PENELOPE 2003 - OECD Nuclear Energy Agency

2.5. Attenuation coefficients 63
directions of movement. As a consequence, there should be little difference between
simulation results obtained with the present method and with exact random sampling
from a more accurate DCS, differential in the energies and directions of the generated
particles.
Compound materials
Let us consider a compound X x Y y , in which the molecules consist of x atoms of the
element X and y atoms of the element Y. The number of electrons per molecule is
Z M = xZ(X) + yZ(Y) and the molecular weight is A M = xA w (X) + yA w (Y), where
Z(X) and A w (X) stand for the atomic number and atomic weight of element X.
In the simulation of pair-production events, we could use the molecular DCSs obtained
from the additivity rule. The simulation of each event would then consist of 1)
sampling the atom which participates in the interaction and 2) generating a random
value of the electron reduced energy ɛ from the corresponding atomic DCS. To save
computer time, penelope generates ɛ by considering an “equivalent” single element
material of the same mass density ρ as the actual medium, atomic number Z eq and
atomic weight A eq given by
Z eq A M = Z M A eq = xZ(X)A w (X) + yZ(Y)A w (Y), (2.104)
i.e. its atomic number (weight) is the mass-average (Z-average) of the atomic numbers
(weights) of the constituent atoms. The reduced energy is sampled from the DCS of the
element with the atomic number closest to Z eq . Usually, this approximation does not
alter the simulation results appreciably and permits a considerable simplification of the
program and a reduction of the simulation time.
2.5 Attenuation coefficients
The photon inverse mean free path for a given mechanism is known as the partial
attenuation coefficient of that mechanism. Thus, the partial attenuation coefficient for
photoelectric absorption is
µ ph = N σ ph , (2.105)
where N = N A ρ/A M is the number of atoms or molecules per unit volume and σ ph is
the atomic or molecular photoelectric cross section. The photoelectric mass attenuation
coefficient is defined as µ ph /ρ and, therefore, is independent of the density of the material.
Analogous definitions apply for the other interaction processes. The total mass
attenuation coefficient is obtained as
µ
ρ = N A
(σ Ra + σ Co + σ ph + σ pp ) . (2.106)
A M
As mentioned above, penelope uses tables of total cross sections for photoelectric
absorption and pair production obtained from the database EPDL (Cullen et al., 1997)