Particle Detectors

Abstract

The subject of the second chapter is the interaction of particles with matter. The first section discusses the mechanism by which various types of particles interact with different media. Particular emphasis is given to the concept of energy loss and range in matter. The second section focuses on the experimental techniques for particle identification . The third section is dedicated to the functioning of particle detectors.

Appendix 1

The computer program below illustrates the numerical evaluation of the information $I_{\varepsilon _\pi }$ from Problem 2.28. The algorithm approximates the Rieman integral by the finite sum of rectangles:

$$ \int dx \, f(x) \approx \sum _i \, f \left( \frac{x_{i+1}-x_i}{2} \right) \cdot \varDelta x $$

The integral to be approximated is given by:

$$\begin{aligned} I_{\varepsilon _\pi } = \text{ E }\left[ - \frac{\partial ^2 f(x, \varepsilon _\pi ) }{\partial ^2 \varepsilon _\pi } \right] \equiv \int _{-\infty }^{+\infty }dt \, f(t, \varepsilon _\pi ) \left[ -\frac{\partial ^2 \ln f(x, \varepsilon _\pi ) }{\partial ^2 \varepsilon _\pi } \right] , \end{aligned}$$

(2.139)

with:

$$\begin{aligned} \frac{\partial \ln f(x, \varepsilon _\pi ) }{\partial \varepsilon _\pi } = \frac{\mathscr {N}(t; \; t_\pi , \sigma _t) - \mathscr {N}(t; \; t_K, \sigma _t) }{ f(t, \varepsilon _\pi ) } \end{aligned}$$

(2.140)

$$\begin{aligned} \frac{\partial ^2 \ln f(x, \varepsilon _\pi ) }{\partial ^2 \varepsilon _\pi } = -\frac{\left[ \mathscr {N}(t; \; t_\pi , \sigma _t) - \mathscr {N}(t; \; t_K, \sigma _t) \right] ^2}{ f(t, \varepsilon _\pi )^2} \end{aligned}$$

(2.141)