Biomedical Engineering Reference
In-Depth Information
species in this study, its TCS is almost identical to that for THF, 3-h-THF and
pyrimidine. We believe this simply reflects that di-hydropyran has a permanent
dipole moment which is amongst the smallest of the bio-molecules we consider, so
that a “compensation effect” between the two long-range interactions is prevalent
again here. Below
eV the situation is complicated by the energy resolution
convolution effect on our measured TCSs. As a consequence we do not consider
that energy regime further in this paper.
In their study on positron scattering from H
2
O and HCOOH, Makochekanwa
et al.
[
20
] were able to directly measure the positronium formation integral cross
sections for both species. They found similar qualitative behaviour for the shapes of
both TCSs as a function of energy, in particular no structure was noted. Of great
interest from this study was that the ratio of the maximum values of the TCSs
for these species seemed to scale with the ratio of their dipole polarisabilities. We
believe that this observation, at least to some extent, helps explain the behaviour in
Fig.
9.2
for positron energies (
0:6
E
Ps
in each molecule. In particular,
the conformers of THF and 3-h-THF, as well as pyrimidine, all have (see Table
9.1
) similar values for
E
0
) greater than
˛
and this is reflected in Fig.
9.2
by them all having similar
TCS values for
E
0
>E
Ps
. Di-hydropyran has a larger dipole polarisability than
those three aforementioned molecules, and so in Fig.
9.2
we observe that it has the
largest TCSs (remember the y-axis is a log scale) of all the species we consider
for
E
0
>E
Ps
. Finally, for water and formic acid, the trend in their TCSs is also
consistent with the idea that the dipole polarisability is playing a major role in
the scattering dynamics for these molecules in this energy regime. The above
conclusions are entirely consistent with the findings in Danielson
et al.
[
48
]. In
that study the dependence of positron-molecule binding energies on the molecular
properties of the species considered were investigated, with similar results to those
we have outlined here being found.
A “curious” feature of the present measurements, which has puzzled us (in the
absence of theoretical guidance) for some time, is that the energy dependence of
our pos
itro
n TCSs at energies below a couple of eV, mainly seems to fall like
1=E
0
1=
p
E
0
.Inthe
or
1=E
0
case this behaviour is seen with the targets pyrimidi
ne,
formic acid, 3-h-THF and water. On the other hand, di-hydropyran shows a
1=
p
E
0
dependence while the be
hav
iour of THF lies somewhere in between. We have also
seen these
1=
p
E
0
trends in our measurements on atoms [
15
] and other
molecules (e.g. [
22
]), so that we do not think it can simply be a coincidence.
1=E
0
or
9.4
Conclusions
We have systematically examined our positron-bio-molecule TCS scattering data,
in an attempt to uncover any underlying trends in that data. We believe that a
strong semi-quantitative link between the value of the target dipole polarisability
and the strength of the total cross section has been established, with the permanent
molecular dipole moment also playing an important, if perhaps more secondary,
