Time dependent modelling of fission of superheavy elements

Abstract

In nuclear physics, spontaneous fission halflives are central in many areas, such as the study of superheavy nuclei and astrophysical nucleosynthesis. In this thesis, a new method for obtaining spontaneous fission halflives from collective coordinate energy landscapes is proposed, tested, and compared to experimental results.

The new method uses the Rayleigh quotient iteration to find the time dependent solution for the ground state in different energy landscapes. It is tested in a toy model of a rectangular barrier with an absorbing region outside the barrier against the time dependent solution of the Schrödinger equation using the Crank-Nicolson method to find the decay rate. The Rayleigh method is found to perform well for a wide range of halflives, unlike the Crank-Nicolson method, which becomes unfeasible when halflives are too long. The tests also show that the Rayleigh method is sensitive to resonances if the absorption is too low or too high. This suggests that the Rayleigh method may be used to successfully capture resonances in double barrier fission.

The Rayleigh method is also tested on potential landscapes obtained from HFB deformed calculations, comparing different interaction functionals and collective mass prescriptions. While some differences are found between different functionals, the largest differences are found between mass prescriptions, in some cases spanning more than 20 orders of magnitude. Additional investigations are proposed to further study and overcome this problem. In this work, the Reyleigh method is proposed to calculate ground states and half-lives of nuclear fission processes, discussing results and limitations.

Popular Abstract

Calculations of rate of fission, the division of atoms into two smaller fragments, is often done approximately, missing many important effects. In this thesis, we introduce a method which finds the state the nucleus reaches after a long time, and we calculate the rate from that.
This is an improvement over taking small steps in time, calculating how the fission happens over time. To get accurate results, these steps would have to be extremely small and it would take many steps to find the fission rate.
When the core of an atom, the nucleus, is large enough, it can split into two, releasing energy. This is called fissioning, and is commonly associated with nuclear power, where the energy is used to produce electricity. But fission plays a role in many more situations, such as the creation of heavy elements in stars and neutron star collisions, which affects us all since these elements are what we are made of.
Describing fission is not easy, as nuclei consist of many particles interacting in unpredictable ways. And since it is so small, quantum mechanics must be used. Most attempts avoid describing each particle’s motion, but instead look at the amount of deformation. This works because a nucleus functions very similarly to a water droplet, which properties are mostly decided by its shape, as its density is almost constant. The deformation is then used in the same way as the location of a ball moving across a landscape, where the height of the landscape corresponds to the energy required to deform the nucleus to a particular deformation.
In the case of spontaneous fission, this landscape looks like a valley separated from a large cliff by a hill. If the ball would be able to climb over the hill, it would quickly roll down the cliff, gaining speed and energy. This is what happens in fission, and the energy release is the reason nuclear power work. But because of quantum mechanics and a concept called tunneling, the ball does not need to have the energy to reach the top of the hill, as there is a small chance it will simply pass right through it.
Finding this probability is the key to calculating how quickly it will happen, and therefore the rate of the fission. There exists a formula which calculates this, using the shape of the hill, but it is only an approximation. It does not, for example, take into account interference. Since the ball is quantum mechanical, it is described as a wave, and when waves meet they can, like rings on water, cancel or amplify each other. This is interference, and it could in some cases affect the tunneling probability.
By instead calculating the wave itself, we have in this thesis found a new way to calculate the rate of fission. Since wave effects are inherently part of the solution, it does not have the limitation mentioned, and could be used in cases where interference plays a large role.

• author: Boström, Johan
• supervisor: Andrea Idini
• organization: Mathematical Physics; Department of Physics
• course: PHYM01 20211
• year: 2021
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: Rayleigh quotient iteration, Crank-Nicolson, GCM, ATDHFB, HFB, quadrupole deformation, collective mass, fission halflife, nuclear fission, nuclear physics
• language: English
• id: 9057010
• date added to LUP: 2021-06-22 14:42:57
• date last changed: 2021-06-22 14:42:57