Alpha-particle spectroscopy

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.

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 = ΣM_products - ΣM_reactants).[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 Q_α-values for the emission of alpha particles.

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

Q_α = -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 (T_α) will be slightly less:

T_α = (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 T_D = (m_α / m_P) Q_α = (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.