I have this problem where a neutrino interacting with deuterium decay in 2 protons and 1 electron. This electron will produced Cherenkov photon. The specific energy loss of heavy water is $dE/dx=2MeV/cm$ and the maximum energy of the electron is $14MeV$. We want to know how many Cherenkov photons on the track of the electron if the refraction index of the heavy water is $n=1.33$ and $N_{\gamma}=4.9\times10^{4}\Big(1-\frac{1}{\beta^2n^2}\Big)photon/m$, where $\beta=v/c$.

I've seen things about the Frank-Tamm formula which can be written as:

\begin{equation} \frac{d^2N}{dxd\lambda}=\frac{2\pi\alpha}{\lambda^2}\bigg(1-\frac{1}{\beta^2n^2}\bigg) \end{equation}

This equation give us the number $N$ of generated photon within a wavelength interval $d\lambda$ per unit distance $dx$.

My problem is that I don't know how to begin the problem. I have problem to find the $\beta$ and to understand how it will affect the answer.

  • $\begingroup$ There are a series of problems to solve here, starting with the kinetic energy of the electron in the quasielastic interaction, then the path length during which the electron exceeds $c/n$ (noting that Cerenkov light is not the only energy loss mechanism) and then applying the Frank-Tamm formula in some proper approximations. $\endgroup$ – dmckee --- ex-moderator kitten Feb 15 '16 at 1:53
  • $\begingroup$ I don't know what is quasielastic interaction and I'm not sure how I should apply the Frank-Tamm formula. $\endgroup$ – frankys Feb 15 '16 at 1:58
  • 1
    $\begingroup$ Hi and welcome to the Physics SE! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. $\endgroup$ – John Rennie Feb 15 '16 at 12:30
  • $\begingroup$ Even if this question is related to a homework I didn't see it as the homework question itself. I'm looking to understand the physics of the Cherenkov radiation behind this. Excuse me if I made a mistake in my way of looking at my problem. $\endgroup$ – frankys Feb 15 '16 at 12:37