# What is the meaning of $\beta \gamma$ in Bethe Bloch Plot?

Why is the stopping power in Bethe Bloch-Plot shown against $$\beta\gamma$$ on the horizontal axis? Respectively what is the meaning of $$\beta \gamma$$?

• Without knowing what particular plot you are looking at, this is pretty hard to answer. Aug 3, 2017 at 17:12
• Ahhh... $\beta \gamma = p/Mc$ where $M$ is the rest mass of the particle. This means the master curve can be used for muons, pions, protons, etc. Aug 3, 2017 at 17:43

$\beta\gamma$ appears often in particle physics, and is convenient for plots. As noted, $\beta\gamma = p/Mc$, and at non-relativistic speeds it is simply $\beta$, or at relativistic speeds $\gamma$.
Thus, $\beta\gamma$ characterises whether we are in a relativistic regime. As the incident particle becomes relativistic, $\beta\gamma >1$ known as the relativistic rise, and this can be explained in terms of the transverse field strengthening.
Furthermore, around $\beta\gamma \approx 3$, there is a region where energy loses are minimised.
• Thanks! It sounds like a helpful term to describe some behaviours. When I rearranged it correctly $\beta \gamma$ is the momententum with a relativistic factor. Is that right? So finally it is stopping power against momentum?