Biomedical Engineering Reference
In-Depth Information
for example [
5
]). Thus, further theoretical models as well as experimental data on
ion-induced collisions at the DNA level remain crucial to go beyond the simple
approximation which consists in modelling the biological matter by water as usually
done in the existing track-structure numerical simulations. However, ionization and
fragmentation of isolated nucleobases have until now received only little interest
and have been essentially focused on the cross-section determination for electron-
induced collisions. Indeed, ion-induced collisions have rarely been reported in the
literature and to the best of our knowledge only few works exist (see for example
[
6
]). On the theoretical side, we essentially find two recent approaches, namely, a
first (semi)-classical one based on the CTMC-COB approach (previously tested for
water [
7
]) and a second quantum-mechanical one [
8
] providing doubly and singly
differential as well as total cross sections for proton, ˛-particle and bare carbon ion
beams impacting on adenine, cytosine, thymine and guanine bases.
The present chapter deals with the theoretical models we have recently
developed - within the quantum mechanical framework - for describing the
ionization and the electronic capture processes induced by heavy charged particles
in both water and DNA components. The obtained results will be reported in terms
of multi-differential and total cross sections by pointing out the relative importance
of the target description.
In the following sections, atomic units (a.u.) are used throughout unless indicated
otherwise.
16.2
Theoretical approach
Let us first consider the processes of electronic capture and ionization induced by
bare ion beam impact on mono-electronic atoms. This description may be then
extended and applied to the case of multi-electronic atomic and molecular targets.
The involved particles being charged, let us remind that the interactions are governed
by long-range Coulomb forces, which might be small but never equal to zero
even at infinite long distances. As a consequence, the wave function representing
this situation can not be written as a product of free-particle (plane-waves) wave
functions. The long-range nature of the potential results in the appearance of a
Coulomb phase or distortion. Thus, the initial and final state wave functions in
the three-particle system considered are chosen in such a way as to represent the
physical problem and the correct asymptotic conditions at very large distances. This
is of fundamental importance to avoid the presence of divergences in the scattering
matrix elements associated with the population of elastic intermediate channels [
9
].
According with the studied reactions, different approximations which verify
correct boundary conditions are employed. We will present them into the straight
line version of the impact parameter approximation, where the internuclear vector
R, the impact
and the collision velocity
E
E
v
are related by the expression
R
DE
CE
v
t;
(16.1)
