# Geiger-Nuttall law

Geiger-Nuttall law is semi-empiric relation between half-life $t$ of a nucleus that undergoes the alpha–decay and the energy $E$ of this decay. This relation can be partially justified with the Gamov model.

The Wolfram site [1] suggests the following relation:

$\displaystyle \lg\left(\frac{t}{\rm Second}\right) \approx A + B \frac{Z}{\sqrt{Q/\rm MeV}}$

where $Q$ is energy of the emitted alpha-particle, $Z$ is atomic number of the daughter nucleus, and constants

$A=-46.85$

$B=1.454$

in the rough approach are supposed to be the same for all nuclei. However, the modification for odd-even properties of nuclei may improve the approximation.

The approximation above can be justified with the tunnelling effect, assuming primitive nuclear potential for the almost-coupled alpha-particle.

## Range of validity

In most of cases, the Geiger-Nuttall gives the correct order of magnitude of fall–time $t$.

The coefficients A and B allows the physical interpretation, being considered not as constants, but as functions of the atomic number $Z$. [2]

## Confusion

Some authors write the Geiger-Nuttall law in a wrong form, violating dimensions [3].

## References

1. http://demonstrations.wolfram.com/GamowModelForAlphaDecayTheGeigerNuttallLaw/ S. M. Blinder. (2017)
2. http://www.sciencedirect.com/science/article/pii/S0370269314003761 On the validity of the Geiger–Nuttall alpha-decay law and its microscopic basis. Physics Letters B, Volume 734, 27 June 2014, Pages 203-206. The Geiger–Nuttall (GN) law relates the partial α-decay half-life with the energy of the escaping α particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: (1) the empirical coefficients that appear in the GN law have a deep physical meaning, and (2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the α formation probability on the neutron number is not linear or constant, the GN law is broken. For the α decay of neutron-deficient nucleus 186Po, the difference between the experimental half-life and that predicted by the GN law is as large as one order of magnitude.
3. http://scienceworld.wolfram.com/physics/Geiger-NuttallLaw.html Eric W. Weisstein. Geiger-Nuttall Law. 1996-2007.