Biomedical Engineering Reference
In-Depth Information
15.3.1
Experimental optical data
The first step is the description of the optical energy loss function (OELF hereafter)
of the target. Presently there are only two sets of experimental ELF data for liquid
water in the optical limit .k
D
0/ that cover a sufficient part of the valence energy-
excitation spectrum.
The first set comes from the Oak Ridge group [
15
], which provides, from
reflectance measurements on liquid water surfaces, the real refractive index, n,and
the extinction coefficient, , of the complex index of refraction
i over
the excitation-energy range 7.6-25.6 eV. For more than 25 years the Oak Ridge data
were the sole source of information on the dielectric response of liquid water in the
VUV range. The OELF limit is obtained from the ¨-dependent
n
Q
D
n
C
n as follows:
Q
Im
Im
i.!//
2
1
1
2n.!/ .!/
D
D
.2n.!/ .!//
2
:
(15.4)
2
.!//
2
".k
0; !/
.n.!/
C
.n
2
.!/
C
The second set of optical data comes from the Sendai group [
16
], which used
inelastic X-ray scattering spectroscopy (IXSS) to measure the generalized oscillator
strength (GOS) of liquid water at nearly vanishing momentum transfer .k
0/.The
IXSS data extend from 6 to 160 eV excitation energies, providing a near complete
knowledge of the dielectric response properties of the valence-shells of liquid water.
The OELF limit is then obtained as:
Im
!
pl
2!
1
df.k
0; !/
D
;
(15.5)
".k
0; !/
d!
with df.k
0; !/=d! being the GOS at k
0. The nominal pl
asmon
energy of
4
q
n
e
a
0
Ry, where
the material,
„
!
pl
, is determined from the relationship
„
!
pl
D
0:529
˚
AandRy
n
e
is the target electronic density, a
0
D
13:606 eV is the Rydberg
energy. For liquid water of mass-density 1 g=cm
3
,wehaven
e
D
D
10
23
cm
3
,
3:34
so
„
21:4 eV.
In Fig.
15.1
we present the ELF of liquid water at the optical limit, k
!
pl
D
0,
obtained from the data of both groups, which will be called REF [
15
]andIXSS[
16
]
data hereafter. Although the shape of the ELF given by both sets (REF, IXSS) of
data is similar, there is a sizeable disagreement with respect to the intensity of the
main excitation peak at
21 eV. Specifically, in the IXSS data the peak intensity is
reduced by a factor of 1.5 compared to the REF data. A reduction of that magnitude
has also been observed in the spectrum of ice water, both in its hexagonal and
amorphous forms [
31
-
33
]. This has often been used as an argument in favour of
the IXSS data, particularly in view of the fact that amorphous ice has characteristics
similar to liquid water [
34
].
