Positron cross sections and transport in water

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.