Biomedical Engineering Reference
In-Depth Information
water, and the San Diego group [
21
], for molecular hydrogen, are over the common
energy range of interest, in good accord with the present [
5
,
7
,
22
] to typically
˙5
%.
We believe this comparison provides some veracity for the total errors we cite.
9.3
Results and Discussion
In Fig.
9.2
we present our measured total cross sections as a function of energy
for positron scattering from the six bio-molecules we have studied [
4
-
9
]. The
results in this figure should be studied in conjunction with Table
9.1
,wheresome
of the important physico-chemical properties [
6
,
8
,
23
-
46
] of those species are
summarised. Please note that the errors plotted in Fig.
9.2
are statistical only, and
all are at the one standard deviation level. For each molecule the trend in the TCS
as a function of energy is quite clear, namely the TCS decreases in magnitude as
the incident positron energy increases until the respective positronium formation
thresholds (see Table
9.1
) are reached. With the opening of the positronium
formation channel there is a dramatic change in the slope of the TCS, so that
its magnitude at higher energies (at least to the upper limit in energy of our
investigations) essentially sits on a plateau. The low energy behaviour of each
species, where the elastic, rotational and vibrational channels are open, has been
discussed by us previously and is thought to be due to the long-range dipole
interaction between the respective species and the incident positrons. Above the
energy for positronium formation (
E
Ps
), the electronic-state and direct ionisation
channels open progressively and also contribute to the plateau in the TCS that we
observe in each species (see Fig.
9.2
).
If we now compare the behaviour between the respective species, then several
general trends also emerge. Below the relevant
E
Ps
and down to about 0.6 eV,
the magnitude of each species' TCS seems strongly correlated to the value of its
dipole polarisability (
). For instance both the conformers of THF [
47
] and 3-h-
THF, as well as pyrimidine, have similar values for their dipole polarisabilities,
and their corresponding TCSs in this energy range are almost identical. Below 0.6
eV the TCS of 3-h-THF is rather larger than those of the other species (THF and
pyrimidine), but this can be understood in terms of its next-lowest-energy conformer
(which is present in our 3-h-THF sample) having a much bigger permanent dipole
moment (
˛
) than the others. Similarly, these three species, in this same energy
range, have significantly larger TCSs than those for water and formic acid, whose
dipole polarisabilities are both much lower in value (see Table
9.1
). While it might
appear that water (H
2
O) and formic acid (HCOOH) do not entirely fit the trend we
are espousing, as for
˛
HCOOH
˛
H
2
O
,
this can be understood in terms of a sort of “compensation effect” due to
E<1
eV their TCSs are almost identical yet
H
2
O
>
HCOOH
. Hence both these long-range interactions are important when looking at
the comparative behaviour of these systems. The behaviour of di-hydropyran (see
Fig.
9.2
) can also be understood in this same light, for energies between 0.6 eV
and its
E
Ps
(see Table
9.1
). While it has the largest dipole polarisability of all the
