The process of beta decay is an extremely fascinating phenomenon. I cannot think of any other physical process that is so rich in fundamental physics. Please allow me to elaborate.

¹³⁷Cs Decay Modes

Let’s start by examining a very-well known cesium-137 decay diagram – Fig. 1.

Fig. 1. Cs-137 beta decay modes.

The diagram reads as follows: the element #55 – cesium (which is a spin 7/2 fermion with positive parity and the atomic weight of 137 amu) is not stable and decays with a half-life of 30.17 years by emitting a beta-particle (β is just another name for a high-energy electron). In 94.6% of the cases the β-particle carries away an energy of 0.512 MeV = 512 keV and the ¹³⁷Cs transmutes into a meta-stable state state of the element #56 – barium (which is a spin 11/2 fermion with negative parity and the atomic weight of 137 amu). Please forgive me for having to leave the discussion of spin, parity, Bose and Fermi statistics, weak interaction and the law of conservation of energy and momentum until the next post – there is just too much physics for one article!

The excited state of barium-137 is labeled by the letter “m” in the ^137mBa notation; the letter “m” stands for meta-stable, which is just a fancy word for “unstable” but nevertheless able to persist an extended period of time that appears meaningfully long for us, humans (it is interesting to note that the perception of time, which is a subjectively human experience finds its way into supposedly objective field of physics!)

The excited state ^137mBa (which is characterized by the excitation energy of 0.6617 MeV = 661.7 keV) decays with the half-life of 2.55 minutes into the ground state of barium-137, which is stable. This de-excitation is accompanied by the emission of a gamma ray with the characteristic energy of 661.7 keV that we commonly use for gamma detector calibration. A total of 85.1% of all ¹³⁷Cs nuclei decay in this way (i.e. 85.1% of all ¹³⁷Cs nuclear decays result in 661.7 keV gamma rays).

In 5.4% if the cases ¹³⁷Cs decays directly into the ground state of ¹³⁷Ba by emitting a 1.174 MeV β-particle with no associated gamma. There is no gamma emission because the β-particle carries the entire excess energy released in the process of decay of ¹³⁷Cs.

Before I dive deeper into the underlying physics, I want to briefly point out that the main 661.7 keV line that we associate with ¹³⁷Cs actually originates from barium!

¹³⁷Cs Beta Spectrum

I want to draw your attention beta spectrum of ¹³⁷Cs first – Fig. 2.

The beta spectrum has two distinct features:

• a broad peak corresponding to the main decay mode of ¹³⁷Cs → ^137mBa with peak energy of 512 keV, which matches a trough on the spectrum centered around channel 3000, and
• a narrow peak centered around channel 3,500, which corresponds to 661.7 keV energy of the internally converted electrons ejected from barium-137 during the ^137mBa → ¹³⁷Ba de-excitation process.

In the latter case, rather than being emitted a barium de-excitation gamma ray transfers its entire 661.7 keV energy to a K-shell electron that instantly escapes the atom leaving a vacancy, which is promptly filled by an electron from the top shell. This vacancy-filling process emits a characteristic 32 keV x-ray known as the barium Ka line.

So here is a second fun fact about the ¹³⁷Cs gamma spectrum: the 32 keV peak is actually a barium x-ray fluorescence (XRF) line! One may find it confusing that both the 661.7 keV and 32 keV lines that we commonly associate with ¹³⁷Cs actually originate from ¹³⁷Ba.

¹³⁷Cs Gamma Spectrum

Let’s take another look at ¹³⁷Cs gamma spectrum – Fig. 3.

We know that the 661.7 keV peak is actually emitted by barium-137 when the excited nucleus of barium relaxes to its ground state (so this is a nuclear line); and the 32 keV peak is also emitted by barium-137 when the atom looses one of its electrons due to the internal conversion process (so it is an atomic or XRF line).

Compton Shelf

Then what about the continuum from 32 to 480 keV? This continuum is called Compton shelf , it originates from Compton scattering of gamma rays within the scintillator. Because gamma ray propagation is a probabilistic process that involves both absorption and scattering, only a portion of 661.7 keV gamma rays deposit their full energy into the detector forming the photopeak; some gammas bounce off and leave the detector thus depositing only a portion of their energy and giving rise to the Compton shelf on the gamma spectrum.

Compton Peak

Some scattered gammas will find their way back into the detector by reflecting from dense material in the vicinity of the source and give rise to the Compton peak (also known as the backscatter peak) at 180 keV. Note that the sum of the energy of the Compton peak (180 keV) with the energy of the Compton edge (482 keV) adds up to the the energy of the photopeak (662 keV). Fig. 4 is adapted from this excellent paper, which gives an example of how one can enhance the Compton peak by locating a thick slab of aluminum next to a ¹³⁷Cs source.

Note that the presence of a dense material in the vicinity of the detector/source will also result in XRF peaks characteristic of the composition of the material when the source is fairly strong. To reduce these parasitic effects it is best to position the detector and the source away from metal parts when possible.

Compton Suppression

Compton scattering is considered a parasitic effect for two reasons:

1. Compton scattering reduces the height of the photopeak;
2. Compton scattering produces continuum that merges with background and thus further reduces the photopeak height wrt background.

The photopeak height is critical when one needs to accurately measure the radioactive material content or when one is trying to extract the lines of a very weak source from background (e.g. using an HPGe detector). To improve the signal to noise ratio Compton suppression is often used.

A common Compton suppression technique involves surrounding the detector with another scintillator material and looking for coincidences between pulses in the main detector and in the scintillator used for Compton suppression. A coincidence means that a gamma ray underwent Compton scattering in the main detector, left the detector and was absorbed by the Compton suppression scintillator. Therefore this gamma is rejected from spectrum because it does not contribute to the photopeak but instead makes up the Comtpon shelf/background that we are trying to suppress.

BGO

There is another way to reduce the magnitude of Compton continuum and thus improve the signal-to-noise ratio when counting a photopeak. I am talking about the Bismuth Germanate (BGO) scintillators. Because BGO is a high-density material Compton scattering in BGO is less pronounced than in NaI. Thus, the photopeak appears taller in BGO scintillators making them more suitable to photopeak counting compared to NaI scintillators. Unfortunately the energy resolution of BGO scintillators (~10% FWHM @ 662 keV) is not that great compared to Na. Therefore BGOs are not commonly used for gamma spectroscopy applications.

Conclusion

As you can see, an entire textbook in physics is hiding in plain site behind the good old ¹³⁷Cs gamma spectrum. And I have not even scratched the surface of the really interesting physics behind the beta-decay. I will save it for another post. It will suffice to say that beta-decay is easily one of the most mind blowing phenomena that is still not fully understood. In the next post I will show that by questioning our understanding of beta decay we may pave a way to discovering really exciting new physics!