How Accurate is the Law of Nuclear Decay in Describing Radioactive Processes?

[pivoxa15]

Radioactive decay is normally characterised by 'the rate of decay is linearly proportional to the number of nuclides avaliable'. i.e dN/dt=-aN (a>0)

How correct is this law? Are there better models of describing nuclear decay? If so what are they?

 

[mathman]

The basic law is quite accurate. The physical assumption is that the probability of an atom decaying is independent of another atom decaying.

 

[pivoxa15]

So this law is like the inverse square gravitational and electrostatic laws in that they are very simple but extremely accurate and only when one goes down to several decimal points does it break down?

 

[CarlB]

How correct is this law?

In practice, in most situations, it works very well. However, not always. The problem is that quantum mechanics is a quadratic theory, while radioactive decay follows a linear relation. Consequently, things only decay following the exponential law for times that are not too short and not too long.

Here's some slides showing the issue:
http://www.drake.edu/artsci/physics/petridis_other_files/dnp_talk_10_19_01.ppt


Here are some references:
http://arxiv.org/abs/quant-ph/0202105
http://www.aip.org/pnu/1997/split/pnu327-2.htm
http://arxiv.org/abs/physics/0505042
http://arxiv.org/abs/quant-ph/0411145
http://arxiv.org/abs/quant-ph/9806079

From the peer-reviewed literature:
http://prola.aps.org/abstract/PRA/v63/i6/e062110

There are tons of articles on this. Search for "Zeno" or "non exponential decay".

Carl