Biomedical Engineering Reference
In-Depth Information
14.5
Positron transport in liquid water
One of the most vexing questions within the field of radiation damage at present
is how to accurately treat the transport of electrons, positrons and other charged
particles in soft-condensed matter. Commonly, one implements a gas-phase as-
sumption, whereby the gas phase results are scaled to the liquid phase through
an increase in the density. For soft-condensed systems, this assumption can be
quantitatively and qualitatively in error. Amongst other things, specifically the
possibility of simultaneous many body coherent scattering from the correlated
constituent molecules is neglected. It is consequently important for theories to
consider the structure of the material. One of the key elements of our program
is to further explore techniques for adapting accurately measured/calculated gas-
phase cross-sections for electron and positron interactions for use in the analysis of
macroscopic phenomena in soft-condensed systems.
In a recent article [
21
], a first step towards this goal was made by generalizing
the somewhat heuristic Cohen-Lekner two-term kinetic theory, to account for
the effects of coherent scattering from correlated molecules in the material. The
resulting multi-term solution of Boltzmann's equation is valid for both electrons
and positrons in structured matter. The reader is referred to [
21
,
22
] for details
on the derivation and solution of the new kinetic equation. It will suffice here to
comment that the solution technique adapts much of the mathematical machinery
developed previously for treatment of electron and positron swarms in the gas
phase. Importantly, the inputs to this model are the measurable single-particle
scattering cross-sections and the measureable static structure factor for the medium.
The theory has been applied to both real viz., liquid argon [
21
,
22
] and model
systems [
22
]. New phenomena including structure-induced NDC and structure-
induced anisotropic diffusion have been predicted.
In Figs.
14.5
and
14.6
, we present results for the drift velocity and Ps-formation
rate of positron swarms in liquid water at 300K respectively. The results are
compared with the corresponding results for the positrons in water vapour. We
implement the same set of cross-sections used in the gas-phase case considered
above, and utilize the static structure of water detailed in [
23
] to account for the
structural properties of liquid water. The differences between the two different
phases correspond to regions where the average de Broglie wavelength is greater
than the inter-particle spacing, and coherent scattering effects are thus significant.
The manifestation of coherent scattering effects is an effective reduction in the
momentum transfer cross-section describing the process. This facilitates enhanced
energy transfer from the field into the swarm in the liquid phase. The enhanced drift
velocity for positrons in the liquid phase over the vapour phase for a given reduced
electric field then follows. As the reduced electric field and hence mean energy of
the positrons increase, the average de Broglie wavelength reduces and the impact of
coherent scattering effects is reduced and the differences between transport in the
two different phases is consequently reduced.
