# Maths formula links clouds, marriages and atoms

**
28 February 2019 **

UCL scientists have made a new discovery that will help describe and predict how collision probabilities involving subatomic particles vary with energy.

The same mathematical formula which describes the probability distribution of phenomena such as periods of incubation of diseases, size of clouds, abundance of species, age of marriage, fluctuations in economic variables, etc, also applies at the quantum level, UCL scientists find.

The discovery, published today in Scientific Reports, will help in describing and predicting how collision probabilities involving subatomic particles vary with energy. It is expected to impact on a fundamental issue in physics, that of the boundary between the classical and quantum domains.

Professor Gaetana Laricchia (UCL Physics & Astronomy) who led the work, said: “The question of where the classical world ends and the quantum one begins is a major concern in physics. Our finding is particularly exciting because of its breadth and simplicity, and because it links systems normally described by quantum theories to those in the classical regime.”

“Our initial investigation arose in the context of atomic collisions with positrons”, the positron being the antimatter counterpart to the electron, that is the same mass but opposite charge.

“At first, we noticed similarities among different atoms. So we searched for a common mathematical expression and found that a formula - the “lognormal distribution” - widely used for large scale phenomena, unexpectedly worked well not only for different atomic targets but also different projectiles and processes.””.

The prediction and measurement of collision probabilities at the quantum level engage theorists and experimentalists worldwide, quantum theoretical approaches requiring complex calculations and being currently restricted to given physical systems, processes or energy regimes.

In the present statistical description, observed to be valid over a broad energy range, the only quantum input is the minimum energy required for the process under consideration.

In analogy with studies of clouds and marriages, the authors conjecture that the behaviour arises if the outcome of the collision is the product of many independent random effects.

The generality of the analysis, namely its independence from the details of the forces at play, is reinforced by their finding that the formula also applies to solid state and nuclear physics problems.

### Links

- Article in
*Scientific Reports* - Professor Gaetana Laricchia's academic profile
- UCL Physics & Astronomy
- UCL Positron Group
- The work is funded by the Engineering & Physical Sciences Research Council