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Transcript of Gamma-Ray Spectroscopy - Trinity College sheridev/labs/ ¢  Gamma-Ray Spectroscopy Evan...

  • Gamma-Ray Spectroscopy

    Evan Sheridan with Niall Robertson 11367741

    November 25th 2013

    Abstract

    γ-ray spectroscopy is investigated using a Cs137 , Co60 and Na22 coupled with a scintillator, photocathode, photmultiplier and the Maestro software. Using Cs137 , the dependence of H0 , the γ-ray energy, on V is theoretically deduced as H0 ∝ V n. This dependence is verified theroet- ically with n, the dynode number, being found as 7.78477±0.02261. The dependence of FWHM on V is also investigated and verified. The averagre resolution of the the detector with a varying PM using Cs137 voltage is found to be R̄ = 0.070525±0.004765908. The energy spetra of Cs137 , Co60 and Na22 are obtained and analysed, illustrating the various ways γ-rays intereact with matter. Using the Na22 and Co60 spectra the efficiency of the detector is found to be 18% at 511 keV and 4% (using Na22 )in the interval 1.17 MeV and 1.32 MeV. Finally the abundance ratio, half life and branch ratio is are found for K40 and compared against the theoretical values given .

    1

  • Introduction and Theory

    In this experiment we primarily deal with how γ-rays interact with matter and how their inter- action can reveal the properties of radioactive elements. When radioactive atoms decay by beta emission γ-rays are emitted. In this experiment we deal with Cs137 , Co60 and Na22 , where in their energy spectrum well defined peaks can be found at the corresponding γ-ray energy. The γ-ray spectrometer enables us to record these energy spectra appropraitely and consists of 3 main parts: the scintillator, photomultiplier and multichannel analyser. The γ-ray undergoes a number of transitions. After beta emission it can undergo Compton Scatter- ing on the Lead Shield and in the scintillator giving the γ-ray photon a defined energy. Interactions in the scintillator(the production of electron hole pairs and the subsequent recombination of these) induce Photoelectric Absorption and subsequently lead to photons incident on a photocathode. These photons may then excite electrons which are accelerated towards the photmultiplier where at each dynode the number of electrons will be multiplied by the time they reach the anode. These additional electrons then produce extra charge on the anode that give rise to a voltage pulse that can be interpreted by the multichannel analyser. The spectra can then be produced using the Maestro software and the decay series of the radioac- tive elements can be interpedted. Instead of well defined peaks as should be expected there are broad peaks which are a result of statistical fluctuations at each stage of the process before the voltage pulse is induced.

    Interaction of γ-rays with matter

    Primariliy γ-rays can interact with matter, much the same way as light does, and we consider 2 ways in whcih it does so in this experiment :

    •Photoelectric Absorption

    •Compton Scattering

    Photoelectric Absorption

    We consider the γ-rays incident on the scintillator. The γ-ray photon ejects an electron from one of the shells of the thallium atoms in the scintillator with energy :

    Ee = Eγ − Eb Now the emission of this electron leaves a vacacny in the thallium atom that can be filled by a free electron. This free electron in turn emits a photon of energy Eb and this photon undergoes photelectric absorption in another thallium atom exciting another electron with energy Eb . The combined energy of these two electrons is Eγ , giving rise to the “total energy peak” in the energy spectrum.

    Compton Scattering

    Now when we talk about Compton Scattering we are talking about the γ-ray photons being scat- tered on the lead shield by electrons there. So, the source emits γ-rays and then it collides with electrons on the shield. Only γ-rays along a straight line to the scintillator will reach the scintil- lator so we only consider γ-ray photons that have been scattered through 00 or 1800. Intuitevly the γ-rays that are scattered through 1800 will have less energy because it actually scatters and imparts some of it’s energy to an electron in the shield.

    1

  • The γ-ray photons that are scattered through 1800 give rise to a phenomena called the “Backscat- tering peak” in in the energy spectrum (which is given by a lesser enegy because the excited electrons due to these γ-ray photons in the scintillator will have a less energy) while the other γ-ray photons give rise to the “Compton edge”, whereby electrons in the scintillator will acquire maximum energy from the incident unscattered γ-ray such that there will be a sudden dip just before the “total energy peak” due to photoelectric absorption in the scintillator.

    We have the following argument :

    λ ′ − λ = h

    c2me (1− cos(θ))

    using the conservation of momentum and energy for an incident photon on a rest electron. Having λ = 1hf we get the following for the energy of the scattere photon:

    hf̃ = hf

    1 + hf(1− (

    cos θ m0c2

    ) )

    and thus gives rise to the inequality :( hf

    1 + 2hf m0c2

    ) ≤ Eγ ≤ hf

    where the minimum value corresponds to the “Backscattering peak” and the maximum the “Comp- ton edge”.

    Operation of the Photomultiplier

    The Photomultipler setup is given by :

    Incident photons on the photcathode will excite electrons from it and then are accelerated through a potential difference towards the first dynode in the electron multiplier.

    Now these electrons in turn excite more electrons from the dynode. Each incident electron on the dynode will excite a mean m number of electrons. Thus for n dynodes there will be an excitation

    2

  • of mn electrons.

    Therefore the total charge Q at the anode is given by Q = (e−m)n and the voltage pulse induced is V = QC with C the anode capacitance, but this is H0 , the γ-ray energy and thus :

    H0 = (e−m)n

    C

    ⇒ H0 ∝ V n

    showing the proportionalality relation we will use.

    R dependence on H0 at constant PM Voltage

    Since :

    R = H2 −H1 H0

    at constant PM voltage we expect that since H0 ∝ V n then FWHM ∝ V n also as the resolution will remain constant at a constant PM voltage, we expect.

    Nuclear Physics Terms

    We have :

    −dN dt

    = λN

    the negative sign indicates that N decreases as t increases with dNdt being the number of particles decaying per unit time.

    λ is the decay constant of a radioactive substance, with λ = 1.76x10−17s−1 for K40 which will be used in the experiment.

    The Half Life of a radioative substance is the time it will take for exactly half of the number of particles in the substance to decay, it is denoted by τ 1

    2 and τ 1

    2 = 1.26x109 years for K40.

    The Abundance Ratio is the amount of a radioactive substance that is present in an element, for instance, the abundance ratio of K40 in potassium is 0.011%.

    The Branching Ratio of a radioactive substance is the percentage of a particular type of decay if a radioactive substance has more than one channel of decay. For K40 the branching ratio for the emission of a γ-ray is 11%.

    3

  • The Experiment

    Preliminaries

    The Maestro software must be initialised so that the data from the spectrometer can be interper- ated. The software was started up on the computer.

    Firstly, we got the laboratory technician to administer the installation of the Cs137 source that will be used for the first part of the experiment.

    We modified the settings in the Maestro software so that the photomultiplier(PM) voltage is set to 600V . The calibration of the energy scale was necessary for the correct results so at channel zero the energy is calibrated to 0 keV and at the peak position set the channel to 662 keV.

    Part 1

    •To record and analyse the effect on a spectrum of changing the photomultiplier voltage

    Using the Maestro software we found the total energy peak for Cs137 . As well as this we found both the position H0 and its full width at half height (FWHM ).

    We found the limit of detection at low voltage by varying the PM voltage until the the Maestro software no longer detects the γ-ray peaks.

    Now the the varitaion in H0 , FWHM and R as a function of PM voltage can be measured. We used this data to verify that H0 ∝ V n and furthermore deduce how FWHM and R will depend on V.

    Part 2

    With the help of the lab technician to install the radioactive sources,we recorded the spectra for Cs137 , Co60 and Na22 .

    The calibration of each element was considered, the first peak for Cs137 being at 1.17 meV and the strongest peak in Na22 being at 511 keV.

    By using the decay chains for the respective elements we predicted what values one should find for the energy of the γ-rays peaks.

    For all the single peaks record R and we deduced how R should vary with the peak energy at a fixed PM voltage.

    Part 3

    By using the spectra obtaned in Part 2 and the equations for the detector efficiency the detection efficiency of the γ-ray spectrometer was found using first Na22 and then Co60 .

    Using 3.625 g of KCl and its energy energy spectrum the abundance ratio, half life and branching ratio of K40 was found.

    4

  • Results and Analysis

    Part 1

    The following table illustrates the effect of varying the PM voltage for a Cs137 sample :

    V (Volts) H0 (keV) H1 (keV) H2 (keV) FWHM (keV) R

    500± 1 157.36± 2.7 159.54± 2.7 163.1± 2.7 3.567± 3.81 0.02264± 0.02418 550± 1 333.71± 2.7 320.38± 2.