Geiger-Nuttall rule

The Geiger-Nuttall rule is an empirically determined rule in nuclear physics for estimating the half-life of radionuclides that are subject to alpha decay .

The rule was established in 1911 by Hans Geiger and John Mitchell Nuttall and is based on the observation that shorter-lived nuclides emit alpha particles of higher energy. The rule has been revised several times and exists in many variants. The kinetic energy of the alpha particle and the atomic number play the main role in all of them ; further correction terms are common. The half-life can be estimated by ${\displaystyle E}$ ${\displaystyle Z}$

${\displaystyle \lg T_{1/2}=a_{1}{\frac {Z}{\sqrt {E}}}+a_{2}+...}$

where and are constants fitted to the observations. ${\displaystyle a_{1}}$ ${\displaystyle a_{2}}$

This relationship, which was initially determined empirically in 1911, is explained by the tunnel effect and was theoretically proven in 1928 by George Gamow . This derivation with the help of the WKB method contributed significantly to the recognition of quantum mechanics. The probability that the alpha particle will tunnel through the Coulomb barrier and thus leave the core increases exponentially with its kinetic energy. Such an explanation is not possible with the help of classical physics.

The rule is an estimation rule with considerable inaccuracies that does not care about the structure of the nucleus or aspects of the nuclear spin. Variants with some correction terms still have typical errors of one order of magnitude for short-lived nuclides and more than three orders of magnitude for extremely long-lived nuclides.

For the decay of ²⁰⁸ Pb, which is energetically possible, half-life times between 10 ¹¹⁵ and 10 ¹⁴⁵ seconds are obtained, depending on the formula . B. the age of the universe is only about 10 ¹⁷ seconds.

credentials

1. ↑ T. Fließbach: Quantum Mechanics. Spectrum Academic Publishing House.