Simulations of Particle Interactions with Matter

Overview

Particle Detection

A device detects a particle only after the particle transfers energy to the device.

Energy intrinsic to a device depends on the material used in a device

Some device of material with an average atomic number ($Z$) is at some temperature ($T$). The materials atoms are in constant thermal motion (unless T = zero degrees Klevin).

Statistical Thermodynamics tells us that the canonical energy distribution of the atoms is given by the Maxwell-Boltzmann statistics such that

$P(E) = \frac{1}{kT} e^{-\frac{E}{kT}}$

$P(E)$ represents the probability of any atom in the system having an energy $E$ where

$k= 1.38 \times 10^{-23} \frac{J}{mole \cdot K}$

Note: You may be more familiar with the Maxwell-Boltzmann distribution in the form

$N(\nu) = 4 \pi N \left ( \frac{m}{2\pi k T} \right ) ^{3/2} v^2 e^{-mv^2/2kT}$

where $N(v) \Delta v$ would represent the molesules in the gas sample with speeds between $v$ and $v + \Delta v$

Example 1

What is the probability that an atom in a 12.011 gram block of carbon would have and energy of 5 eV?

First lets check that the probability distribution is Normailized; ie: does $\int_0^{\infinity} P(E) dE =1$?