Investigating the Absorption of Radiation in Matter using G-M Counter

Abstract

 In this experiment we will learn about the pulse height analysis technique using NaI(Tl) scintillation detectors for nuclear spectroscopy and to study the decay scheme of some nuclei. We find the energy from the plots and our results are in a good agreement with the theoretical values.

Introduction

The discoverers of radioactivity were Wilhelm Röntgen, Henri Becquerel, and Marie Curie in the late 1890s. Marie Curie and her husband Pierre discovered polonium and radium in 1898. many nuclei are unstable and can decay spontaneously to some other combination of A nucleons that has a lower mass. These decays take different forms. The simplest is that of a gamma ray, which represents the nucleus changing from an excited state to a lower energy state (no change in N or Z). Other modes of decay include emission of a particles, b particles, protons, neutrons, and fission.

Most α and β decays, and in fact most nuclear reactions as well, leave the final nucleus in an excited state. These excited states decay rapidly to the ground state through the emission of one or more γ-rays, which are photons of electromagnetic radiation like X-rays or visible light. Gamma rays have energies typically in the range of 0.1 to 10 MeV, characteristic of the energy difference between nuclear states, and thus corresponding wavelengths between lo⁴ and 100 fm. These wavelengths are far shorter than those of the other types of electromagnetic radiations that we normally encounter; visible light, for example, has wavelengths lo⁶ times longer than γ-rays.

What is the structure of the nucleus? Just as the atom is composed of electrons, and the electrons rotate in orbits of a specific energy, the nucleus also consists of nucleons, and these nucleons are distributed in orbits of a specific energy. As we mentioned, in order the nucleus to be stable, it must be present at the lowest energy level called the ground state. The nucleus always seeks to reach stability through different nuclear processes, including the release of rays. If the atom is at a higher energy level it is excited.

We can get the gamma radiation from β- unstable nuclei, or nuclear reactions. In this experiment we will use unstable nuclei, such as ⁶⁰Co, ¹³⁷Cs etc. A typical nuclear energy level diagram is shown in Fig (1).

To plot such a level scheme, we first need to have the nucleus in an excited state. When it decays to one of its lower states it will emit electromagnetic radiation in the form of γ-ray. Normally, nuclei exist in their ground states (lower possible energy states), and the average time during which they stay in their excited states is very short.

The method we will follow in this experiment to get the gamma ray radiation is to populate excited nuclear states through the decay of β-unstable parent nuclei. An example of this is the decay of (¹³⁷CS). Its decay scheme is shown In Fig. 2.

^{Figure 2: Decay scheme of 137Cs.}

Nuclear level schemes are normally obtained by detecting the number of γ-rays at each particular energy, and then plotting this number N versus the γ-ray energy Eγ. This so-called pulse height spectrum is normally obtained using a γ-ray spectrometer. The most common types of such spectrometers are the semiconductor and the scintillation spectrometers. In this experiment we will use the latter type and in particular the NaI scintillation detector.

1- Scintillator Spectrometer

One of the most important analytical techniques in any branch of physics is the determination of the energy or wavelength of photons or particles. Thus, we will use a spectrometer to analyze the wavelength of visible photons and we could measure the frequency of radio-wave photons as they resonate with precessing protons or other nuclei in a magnetic field (NMR). As the energy of photons increases to the keV and MeV range, it is possible to directly measure the energy of the photons, rather than the wavelength or frequency.

The scintillator detector absorbs the gamma ray photon generating either a photoelectron, a Compton scattered electron, or creating a pair of electrons simultaneously. In each case these high energy primary electrons create a cascade of secondary electrons in the conduction band which then eventually slow down and undergo recombination with holes in the valence band. In a good scintillator crystal, a 1 MeV photon photopeak will produce a “scintillation” of about 10⁴ visible photons. In the case of sodium iodide (NaI, an alkali halide crystal), a small amount of thallium (Tl) is added to enhance the radiative probability during the recombination process.

These thallium trapping and radiative centers lie somewhat below the conduction band so that the radiated photons are emitted with less energy than the band gap of the pure crystal. The band gap of NaI is ~3.9 eV (~320 nm) and the Tl- related emission is peaked in a band near 3.0 eV (410 nm; blue light). In the NaI:Tl scintillator, γ absorption yields light output (and energy resolution) at the rate of 38 photons/keV; the typical response time for NaI:Tl is 250 ns. Conversion to an electrical pulse is done with a photomultiplier tube (PMT). In gamma rays, the electronics are set up to further amplify the PMT pulse in a linear fashion and then do pulse-height analysis. That is, the electronics generate a histogram of pulse heights over a large number of detected gamma ray events.

It is important to recognize that some gamma rays may pass completely through the NaI crystal and others may undergo Compton scattering in which the recoil electron deposits all of its energy into a cascade of other electrons but the Compton-scattered photon may exit the crystal without depositing any further energy. Thus, in addition to the photopeak (which will exhibit the full gamma-ray energy), there will be a broad Compton background with an edge at a maximum energy called the Compton edge. This edge comes from photons which Compton scatter backwards (180^o ) and hence give up a maximum amount of energy to the Compton electron which can then generate a cascade of other electrons. In those cases where the recoil electron receives maximum energy from the gamma photon, the backscattered gamma ray photon will have a corresponding minimum energy given by the energy of the incident gamma photon minus the maximum energy of the Compton electron (at the Compton edge). When the (minimum energy) backscattered gamma photon is also detected, it will contribute to a “backscattered photon” peak. The geometry of the NaI:Tl and PMT are shown in Fig.3.

3- The Photomultiplier Tube

This is the device that converts the light scintillations into an avalanche of charges, as an intermediate step to converting them to voltage pulse. It basically consists of a semitransparent cathode and a number of electrodes at positive potentials relative to the cathode and to each other. These electrodes are called dynodes. The surfaces of the dynodes are covered with a layer of material with a high secondary emission coefficient. In other words, if one electron is incident on these layers, then multiple secondary electrons are emitted. Now, when the light scintillations are incident on the cathode, primary electrons are emitted which, when falling on the dynodes of the photomultiplier, get multiplied. This is shown in Fig.6

Apparatus

The setup used In this experiment consists of the following:

1. Radioactive sources

These are usually β unstable materials that provide us with nuclei in their excited states. These nuclei will decay to their ground states with very short lifetimes compared to their parent β unstable nuclei.

For example, in Fig. 3, while the β unstable ¹³⁷Cs nucleus has a lifetime of 0.947*10^⁹ s, its daughter, the ¹³⁷Ba, decays from its excited state to the ground state with a lifetime of 2.55 min. Sources that will be used are ⁶⁰Co, ¹³⁷Cs and ²²Na. The decay schemes of these sources are shown in Fig. 7.

2. The nuclear spectrometer

It consists of the scintillation detector with its photomultiplier tube, preamplifier, amplifier, Single Channel Analyzer (SCA), a power supply and a counter. In the apparatus, we will use in this experiment, the preamplifier is hooked to the photomultiplier and the amplifier and the single channel analyzer are in one electronic module. The SCA could be used in the discriminator or window modes. You will use the window mode of operation.

Methodology

Procedure

1. Arrange the apparatus as shown in Fig. 8 below. Then turn the power on.

2. Set the high voltage on the photomultiplier tube to the proper value given to you by the instructor. This value is different for different photomultipliers.

3. Place the ¹³⁷Cs source at an appropriate distance from the detector, at about 2 cm in front of it. This is normally determined by the activity of the source.

4. Set the single channel analyzer to the window mode and fix the window width at a proper value (Consult the SCA manual for that).

5. Start counting for an appropriate period, about 10 seconds, with the lower knob of the SCA at a certain value which determines the channel number.

6. Change the channel number, by changing the setting of the lower level knob of the SCA and count for the same period of time. Then do the same thing for a wide range of channels. In the current setup used in the lab, steps 4 and 5 are done automatically.

7. Repeat steps 3 to 6 for the other available sources (⁶⁰Co and ²²Na)

8. Get an unknown source and repeat steps 3 to 6.

Data Analysis

Source	No. of channels	E theoretical (MeV)	E experimental (MeV)
Co	484	1.173	1.892
	542	1.333	1.34
Na	226	0.511	0.5184
	529	1.275	1.3062
Cs	308	0.662	0.7316

We calculate the experimental value of the energy from the equation of the line in the plot above (y = 0.0026x - 0.0692).

 

To estimate the true value of our slope and y-intercept we use the least square method:

Where a is the intercept and b is the slope, we can find the error in a (δa) and error in b (δa) using the following equations:

 Where s is the standard deviation  

X =No. of channels	y= E theoretical (MeV)	x*y	x2	(y-a-bx) 2
484	1.173	567.732	234256	0.023901
542	1.333	722.486	293764	0.021141
226	0.511	115.486	51076	0.021258
529	1.275	674.475	279841	0.028764
308	0.662	203.896	94864	0.043264

According to the equations above:

a = -0.0692

b = 0.0026451

s = 0.009251

δa = 0.0142

δb = 3.25*10^-5

a= -0.0692∓ 0.0142

b= -0.0026 ∓ 3.25*10^-5

Corrected Y=0.0026451 x-0.114303

no. of channels	E experimental (MeV)	Corrected value of energy
484	1.892	1.16593
542	1.34	1.31934
226	0.5184	0.483489
529	1.3062	1.284955
308	0.7316	0.700388

Conclusion

1- The basic principle of a scintillation detector is to convert high-energy particles into many lower-energy particles, and therefore the detection of the number of these lower-energy particles is equivalently a detection of the energy of the original particles.

2- We can infer the quantization nature of the nucleus through the specific energy of gamma rays that are emitted from the excited nuclei to reach stability.

3- For the high energy we cannot use the spectrometer to detect photons, in this case we will depend on the interaction of the photon with matter.

4- Gamma rays interact with matter by three processes: 1.Photoelectric effect 2.Compton effect 3.Pair production.

5-   A scintillation spectrometer consists of three main parts: a scintillator, a photomultiplier tube, and the electronic system to process and count the resulting signal.

References