Final Lab Report 3 (MH and LG) Cosmic Ray Decay


Cosmic particles are found everywhere in the Universe from various high and low energy interactions. Muon and Gamma decay are two of the most frequent decays studied because muons are one of the most common particles and gamma rays are found everywhere in the Universe from many different type of radioactive decays. We used scintillators in order to produce the two different decays. For the gamma decay, the goal was to find an unknown radioactive sample and to find the different ages of two Cesium-137 samples by using Cesium-137 and Cobolt 60 to calibrate the energies. After analysis, we found that the unknown sample given to us was Sodium-22. We also found that one of the Cesium-137 samples was 17.583 years old and the other was 37.80 years old. The goal for the muon decay was to analyze long term data to see if we could calculate the time dilation effect commonly calculated using muons.

EDITOR’S NOTE: The goal for the muon decay experiment was to be able to report a lifetime (halflife) for the free decay of muons. (Looking for evidence of time dilation would be a bonus) That said, the abstract is about your results. What did you measure for the muon lifetime? And what was the accuracy of the \({}^{137}Cs\) measurements?


Muon Decay

The muon is an elementary particle with similar properties to an electron. Muons are formed high in the Earth’s atmosphere by energetic cosmic rays. The high energy rays produce an assortment of particles, some of which are negatively charged pions which eventually decay into muons (which are also negatively charged). These muons continue to travel down through Earth’s atmosphere, but are unstable themselves and thus decay. Muon decay will always produce three particles, which include an electron and two different types of neutrinos. The decay will vary slightly depending on whether it is a muon(\(\mu^{-}\)) that decays or its antiparticle, the antimuon (\(\mu^{+}\)) . More precisely, muons will decay into to an electron, an electron anti-neutrino, and a muon-neutrino, while an antimuon will decay into a positron, an electron anti-neutrino, and a muon-antineutrino. (Melissinos 2003) Formulaically,

\begin{equation} \mu^{-}=e^{-}+\overline{v_{e}}+v_{\mu}\\ \end{equation} \begin{equation} \mu^{+}=e^{+}+v_{e}+\overline{v_{\mu}}\\ \end{equation}

The lifetime of muons and antimuons should be the same, if they are in a vacuum. In matter, muons can interact with protons via the electroweak force, and thus will have shorter lifespans than antimuons. The primary purpose of our experiment was to study muon decay. Muons that travel towards the Earth’s surface can be detected by a scintillation detector. The means by which the scintillator detects the muons will be expanded upon in our Experimental section. From the data collected by the scintillator we could determine an average muon lifetime. Due to the presence of both antimuons and muons, it is essential to remember when calculating the average muon lifetime that the lifetime observed is actually a weighted average of the two different types of muons. From further analysis of the data we can extract values for charge ratio, and the Fermi Coupling Constant.

Gamma Ray Spectroscopy

The radioactive decay of a nucleus for elements Cs-137 and Co-60 was studied by detecting gamma rays which were emitted in response to the decay. Gamma rays are detected through the use of a NaI:TI scintillator crystal. The crystal produces a fast moving free electron which will lose its energy through the excitation of ions in its path as it travels through the crystal. The excitation results in the emission of visible light, which is directed to the photosensitive surface of a photomultiplier tube. The photons then eject electrons via the photoelectric effect. These electrons are collected within the photomultiplier and then amplified in order to yield a current pulse. This current pulse is converted to a voltage pulse, the height of which is directly proportional to the number of photoelectrons. Since the number of photoelectrons is proportional to the number of photons reaching the photomultiplier, and the number of photons is proportional to the initial energy of the freed electron, the height of the voltage pulse is therefore proportional to the initial energy of the freed electron. (citation not found: Melissinos2003)

Thus when a source, such as Cs-137, is placed near the scintillator the photomultiplier will produce a series of voltage pulses, each of which correspond to the decay of a nucleus. These voltage pulses are analyzed using a multi-channel analyzer. The multi-channel analyzer sorts the pulses according the their height, and then counts them to give a spectral energy distribution of the freed electron. The spectral distribution for Cs-137 is shown in Figure  \ref{fig:Cs-137}.