Positron cross sections and transport in water
Date
2016
Authors
Tattersall, Wade
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Abstract
A detailed understanding of the behaviour of positrons and
electrons as they pass through liquids is critical for a number
of applications, from positron emission tomography and ion
therapy to cosmic ray detectors and materials characterisation.
In particular, transport in liquid water is vital for medical
applications because of its similarity to human tissue, and is an
area of continued research. This thesis presents newly measured
experimental cross sections for positrons in water as well as
several Monte Carlo simulation techniques aimed at improving our
models of positron and electron transport. In particular, special
efforts have been made to model the effects of elastic coherent
scattering, which arise due to the position and velocity
correlations between molecules in liquids and other dense media.
The experimental scattering results include the first
measurements of integral and differential elastic positron cross
sections for water vapour, as well as detailed grand total and
positronium formation cross sections for the same. Performed on
the positron beamline apparatus at the Australian National
University, this transmission experiment passed a high-resolution
beam of positrons through a scattering cell containing water
vapour. The parallel component of the energy of the positrons
after scattering was analysed to determine the ratio between the
scattered and unscattered portions of the beam, from which
absolute total cross sections were calculated. The experiment
further utilised a differentiated magnetic field to separate
elastic scattering from the other scattering processes, and to
distinguish between scattering angles in order to measure
angle-differential cross sections.
An original Monte Carlo track-structure simulation code has been
written which aims to precisely model the transport behaviour of
electrons and positrons in dilute gases, dense gases and liquids.
This simulation incorporates several new features to improve its
ability to model systems with high particle loss rates, varying
electric fields and fully-differential ionisation interactions.
Each feature has been rigorously tested against benchmark systems
from the literature and, where necessary, against Boltzmann
equation solutions of new benchmark systems. The simulation has
also been applied to model elements of the positron trapping
apparatus which is a critical component of the positron
scattering experiment.
The simulation's validity has been extended beyond dilute gases
by including a treatment of the coherent elastic scattering that
is caused by the structure of dense media. Following the theories
of Van Hove, Cohen and Lekner, either a static or dynamic
structure factor can be combined with gas-phase cross sections to
form a modified scattering cross section that partially accounts
for the temporal and spatial correlations of nearby molecules.
The benchmarked Monte Carlo simulation techniques are then used
to calculate transport profiles for positrons in liquid water,
using the measured water cross sections. These profiles are
estimates of the spatial distributions of positronium formation
and energy deposition, from the positrons' emission until their
first positronium formation event. Comparisons between
simulations employing different cross section sets demonstrate
the importance of a complete and accurate set of scattering cross
sections for positrons in water.
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Keywords
positron, scattering, water, swarm, transport, Monte Carlo, diffusion, energy deposition
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Thesis (PhD)
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