Gamow factor

The Gamow factor ( to George Gamow ) used to calculate the probability of tunneling of a particle within the nucleus, that is the probability that it can overcome the Coulomb barrier and leave the nucleus. With the Gamow factor, for example, the alpha decay can be modeled mathematically.

Alpha decay

In alpha decay, an alpha particle leaves ( a 4He nucleus ), which consists of two neutrons and two protons, the atomic nucleus, which thus loses its mass and charge. Its atomic number Z, neutron number N and mass number A change is therefore:

• .

Since it effectively as a Fermi gas in the potential well can consider the ground state of a nucleus, it is plausible that with a certain probability together find several nucleons inside the nucleus and can form a bound state. This binding energy is released, which increases the probability that the particles formed tunnel through the Coulomb barrier of the residual nucleus.

Intuitively it is clear that the probability for the formation of such Nukleonverbindungen in the core strongly decreases with increasing number of participating nucleons. The formation of alpha particles is actually common, and since 4He is a doubly magic nucleus, a correspondingly large binding energy is released.

The transmission happens with a probability, which can be calculated via the WKB approximation:

Here, the radius of the core and the width of the potential well, which must tunnel through a particle energy. For the Coulomb potential of the residual nucleus gives:

The overall rate at which a core is divided by alpha emission, taking into account the probability of the formation of an alpha particle in the core and the frequency at which the alpha particles in the core rotates potential is given by:

Here is.

The resulting calculated life depends consequently very much on and so on. This explains why the lifetimes occurring in nature between a few nanoseconds and 1017 years vary.