I'm reading some papers that compare different values for a materials opacity to a particular particle. The first is given as $\frac{dE}{dX}$, a single particles energy loss per unit column depth (X = $x\rho $) to a continuous process.
Makes sense. So then the author goes on to compare his value to that of other authors, who have their opacities for the process expressed in $\kappa $ given in $cm^{2}/g $.
They're both presented as measuring the same thing, but I usually think of $ \kappa $ as being an opacity for a large group of particles that are removed discretely from a beam, so that the total energy in the beam dies of exponentially (since energy loss per distance is proportional to the number of particles left in the beam). $\frac{dE}{dX}$ is due to a continuous process acting on all the particles, and so would have a roughly linear effect per distance.
So my question is how does one compare the two values. What does $ \kappa $ mean in a context of continuous energy loss.
Thanks