Gamow Model for Alpha Decay: The Geiger-Nuttall Law
Gamow Model for Alpha Decay: The Geiger-Nuttall Law
Alpha emission is a radioactive process involving two nuclei X and Y, which has the form XYHe, the helium-4 nucleus being known as an alpha particle. All nuclei heavier than Pb () exhibit alpha activity. Geiger and Nuttall (1911) found an empirical relation between the half-life of alpha decay and the energy of the emitted alpha particles. Using more recent data, the Geiger–Nuttall law can be written ≈-46.83+1.454Z, where is in seconds, in MeV, and is the atomic number of the daughter nucleus. The observed range of half-lives is huge, varying from years for Nd to sec for Po. We limit our consideration to even-even nuclei. Slightly different values of the parameters pertain when odd or nuclei are involved.
A
Z
A-4
⟶
Z-2
4
+
2
Z=82
t
1/2
Q
log
10
t
1/2
Q
t
Q
Z
2×
15
10
144
60
3×
-7
10
212
84
Z
A
George Gamow in 1928, just two years after the invention of quantum mechanics, proposed that the process involves tunneling of an alpha particle through a large barrier. The barrier is created by the Coulomb repulsion between the alpha particle and the rest of the positively charged nucleus, in addition to breaking the strong nuclear forces acting on the alpha particle. Gurney and Condon independently proposed a similar mechanism. A plot of the nuclear potential also shows the alpha-particle wavefunction (r). The amplitude of the transmitted wave is highly magnified
ψ
α