Biomedical Engineering Reference
In-Depth Information
Fig. 15.6
Stopping power
of liquid water for a proton
beam, as a function of the
incident energy, evaluated
from different models to
calculate the Bethe surface.
In all cases the same fitting to
the OELF from the IXSS data
[
16
] was used. The
contribution from both, H
C
and H
0
are included in the
calculation. See the text
for more details
power obtained by the damped Ritchie method [
21
] as compared with the MELF-
GOS model in the whole proton energy range. Despite the fact that the empirical
IED model [
20
,
60
] includes the damping dispersion, providing a broad ELF and
correctly predicts the peak position of the ELF, it provides a S value smaller than the
one obtained by the MELF-GOS model, in all the range of energies evaluated. This
is because the IED model underestimates the experimental ELF at all momentum
transfer (see Fig.
15.3
).
The results of the stopping power of liquid water for an incident proton beam,
calculated by several studies in the literature [
9
,
19
,
22
,
64
,
65
], are depicted in
Fig.
15.7
together with experimental data, the semiempirical code SRIM [
66
]and
with the values provided by the ICRU report [
7
]. A short comment follows for
the models that have not been discussed previously; all of them are based on the
first Born approximation. The results by Dingfelder
et al
.[
9
] are based on cross-
section data for several inelastic channels between protons and liquid water, using
the optical measurements of Heller
et al.
[
15
] with a quadratic dispersion scheme.
Emfietzoglou
et al
.[
64
] use the improved extended-Drude model to describe the
Bethe surface of liquid water. The calculations by Akkerman
et al
.[
65
] provide the
stopping power as a sum of valence electron excitation, core-electron ionization,
and Barkas and Bloch terms, with Ashley's approximation for the ELF.
It is worth to notice that most of the experimental data correspond to measure-
ments of protons on D
2
O-ice [
67
,
68
] and on H
2
O-ice [
69
]. These data were used
as input for obtaining the semiempirical [
66
] and tabulated [
7
] curves. The only
experimental results available for liquid water [
70
,
71
], covering the range from 0.3
to 2 MeV, were obtained with a thin liquid jet in vacuum, but its diameter was treated
as a fitting parameter. The deviations for the stopping powers of the different phase
states of water are most noticeable at low proton energies, but they dissapear as the
energy increases [
72
].
