and hand are not always able to satisfy this requirement

The best way to evaluate this source of the systematics is to take 2-3 peaks (preferrably where the background is falling) and obtain the peak value both from the mean of the ROI region (as usual), and by fitting the Gaussian peak on the polynomial background with ROOT (or your data reduction program of choice). The average difference between the two is a pretty good guess of the systematic error. Thus
Task #1a: take at least two peaks and fit them by hand, and from the average derive the systematic error on the values of channel counts. To extract the data into ROOT, save the ICSW plot into a text file and then use this root script to load it into ROOT.

Task #2: determine the content in the mystery source.

HINT: it contains two isotopes. One is easy, but the other one crucially depends on good calibration at high energies.

Task #3: study the resolution of the detector as a function of the gamma ray energy, E.

Task #4: study compton scattering (including back-scattering).

NOTE: in the same way that the peaks are obtained by convoluting a very narrow Breit-Wigner function and a Gaussian resolution function, the "Compton edge" is obtained by convoluting a step function with a Gaussian resolution function, resulting in an Error function sitting on top of a continuous background. The "width" of the Error function (i.e., the width of the corresponding Gaussian resolution function) can be used to eyeball the error on the location of the Compton edge (which you need in order to propagate the errors). If you could actually fit the Compton edge to a sum of an complement error function (TMath::erfc(x) in ROOT), that would be even better. In that case the fit will return the correct (and much more precise) error on the location of the Compton edge.

Task #5: search for annihilation and escape peaks.

NOTE: for this exercise, you need to take data for a long time (here long is a couple of hours; leave the setup running and go to the class).

Reading

PASCO's technical description of the equipment can be found here. The PASCO manual (mentioned above) contains the basic nuclear physics and the description and discussion of all the exercises, as well as an Appendix with an extensive list of isotopes and their transitions. However it doesn't spend much time on the detection of gamma rays (energetic photons) using the scintillator counter, so I append some information below.

How the scintillator counter works

Scintillator counters are usually comprised of: scintillator material (e.g. a crystal), a photomultiplier, and an ADC counter. Briefly, here is what happens:

A charged particle traverses the material of the scintillator, and excites atoms or molecules of the material (using the processes shown in the diagrams below). The excited atoms (molecules) relax into the ground state by radiating quanta of visible light.
That light is collected in a photomultiplier, in which the photoelectric effect is converted each photon into an electron, which then cascades between cathodes releasing more electrons at each step.
The voltage output of the photomultiplier is input into an Analog-to-Digital Converter (ADC), which digitizes the voltage by counting the units of voltage until it reaches the input from the photomultipler. The output of an ADC counter is thus an integer number between 0 and the maximal number of counts.

There is a loss of signal at each step (an "inefficiency") however the ultimate number of ADC counts is almost linearly proportional to the energy of the original particle entering the scintillator material. But once the ADC count scale is calibrated (meaning that there is a one-to-one correspondence between the energy of the incoming particle and the number of ADC counts), we can use the scintillator counter to measure energy of any particle in the similar energy range.

Scintillators are made of two types of material: organic or inorganic. The diagrams below (taken from Melissinos) outline the basic processes that take place when a charged particle traverses the material of the scintillator. Organic scintillator agens are most frequently imbedent in plastic. They are extremely fast, relatively cheap, and easy to handle. (In particle physics they are most often used in conjunction with fast electronics to indicate a passage in order to "trigger" the data acquisition system. In big collider detectors there literally are hundreds of pounds of scintillators used for a number of differen purposes.)

Unfortunately, due to their low atomic mass (as discussed below), the organic scintillators are not optimal for the detection of gamma rays. CsI and NaI crystals are more suitable for that purpose. A passage of a charged particle creates electrons and holes, and a complicated interplay of of various processes ultimate results in the emission of a light quanta. As an aside, Rutherford was the first to use an inorganic scintillator (ZnS) in his scattering experiments with alpha particles.

Photons are neutral, so in order to be detected they have to trigger processes that result in creation of other charged particles, such as:

Photoelectric effect: a bound electron absorbs a gamma ray which gives it enough energy to break free. Almost all of the energy of the gamma ray is converted into kinetic energy of the electron. Photoelectric effect predominates at low energies.
Compton scattering: photon hits a bound electron and scatters elastically, kicking the electron out of the atomic shell. In this case the photon takes away some fraction of its energy. This process at medium energies (below a few MeV).
Pair production: a photon creates an electron-positron pair. As this process is kinematically impossible for a photon in vacuum, it has to take place in the presence of the atoms of material, which ballance the momentum. This process dominates at high energies.

Therefore we can use a scintillator counter to also measure the energy of the gamma rays. For a gamma ray of energy

, the possible features of the energy spectrum will be:

A peak at E = , arising from the photoelectrons. This peak is called the photopeak.
A broad shoulder below indicating the maximal momentum transfer in the Compton scattering.
Background -- encompassing the contributions of other photons from the environment, cosmic rays, electronic noise, etc.
A peak at 511 keV, arising from positive beta rays (positrons) which enter the scintillator and annihilate with electrons of the material, producing two photons of 511 keV each. This peak appears when one of the photons escapes detection. This peak is called the annihilation peak.

Calibration of the scintillator counter

The callibration is performed by using three lines of known energies, usually from the photopeaks and the annihilation peak. Three lines are necessary because of the small non-linearity of the system. The lines should span most (if not all) of the domain that will be used in the measurement.

Useful ROOT scripts

Unfortunately, the SpecTech's data acquisition program cannot make pictures that can easily be incorporated into other editting programs. For this reason I recommend that the spectra be saved as "tab-separated text files", and then another plotting package can be used to parse those files and make histograms. (This will come handy for Spectroscopy Part II when there will be a lot of multi-gaussian fitting.) So I provide a sample ROOT macro to read a tab-separated text file written by SpecTech. The macro can be found here.

Petar Maksimovic

Last modified: Tue Jan 29 01:09:04 CST 2002