# Alpha-particle spectroscopy

Alpha spectrometry (also known as alpha(-particle) spectroscopy) is the quantitative study of the energy of alpha particles emitted by a radioactive nuclide that is an alpha emitter.

As emitted alpha particles are mono-energetic (i.e. not emitted with a spectrum of energies, such as beta decay) with energies often distinct to the decay they can be used to identify which radionuclide they originated from.[1]

[For methods of gamma rays and beta particles, please see gamma spectroscopy and liquid scintillation counting respectively.]

## Experimental methods

Example of how different paths of emitted mono-energetic alpha particles would lose energy and therefore cause signal broadening on the line spectrum. All paths lose energy to the air and detector window. Longer paths lose more energy. Paths iii & iv also show loss of energy passing through the source material itself. The red arrows indicate the magnitude of energy the particle is detected with.

### Counting using a source in a metal disk

It is common to place a drop of the test solution on a metal disk which is then dried out to give a uniform coating on the disk. This is then used as the test sample. If the thickness of the layer formed on the disk is too thick then the lines of the spectrum are broadened to lower energies. This is because some of the energy of the alpha particles is lost during their movement through the layer of active material.[2]

### Liquid scintillation

An alternative method is to use internal liquid scintillation counting, where the sample is mixed with a scintillation cocktail. When the light emissions are then counted, some machines will record the amount of light energy per radioactive decay event. Due to the imperfections of the liquid scintillation method (such as a failure for all the photons to be detected, cloudy or coloured samples can be difficult to count) and the fact that random quenching can reduce the number of photons generated per radioactive decay, it is possible to get a broadening of the alpha spectra obtained through liquid scintillation. It is likely that these liquid scintillation spectra will be subject to a Gaussian broadening, rather than the distortion exhibited when the layer of an active material on a disk is too thick.

## Alpha spectra

Intensity against alpha energy for four isotopes, note that the line width is narrow and the fine details can be seen
Intensity against alpha energy for four isotopes, note that the line width is wide and some of the fine details can not be seen. This is for liquid scintillation counting, where random effects cause a variation in the number of visible photons generated per alpha decay

From left to right the peaks are due to 209Po, 239Pu, 210Po and 241Am. The fact that isotopes such as 239Pu and 241Am have more than one alpha line indicates that the (daughter) nucleus can be in different discrete energy levels.

Calibration: MCA does not work on energy, it works on voltage. To relate the energy to voltage one must calibrate the detection system. Here different alpha emitting sources of known energy were placed under the detector and the full energy peak is recorded.

Measurement of thickness of thin foils: Energies of alpha particles from radioactive sources are measured before and after passing through the thin films. By measuring difference and using SRIM we can measure the thickness of thin foils.

## Kinematics of alpha decay

The decay energy, Q (also called the Q-value of the reaction), corresponds to a disappearance of mass.

For the alpha decay nuclear reaction: ${\displaystyle {\ce {^{A}_{Z}P -> ^{(A-4)}_{(Z-2)}D + \alpha}}}$, (where P is the parent nuclide and D the daughter).

${\displaystyle Q{_{\alpha }}=(m_{P}-m_{D}-m_{\alpha })c^{2}}$, or to put in the more commonly used units: Q (MeV) = -931.5 ΔM (Da), (where ΔM = ΣMproducts - ΣMreactants).[3]

When the daughter nuclide and alpha particle formed are in their ground states (common for alpha decay), the total decay energy is divided between the two in kinetic energy (T):

${\displaystyle Q_{\alpha }=T_{\alpha }+T_{D}}$

The size of T is dependent on the ratio of masses of the products and due to the conservation of momentum (the parent's momentum = 0 at the moment of decay) this can be calculated:

${\displaystyle p_{\alpha }+p_{D}=0}$

${\displaystyle T=0.5mv^{2}}$ and ${\displaystyle p=mv}$, ${\displaystyle \therefore p={\sqrt {2mT}}}$

{\textstyle {\begin{aligned}{\sqrt {2m_{\alpha }T_{\alpha }}}&=-{\sqrt {2m_{D}T_{D}}}\\[4pt]2m_{\alpha }T_{\alpha }&=2m_{D}T_{D}\\[4pt]{\frac {m_{\alpha }}{m_{D}}}T_{\alpha }&=T_{D}\end{aligned}}}

{\displaystyle {\begin{aligned}Q_{\alpha }&=T_{\alpha }+{\frac {m_{\alpha }}{m_{D}}}T_{\alpha }\\[4pt]&=T_{\alpha }{\bigg (}1+{\frac {m_{\alpha }}{m_{D}}}{\bigg )}\\[4pt]&=T_{\alpha }{\bigg (}{\frac {m_{D}}{m_{D}}}+{\frac {m_{\alpha }}{m_{D}}}{\bigg )}\\[4pt]&=T_{\alpha }{\bigg (}{\frac {m_{D}+m_{\alpha }}{m_{D}}}{\bigg )}\\[4pt]\end{aligned}}}

${\displaystyle \therefore T_{\alpha }={\frac {m_{D}}{m_{P}}}Q_{\alpha }}$

The alpha particle, or 4He nucleus, is an especially strongly bound particle. This combined with the fact that the binding energy per nucleon has a maximum value near A=56 and systematically decreases for heavier nuclei, creates the situation that nuclei with A>150 have positive Qα-values for the emission of alpha particles.

For example, one of the heaviest naturally occurring isotopes, ${\displaystyle {\ce {^238U -> ^234Th + ^4He}}}$ (ignoring charges):

Qα = -931.5(234.043 601 + 4.002 603 254 13 - 238.050 788 2) = 4.2699 MeV[4]

Note that the decay energy will be divided between the alpha-particle and the heavy recoiling daughter so that the kinetic energy of the alpha particle (Tα) will be slightly less:

Tα = (234.043 601/238.050 788 2)4.2699 = 4.198 MeV, (note this is for the 238gU to 238gTh reaction, which in this case has the branching ratio of 79%). The kinetic energy of the recoiling 234Th daughter nucleus is TD = (mα/mP)Qα = (4.002 603 254 13/238.050 788 2)4.2699 = 0.0718 MeV or 71.8 keV, which whilst much smaller is still substantially bigger than that of chemical bonds (<10 eV) meaning the daughter nuclide will break away from whatever chemical environment the parent had been in.

Example of how the alpha particle energy detected decreases with increasing air pressure (from right to left).

The recoil energy is also the reason that alpha spectrometers, whilst run under reduced pressure, are not operated at too low a pressure so that the air helps stop the recoiling daughter from moving completely out of the original alpha-source and cause serious contamination problems if the daughters are themselves radioactive.[5]

The Qα‐values generally increase with increasing atomic number but the variation in the mass surface due to shell effects can overwhelm the systematic increase. The sharp peaks near A=214 are due to the effects of the N=126 shell.

## References

1. ^ Siegel, Peter (29 March 2021). "Nuclear decays" (PDF). Physics Department at Cal Poly Pomona.
2. ^ Vajda, Nora; Martin, Paul; Kim, Chang-Kyu (2012), "Alpha Spectrometry", Handbook of Radioactivity Analysis, Elsevier, pp. 380–381, doi:10.1016/b978-0-12-384873-4.00006-2, ISBN 978-0-12-384873-4, retrieved 2021-03-29
3. ^ Choppin, Gregory R. (2002). Radiochemistry and nuclear chemistry. Gregory R. Choppin, Jan-Olov Liljenzin, Jan Rydberg (3rd ed.). Woburn, MA: Butterworth-Heinemann. p. 62. ISBN 978-0-08-051566-3. OCLC 182729523.
4. ^ "Livechart - Table of Nuclides - Nuclear structure and decay data". nds.iaea.org. Retrieved 2021-03-31.
5. ^ Sill, Claude W.; Olson, Dale G. (1970-11-01). "Sources and prevention of recoil contamination of solid-state alpha detectors". Analytical Chemistry. 42 (13): 1596–1607. doi:10.1021/ac60295a016. ISSN 0003-2700.