A positron in an electron gas

Materials consist of large numbers of atoms joined together by chemical bonds. Chemical bonds are formed by electrons which congregate in the regions between atoms because they are strongly attracted to the two neighbouring nuclei. Understanding the behaviour of electrons in materials is the key to understanding their chemical bonding, their conduction of electricity, and their optical properties such as their colour or refractive index.Scientists have developed many techniques for investigating the behaviour of electrons in materials. One such technique is positron annihilation spectroscopy. The positron is the anti-particle of the electron and when an electron and positron come into contact they annihilate one another, their energy appearing as a flash of light. Measuring this light gives information about the material in the region of the annihilation event. Positrons are formed in certain radio-active decay processes, and the birth of a positron is accompanied by a characteristic flash of light. The time between the flash of light signalling the birth of a positron and the flash of light produced at its annihilation event inside a material is only about a billionth of a second, but it can be measured accurately, giving the lifetime of the positron. Measuring the lifetime of positrons is a sensitive and non-destructive method for detecting the size, location, and concentration of defects in materials. Positron annihilation spectroscopy can also give information about other aspects of the behaviour of electrons in materials.The aim of positron annihilation experiments is to study the properties exhibited by a material without the changes due to the presence of the positron. It is therefore necessary to understand how the positron interacts with the electrons to interpret the experimental results. In this project we will perform quantum mechanical calculations of a positron immersed within a gas of electrons. Physicists have found it very useful to consider mean-field pictures of complicated systems of interacting particles. In a mean field theory the particles are assumed to move independently of one another while feeling the average effect of all the other particles. We will study a positron in an electron gas using a form of quantum mechanical mean field theory, and then we will build in the correlations between the motions of the particles using sophisticated quantum Monte Carlo methods, which are computational methods based on choosing random numbers. We will study how the positron attracts electrons to it as it moves through the electron gas and how the interactions with the electrons affects the light which is produced in the electron-positron annihilation event. We hope that our work will give insights into electron-positron interactions and provide some practical help in devising schemes for modelling electron-positron interactions in real materials.