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LUND UNIVERSITY LIBRARIES

Error propagation in nuclear models

Mucenieks, Artis LU (2023) FYSK02 20222
Mathematical Physics
Department of Physics
Abstract
In this thesis we perform error analysis of a nuclear model based on density-functional theory developed in Lund. The Lund model allows us to perform calculations of nuclear spectra more efficiently by constructing a simple effective Hamiltonian reproducing the quadrupole deformation and pairing interaction strength parameters of a spherical Hartree-Fock reference functional. This constraining of the Hamiltonian allows for more efficient computation. The spectra calculated using Beyond mean-field methods to solve the effective Hamiltonian involve approximations. This work allows us to quantify the uncertainties in the model using statistical methods. In particular, we perform a propagation of errors and covariance analysis to determine the... (More)
In this thesis we perform error analysis of a nuclear model based on density-functional theory developed in Lund. The Lund model allows us to perform calculations of nuclear spectra more efficiently by constructing a simple effective Hamiltonian reproducing the quadrupole deformation and pairing interaction strength parameters of a spherical Hartree-Fock reference functional. This constraining of the Hamiltonian allows for more efficient computation. The spectra calculated using Beyond mean-field methods to solve the effective Hamiltonian involve approximations. This work allows us to quantify the uncertainties in the model using statistical methods. In particular, we perform a propagation of errors and covariance analysis to determine the parameters which contribute most to the uncertainties of the calculations of energy spectra E and separation energies T.

The covariances calculated indicate that E and T are largely uncorrelated for low spin states, where as spin I=4 shows a larger degree of covariance. Through statistical analysis, we identify that the major contribution to the errors comes from the choice of the pairing parameter, but the magnitude of this contribution decreases for states with larger spin. We speculate that the different parameter sensitivities of states with spin I=2, 4, can be explained by different deformations in spinning states which lead to a breaking of time-reversal symmetry, which leads to a decreased dependence on the pairing parameter g. (Less)
Popular Abstract
Creating an accurate theoretical model of the nucleus has been something of a stumbling stone for researchers trying to apply the laws of quantum physics. Due to its complex nature the jumble of hundreds of neutrons and protons contained in the tiny nucleus resists any calculations. This has kept theoretical nuclear physics from achieving the successes of e.g. atomic physics where theory and experiment always go hand in hand in their accuracy and pushing the limits of our understanding.

Any explicit computation, attempting to describe the numerous particles and the range of possible interactions between them from the fundamental laws would require too many computational resources. Thus the most successful theories in nuclear physics... (More)
Creating an accurate theoretical model of the nucleus has been something of a stumbling stone for researchers trying to apply the laws of quantum physics. Due to its complex nature the jumble of hundreds of neutrons and protons contained in the tiny nucleus resists any calculations. This has kept theoretical nuclear physics from achieving the successes of e.g. atomic physics where theory and experiment always go hand in hand in their accuracy and pushing the limits of our understanding.

Any explicit computation, attempting to describe the numerous particles and the range of possible interactions between them from the fundamental laws would require too many computational resources. Thus the most successful theories in nuclear physics have been those which treat the numerous particles present in the nucleus by considering the interaction of individual particles with the average of all the other particles present. Performing calculations on the interactions depending on the densities of various properties in the nucleus.
These approaches simplify the computations immensely. With the downside of them being only approximations constructed such that they agree with our existing knowledge accrued by the mass of experiments.

Despite this, an attempt to formulate an effective theory of nuclei cannot be abandoned as there are some nuclei that can not be produced even in a laboratory. Crucially, those nuclei which are common in stars are inaccessible. The properties of these nuclei are of great interest for expanding our understanding of astrophysics and star formation. Therefore a reasonable next step towards a better theory of nuclei could be including error estimates in our models to see how close to experiment we can get.

Here is where we can use statistics to see just how far current theoretical models can bring us when it comes to the nucleus. Through analysis of covariance---that is how the parameters affect one another in the calculations---we can gain insight into which parameters are more important to calculations of different physical properties. This allows us to optimize the models to better reproduce these properties.

Another aspect is the propagation of errors within the model. Observing how the results of calculations change with small changes in our chosen parameters.
This can be carried forward to better understand the capability of the model to predict properties in new nuclei and quantify how confident we are in our calculations.

Now armed with some knowledge of just how wrong we are we can attempt to understand the models better. Using these methods we hope to expand our knowledge of the models and with a close look at these statistical properties to one day improve our understanding of the nucleus. (Less)
Please use this url to cite or link to this publication:
author
Mucenieks, Artis LU
supervisor
organization
course
FYSK02 20222
year
type
M2 - Bachelor Degree
subject
language
English
id
9109755
date added to LUP
2023-02-02 14:14:13
date last changed
2023-02-02 14:14:13
@misc{9109755,
  abstract     = {{In this thesis we perform error analysis of a nuclear model based on density-functional theory developed in Lund. The Lund model allows us to perform calculations of nuclear spectra more efficiently by constructing a simple effective Hamiltonian reproducing the quadrupole deformation and pairing interaction strength parameters of a spherical Hartree-Fock reference functional. This constraining of the Hamiltonian allows for more efficient computation. The spectra calculated using Beyond mean-field methods to solve the effective Hamiltonian involve approximations. This work allows us to quantify the uncertainties in the model using statistical methods. In particular, we perform a propagation of errors and covariance analysis to determine the parameters which contribute most to the uncertainties of the calculations of energy spectra E and separation energies T.

The covariances calculated indicate that E and T are largely uncorrelated for low spin states, where as spin I=4 shows a larger degree of covariance. Through statistical analysis, we identify that the major contribution to the errors comes from the choice of the pairing parameter, but the magnitude of this contribution decreases for states with larger spin. We speculate that the different parameter sensitivities of states with spin I=2, 4, can be explained by different deformations in spinning states which lead to a breaking of time-reversal symmetry, which leads to a decreased dependence on the pairing parameter g.}},
  author       = {{Mucenieks, Artis}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Error propagation in nuclear models}},
  year         = {{2023}},
}