Ghanaian Mathematical Physicist Prof. Francis Ampenyin Allotey (1932-2017) is credited with developing what is known as the Allotey Formalism. However, despite its significance, there is surprisingly little information available online about his achievement.

In this piece, I spoke with Prof. Samuel Yeboah Mensah of the Department of Physics at the University of Cape Coast, who collaborated with Prof. Allotey on several publications. Through this interview, I sought to better understand Prof. Allotey’s nearly forgotten work and its impact on the field of physics.

Hmm, Imagine you’re playing a board game like chess. In chess, you don’t need to know why the Knight moves in an L-shape or what the Knight represents in real life. You just follow the rules of how to move the pieces. Formalism in Mathematics is like this: it’s the idea that math is just about following rules to manipulate symbols (like chess pieces) without worrying about what those symbols mean in the real world. It’s all about the rules of the game, not the story behind it.

What is Allotey Formalism?

Now, let’s say you’re trying to explain why a ball bounces when you drop it. You might create a model using math to describe the forces involved, like gravity and elasticity. Allotey Formalism is similar: it’s a mathematical model developed by Professor Francis Allotey to explain a physical phenomenon, specifically, how soft X-rays are emitted from certain materials like sodium and lithium. Think of it as creating a "rulebook" (the model) to explain how something in nature works (the soft X-ray emission).

“So, when we talk of Allotey Formalism, we mean he developed a mathematical model to explain a physical phenomenon. In this case he applied the electron- hole model to explain the soft X- ray,” Prof. Mensah said.

Why is Soft X-ray important?

Imagine X-rays as different types of light bulbs. Some bulbs are super bright (hard X-rays), and some are dimmer (soft X-rays). The brightness here is measured in kilo electron volts (keV), which is like the wattage of the bulb.

In the atomic world, energy is measured in electron volts (eV), which is like the "currency" of energy at the tiny scale of atoms and electrons.

Soft X-rays are like a special flashlight that can reveal hidden details about materials. For example, if you shine a soft X-ray on sodium or lithium, it can help scientists understand the material’s properties. It’s like using a magnifying glass to see tiny details you can’t see with your eyes alone.

“Some materials radiate soft x-ray. So, you can use it to characterise the material. For example Sodium and many others. In short soft x-ray are used in determining materials,” Prof. Mensah stated.

What Allotey did

Professor Allotey created a mathematical model (the Allotey Formalism) to explain how soft X-rays are emitted from materials like sodium and lithium.

Think of it as writing the first instruction manual for how a specific type of flashlight (soft X-ray) works. Later, other scientists improved his manual to explain how the flashlight works for other materials too. But Allotey was the first to write the manual, which is why many honoured his work by calling it Allotey Formalism.

Why isn’t Allotey Formalism widely known?

In the world of science, new discoveries and models are often built upon by other scientists, and the original creator’s name might not always stick. It’s like inventing a recipe for a cake, and over time, people tweak the recipe and forget who first came up with it. That’s why you might not find "Allotey Formalism" in many scientific textbooks, even though his work was groundbreaking.

“His model actually gave the theoretical explanation of how the soft x-ray is emitted in Sodium and lithium. There has been improvement of his theory by other scientists to explain the soft x-ray emitted by other materials. His achievement is that he is the first to apply this model. That is why we call it Allotey's Formalism. In Scientific literature there is nothing called Allotey Formalism,” Prof. Mensah said.