Lab Exercise - Alpha/Beta-Discrimination

In modern LSC equipment it is possible to discriminate between the α- and β-emissions. The resolution of the α-peaks is relatively poor due to the small number of excitations produced but the background associated with the α-emissions is very small.

The ability to discriminate between α- and β-particles lies in the small difference in pulse shapes. The following steps explain the difference in the pulse profile.

1. The initial interaction of the α-particle is much stronger than the β-particle due to a) the double charge, and b) the low velocity. The α-range is much less than β-range so that the ionisations produce a very high density track. Compared with the β-particle, the α-particle produces fewer excitations (~ 0.4%). Since it is the excitations which contribute to the pulse, equal energies of α and β give an α-pulse height approximately 10% of the β-pulse height. It is the greater density of ions and electrons which will produce the difference in the pulse profile.
2. Due to the density of ions, the probability of recombination of an ion and electron is greater for α than β.
3. Recombination may produce a ground state molecule or an excited molecule.
4. Quantum mechanics postulates the number of states (orientations) is given by 2s + 1, where s = spin. Spin of singlet (S) = 0, spin of triplet (T) = 1. Hence, for a singlet, the number of states = 1 whereas for a triplet, the number of states = 3.
   e^-+X⁺ → X* (exited singlet)
   e^-+X⁺ → X* (exited triplet)
   β produce mainly singlets while α produce mainly triplets.
5. The excited singlet will undergo fluorescence and emit a photon in a very short time.
6. The excited triplets have a longer lifetime due to the low probability of changing spin from 1 to 0. The concentration of excited molecules is such that there is a probability of two 3X* molecules colliding.
   ³X* + ³X*→ ¹X* + ¹X* + phonons
   This is triplet annihilation.
7. The 1X* decays rapidly but has been delayed by the lifetime of the 3X* molecules, i.e. produces "delayed fluorescence".
8. The enhanced delayed fluorescence contribution for α produces a longer tail (30-40 ns) to the output pulse compared with β.

By electronic analysis of the descending portion of the amplifier-integrated pulses, it is possible to almost completely (99.95+%) separate α-pulses from β-pulses.