A Study on Coincidence Method for the Activity Measurement essay

Radiation exposure

Radiation refers to the type of energy that moves in the waveform or particles under high speed. Radiation naturally takes place in the sunlight. Radiation exposure is the subjection to the hazards of ionizing radiation through contamination or irradiation. Radiation exposure also refers to the sum of the charged particles’ initial kinetic energies released by ionizing radiation that is in the uncharged state.

Types of radiation exposure

External radiation

External radiation takes place when an external source with reference to the body produces radiation rays that penetrate and cause ionizing radiation to the body. The exposure may come from x-rays, gamma rays such as cesium, alpha particles, beta particles or neutrons. They are dependent on energy and type of the radiation.

Normally, most of the beta particles do not infiltrate beyond the skin; however, when the intensity of the particles is high they can cause eye damage or skin cancer. Beta particles that are so energetic, for instance those emitted by 32P, have the ability to penetrate into the skin by several millimeters. In such a case, shielding is required to reduce or minimize the external radiation exposure. A sheet of Plexiglas with a maximum of a half inch thick is effective for the beta particles. It is important to note that the shield does not stop all the particles but it stops most of them.  

Gamma and X-rays together with the radiation from the neutron have greater ability to penetrate. When carrying out the evaluation of external radiation exposure they are given primary importance and must be shielded. The beginning of the initially recognizable effects of acute exposure to the radiation is always the reduction of red blood cell count and may happen at 100 rads dose of acute body radiation exposure to the whole body.  The LD50 is approximately five hundred rads in case of failure of medical intervention

Internal radiation exposure

Internal deposition of radioactive materials into the body takes place when there is an uptake through ingestion, inhalation and skin contact. These exposures normally take place when the radioactive elements are airborne, inhaled, absorbed by the lungs, airborne and deposited in the body, are present in food or drinks contaminated with radioactive materials and are ingested or spilled and aerosolize onto the human skin and absorbed, enter through scratches or cuts.  Internal radiation deposition may also come as a result of contaminated hands that one may rub eyes or eat with.

Internal exposure occurs when there is the emission of radiation from radioactive materials within the body.  Even though the cause of external radiation is gamma rays, x-rays, high energy neutrons and betas, all radiation forms including low energy gammas, betas and betas have the ability to cause internal radiation exposure.

Substances taken into the body accumulate in the specific body organs or parts known as target organs. For instance, iodine tends to accumulate in the thyroid gland. The body cannot differentiate between radioactive or stable iodine when ingested or inhaled. Deposition of a significant portion of iodine is done within 24 hours.

Other elements are known to be deposited onto the bones, muscles and soft tissues after ingestion or inhalation include plutonium-239, radium, calcium and strontium, cesium-137. The body has the ability to eliminate such materials at a low speed once incorporated into the structure of the bone; therefore, high doses may take a long time to occur. The bone marrow, a blood-forming organ is very radiosensitive since their cells are in mitotic S-phase activity regularly than any other cells. Thus, a significant radioisotope long term exposure causes such chronic diseases as osteosarcoma and/or leukemia.

The radiation sickness symptoms include hair loss since the skin sheds 2% of the outermost portion per day. It is replaced by the dividing immature radiosensitive cells. Other symptoms include weakness, skin burns nausea and reduction the functionality of organs. Most of the mature cells show the ability to be radioresistant; all immature cells are radiosensitive. 

Reasons to measure radioactivity

Incidences such as the Chernobyl disaster, Kyshtym disaster, Windscale fire and the Fukushima Daiichi reactors disaster on 11 March 2011 left people around the world worried about their radiation exposure. Therefore, it is of paramount importance to know the isotopes’ activities in food and the users of radioisotopes materials to know the target organs for the radionuclides they use or work with so that to ensure protection against radiation hazards and avoid unnecessary exposure. To achieve this objective, activity measurement is required.

Theoretical background

A substance’s radioactivity is measured in the number of decaying nuclei per unit time. The SI unit is Becquerel written (Bq). Bq is equivalent to one disintegration per second (DPS). A unit weight of a substance’s radioactivity is measured by specific activity given in Becquerel per gram. This measurement enables one to compare and determine whether one substance is more radioactive than another. Radionuclide specific activity is inversely proportional to its half-life and atomic weight.

There are two major ways of determining the activity of a substance. These include counting method that gives the total concentration in Becquerel per gram and spectrum method that finds 131I, 137Cs mixed isotopes. The counting method is known to be cheap and economical compared to the spectrum method. It is done in two different ways; through the method of the single detector based on the calculation of efficiency detection and the method of coincidence. 

The Single Detector Method 

The radiation energy, the geometry and properties of the detector (ρ, Zeff), its total count N for a time T must be known. The efficiency of detection can be calculated as follows:

Detection efficiency is ε = εgeo x εint  (Eqn. 1)

Wherewhich defines the probability of transmission through a material and     

The activity is given by. 

The full-energy Peak Efficiency εin (Eqn.1) depends on the energy and the geometrical conditions.  defines the measurement conditions and geometrical efficiency while  defines the intrinsic efficiency and the detector characteristics.

Here, is the angle between the detector and the source. For the point source  . The ratio of the proton number emitted towards the detector by those emitted by the source is given by . is only dependent on the source detector.

 is the ratio of full energy peak counted by the impinging photon numbers. This ratio is dependent on the incident photons energy: their absorption, transmission and full energy deposition. The calculation uses material density and attenuation coefficients data.

This method of activity measurement has difficulties for an accurate calculation.  For accuracy, one must have the exact knowledge of the parameters of the detector, geometry that include position, thickness and materials.

Coincidence Method

This technique is applied in the determination of the absolute activity of sources that emit (γ−γ or γ−β. Such sources include Cobalt 60 (Co60).  This radioactive source emits one beta and two gamma rays per disintegration. A coincidence is said to have occurred when a particle from an event of disintegration is registered at detector one and another particle from the same event is detected at another detector. The activity of a sample can be determined using the coincidence events rate.

Therefore, (N1, N2, NC) must be determined from the counters 1, 2 and the coincidence counter that will be used in the determination of A, without calculating the efficiency.

Since cobalt 60 emits two gamma rays, there will be 2 * A = 2A. Therefore, the absolute activity will be given by

Objectives of the study

  • To apply the method of coincidence to determine the absolute activity of (γ−γ) radioactive source.
  • To investigate the effect of LLD (Lowest Limit of detection) and the distance effect in the method of coincidence.

The setup of the experiment

To achieve the set objectives, the experiment was conducted using the system of NaI(Tl) scintillation detector. This detector has the following characteristics; it has a gain of PMT, high energy resolution, efficient in detection, geometric effects and linearity, and energy calibration.

The experiment involved setting up two scintillation detector systems of NaI(Tl) with high power sources (1100v),SCAs, amplifiers, preamplifiers to both of the detectors. A counter (N1) was connected to the first system of the detector and the second counter (N2) to the second detector.  A coincidence unit was then connected to the two SCAs outputs and to the counter (NC).

The source was placed between the detectors with the appropriate distances. Using proper setup of Low Level of Discriminator of both SCAs for the time, the counts were measured. The LLD levels of SCAS were then set on the spectrum that was measured in advance using MCA.

The counters were set to count for a period of five minutes and locate the sample source. The counting started at N1, N2, NC five times. 

Compton scattering: inelastic photon scattering deflected by electrons.

Results and discussion

Case 1: Low Level Discriminator variation experiment

Two detectors were placed at the nearest point from the Cobalt 60 (Co60) source as shown by the diagram below. N1, N2, Nc  were counted for the different Low Level Discriminator selected from the energy spectrum graph. 

Cobalt 60 source has a nominal activity of A0 = 19.633 kBq as calculated by the manufactures.

The table below shows the experimental data for the three levels; level 1 (0.52v), level 2 (1.5v) and level 3 (1.7v) 

Counter                               level                 1 (0.52v)  2 (1.5v)  3 (1.7v)
N1 1,167,225 637,849 525,304
N2 985,966 522,201 466,899
NC 98,519 28,972 21,568
Measured A (Bq) 19,469 19,161 18,952

The value of A was calculated using the activity equation given by


The Cobalt 60 source emits two gamma rays in a single decay. The direction taken by the rays is random, there is no specific direction. It implies that the two detectors have different probabilities of receiving the ray signals. Thus, it explains the difference in the count N1 and N2.

As the Low-level discriminator levels increase, the activity denoted by A decreases due to the fact that the probability of Crompton scattering detection reduces. There are at least 3 photoelectric effects that are measured; therefore, more error is introduced in the measured activities.  From the table, the study shows that level one is the best. However; there should be avoidance of noise count at low channels of energy. 

Case 2: Variation of Distance

Here, one level of LLD was chosen and counts made at different distances: 5, 10, 15 and 20 centimeters. 

The differences were observed and their different effects to the counts were measured to calculate the activity.

From the energy spectrum, observation of the level 1(0.52v) shows that it contains the scattering.

Counter                               Distance               

 5 cm

 10 cm

 15 cm

 20 cm
















Measured A (Bq)





σA (Bq)





Ratio (%)





As the distance from the source increases, the study shows that the count values decrease, however, the value of activity increases.

The table above reveals that increasing the distance between the source and the detectors reduces the counts. The percentage error also increases in the process as a result of the fewer counts. The study shows that as the distance from the radioactive source increases, the activity (A) also rises steadily but the values of counts decrease.

Error Case 1

The error propagation

and by using the equation;

one can come up with the following information

                              Level                 1 (0.52v)  2 (1.5v)  3 (1.7v)
Measured A(Bq) 19,469 19,161 18,952
σA (Bq) 67.5 118.1 134.6
Ratio (%) 67.5 118.1 134.6

Error analysis

The errors that emanate from the experiment can be analyzed in the following ways; the cables length and the time it takes the rays to arrive at the counter affect the signal. Since the system is not isolated, making it smaller would enable it to have higher chances of receiving the gamma rays more from outside; otherwise, an error is bound to arise. When the detectors are closely spaced, they are more accurate than when placed far away from each other. Putting them close increases detector efficiency.

The errors also occur due to counting statistics, systematic errors where the values are different from the correct ones, and random errors due to random fluctuations in the measurement process or in the radiation detection.


In this paper, it has been shown that coincidence method is an efficient way of estimating and determining the activities of unknown radioactivity sources such as Cobalt 60 (60Co) or Cesium-137 (137Cs).  These are the most significant radioisotopes.

It is important to set the Low-Level Discriminator at the lowest point so that all the Compton scattering events may be included without system noise. The distance separating the detector and the sample determines accuracy of the activity which directly affects the error rate. To minimize the errors, the distance should be minimal.

Further study

Measuring the absolute activities of sources such as Cesium-137 employs two detectors. The gamma rays are measured using the scintillation detector while the beta rays may use Si surface barrier detector. If the distance between the sample and the radioactive source is fixed well, the method of coincidence can provide an efficient detection of the signals in a specific energy level for the. Calculation of the activities of other activities would be possible when there is efficiency in the detection of various gamma energies.

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