Using the concepts of nuclear transformation, decay, and radiation detection, an equation which describes the count rate expected from a neutron activated element in a sample can be derived.

The counts recorded during a count time t_c, following an irradiation time t_i, and wait time t_w, is:

where:

• h = the overall efficiency of the detector set-up, including effects of geometry, detector response, and self-shielding.
• m = mass of the irradiated element, g
• % = abundance of the isotope of interest
• N_A = Avagadro's number, atoms/g atom
• sigma_a = 2200 m/s microscopic absorption cross-section of the irradiated species, cm²
• A = Atomic mass of the irradiated element, AMU
• phi = thermal neutron flux, neutrons/cm²/s
• f = branching ratio for the gamma-ray of interest
• lambda = decay constant of the radioisotope produced, sec
• 1.128 = correction for a Maxwellian distribution of neutrons

The expression clearly indicates the activity of the irradiated material generated by the thermal neutron flux at the location of the irradiation, corrected for decay before and during counting.

Generally, there are two principle objectives to the process of NAA. The first is the qualitative analysis to determine which elements are present in the sample. The second is the quantitative analysis to determine the quantity of each element. The first objective can be readily accomplished if the detection system is energy-calibrated. The second objective can be accomplished by using the relative method or the absolute method. In the relative method, the unknown element has been identified and the activity that is measured is compared to the activity measured from a known quantity of the same radioisotope.

In the absolute method, the efficiency of the detection system at several energies is determined and a efficiency versus energy curve is plotted. The efficiency of the detector is then used to determine the absolute activity of the sample. In this lab exercise, you will determine the elemental composition of an unknown sample and estimate the number of grams of each element using the absolute method.

An "unknown" sample will be activated in the reactor at a power level sufficient to produce adequate gamma emissions for analysis. Note the time lapse from when the sample is removed to when the sample is counted.

1. Calibrate the PC-based multichannel analyzer by using the Co-60 and Cs-137 "button" sources.
2. Allow the spectra to collect long enough to obtain well defined peaks from the
3. primary photons emitted by the sources.
4. Be sure to save your spectra to the hard-drive.
5. Determine the sum counts under the three principle photo-peaks.
6. Record the source activity and date data to calculate the efficiency of the detection system at each of the three gamma energies.
7. Collect the spectra for the unknown sample.
8. Be sure to maintain the same detector-source geometry you had for counting the sources.
9. Allow sufficient time to obtain well defined photo-peaks.
10. Save your spectra to the hard-drive.
11. Wait 15 or twenty minutes and count the unknown sample again for a time equal to the first measurement.

From your calibration data and decay measurement, identify the unknown elements in the sample. Use the decay measurement to estimate the half life of the radionuclides. The half-lives will help confirm your identifications.

Present your efficiency curve for the detector. Using your efficiency data, calculate the activity of the identified radioisotopes and calculate the number of grams of each element.