Why is the stopping power in Bethe Bloch-Plot shown against $\beta\gamma$ on the horizontal axis? Respectively what is the meaning of $\beta \gamma$?
Plot taken from here
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to join this community
$\beta\gamma$ 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.
To elaborate, Lorentz contraction compresses the field in the boost direction, and therefore the transverse field is strengthened relative to the longitudinal part.
Furthermore, around $\beta\gamma \approx 3$, there is a region where energy loses are minimised.