Grant: Discovery Grants Program - Individual

In our everyday experience, particles trapped inside energy wells can escape only if they have more energy than the energy barrier; a marble trapped in a bowl stays inside unless it has enough energy to rise to the top of the bowl and get out. For microscopic particles it is possible for a particle to escape even if its energy is less than the barrier. This phenomenon is call "tunnelling." Tunnelling has been investigated almost solely for single particles. Investigations into the tunnelling of molecules began relatively recently. The simplest molecule consists of two atoms and thus has an elongated structure: this is what makes the study of tunnelling of molecules interesting and challenging. In order to escape confinement inside an energy barrier, both atoms need to tunnel out, and there are several ways this can happen. For example: the molecule breaks up into two atoms. In the proposed research we investigate how the possible breaking up of the molecule affects the probability of tunnelling. In previous work we found that for special values of the molecule's total energy, the probability is 100%, and is called "resonant tunnelling." In the case of molecular tunnelling, we want to find out how the possibility of molecular break-up will affect these resonances, i.e. we know that the probability will go down, but the question is by how much and why that amount? We will first consider a molecule moving along a straight line. We will extend our work to the more realistic case where the molecule moves in three dimensions. Our goal is to understand why the probabilities of tunnelling and reflection have the values they do and why they change with the energy of the molecule as they do, and not some other way. We will also study the special case where the molecule is very weakly bound, i.e. it will certainly break apart in attempting to tunnel. This will also be done for one and three dimensions. Our ultimate objective is to extend our study so that it can be compared with real molecules and other pairs of particles. We will also do two other investigations in the behaviour of quantum mechanical systems. This work will eventually have practical applications; the specific details are not known at this time.