Biomedical Engineering Reference
In-Depth Information
Fig. 15.4
Stopping power
of H
C
(solid line) and H
0
(dashed line) in liquid water,
S
C
and S
0
respectively, as a
function of the incident
energy. The calculations are
done with the MELF-GOS
method, starting from a fitting
to IXSS experimental data
in the optical limit [
16
]. The
inset contains the charge
fractions of H
C
(solid line)
and H
0
(dashed line),
C
and
0
respectively, as a function
of the projectile energy,
obtained from [
25
]
affect the contribution of H
C
or H
0
to the total stopping power S ,Eq.
15.1
,at
different energies. The latter contributes only at low projectile energy, having its
maximum at around 25 keV and being insignificant at energies higher than 200 keV,
whereas the maximum of the former appears at around 130 keV, being
3 times
larger than the contribution from H
0
and extending to higher energies. Therefore the
stopping power S for energies larger than the maximum stopping power is mainly
due to H
C
, whereas at energies in the range of a few keV the stopping of H
0
becomes
more significant.
In what follows we check the influence in the electronic energy loss of protons
due to the input data used to construct the OELF of liquid water, from which the
Bethe surface is obtained. In Fig.
15.5
we show the stopping power and the energy-
loss straggling of protons in liquid water obtained through the MELF-GOS model,
from Eqs.
15.1
-
15.3
after using the two different sets of experimental data for liquid
water in the optical limit [
15
,
16
]. Solid lines derive from the IXSS data [
16
] whereas
dashed lines come from the REF data [
15
]. These results depicted in Fig.
15.5
prove
that, despite the strong differences (around 50% over the maximum energy transfer,
as shown in Fig.
15.1
) between the IXSS and the REF data of the OELF for liquid
water, the discrepancies in the stopping power are lower than the 10%, mainly
around the maximum stopping, whereas divergences in the energy-loss straggling
are smaller in all the energy range.
After making clear the differences in the S and
2
of liquid water due to
the OELF used as input in the dielectric formalism, in what follows we discuss
the significance on the proton stopping power due to the different schemes used
to extend the valence excitation spectrum of liquid water over all the energy-
momentum transfer. In Fig.
15.6
we show S , as a function of the proton incident
energy, obtained from the different models described previously: the extended
Drude model [
17
], the damped Ritchie model [
21
], the IED method [
20
,
60
],
the Ashley model [
18
], and the MELF-GOS method based in the Mermin ELF
[
19
,
22
,
52
,
61
]. All the calculations are based on the IXSS experimental data
