Alpha radioactivity

A nuclear enigma

Some heavy nuclei, such as uranium, are radioactive: they spontaneously emit an alpha particle (a helium nucleus, 2 protons + 2 neutrons). In the 1920s, this posed a formidable paradox.

Inside the nucleus, the alpha particle is held back by a colossal energy barrier (the nuclear force). Yet measurements showed that the emitted alpha particle does not have enough energy to cross this barrier. Classically, it should stay trapped forever. How does it get out?

   Energie
      ^      barriere nucleaire (tres haute)
      |         ______
      |        /      \\
      |       /        \\
      |      /          \\    <- energie de la particule alpha
      |. . ./. . . . . . \\. . . . . . . . . . .  (elle est SOUS la barriere !)
      |    /|  particule  |\\
      |   / |    alpha    | \\_______
      |__/  |   piegee    |         '-------
           interieur    barriere    exterieur
           du noyau                  (liberte)

The solution: tunnelling (Gamow, 1928)

George Gamow understood that the alpha particle passes through the barrier by tunnelling. It does not have the energy to go over the top, but it has a probability — often tiny — of tunnelling straight through. The mystery of alpha radioactivity was solved by quantum mechanics.

   la particule alpha "cogne" la barriere des milliards de
   milliards de fois par seconde de l'interieur...
   ... et a CHAQUE fois, une proba infime de sortir par effet tunnel
   -> tot ou tard, elle sort

Why lifetimes are so variable

This model explains an astonishing observation: the half-lives of alpha nuclei span an enormous range, from the microsecond to billions of years. How can the same mechanism give such different durations?

The answer lies in the exponential dependence of tunnelling. A small difference in the height or width of the barrier (hence in the energy of the alpha particle) changes the probability of crossing by a colossal amount:

   Noyau              Energie alpha    Demi-vie
   -----------------  ---------------  ---------------------
   polonium-212       elevee           0,3 microseconde
   uranium-238        faible           4,5 milliards d'annees

   (un petit ecart d'energie -> un ecart de demi-vie de 10^24 !)

This extreme sensitivity — the Geiger-Nuttall law — is the direct signature of tunnelling. No classical theory could relate these lifetimes; tunnelling explains them quantitatively.

In summary

An alpha particle is trapped in the nucleus by an energy barrier that it does not have the energy to cross classically. It escapes by tunnelling (Gamow, 1928). The exponential dependence of the crossing probability explains the immense range of half-lives (from the microsecond to a billion years): a small variation in the barrier radically changes the rate of decay. Alpha radioactivity is a macroscopic proof of tunnelling.