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Titel | Few-Body Systems in Lattice Effective Field Theory |
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Autor | Nico Klein |

Publikationsform | Dissertation |

Abstract | Nuclear lattice effective field theory is a novel approach in nuclear physics combining classical effective field theory with lattice methods and newly available computational resources. It is particularly successful for few- and many-body systems, where one calculates ground state and scattering state properties using ab initio techniques. Thanks to the discretization of space and time, one can use Monte Carlo methods to evaluate physical observables and additionally, one may use discretization improvement programs as well for the reduction of lattice spacing artifacts. In contrast to lattice quantum chromodynamics, the lattice spacing does have a physical meaning, namely the cutoff which is inherent to any effective theory. Hence, it is necessary to understand the discretization effects. Such a study has been a missing part of nuclear lattice effective field theory as most calculations have been performed at a fixed lattice spacing of a=1.97 fm. I will have a thorough look at it and examine the problem from different perspectives in the following. Due to computational limitations we restrict ourselves to few-body systems, where we have a lot of data from Nijmegen partial wave analysis for nucleon-nucleon scattering, very precise knowledge on the bound state of triton and helium-4 and also various correlation theorems. The Tjon line is such a correlation theorem between triton and helium-4 binding energies which states that the two-nucleon interaction results in a correlated prediction of triton and helium binding energies while a three-nucleon interaction that fixes the triton binding energy automatically reproduces the right helium-4 binding energy. The first project looks at the deuteron binding energy and low-energy scattering observables, namely the S wave scattering length and effective range in dependence on the lattice spacing for various regularization schemes. We employ lattice spacings up to a = 0:5~fm and we show that the neutron-proton system with and without pion exchange becomes stable if the regularization scheme is chosen rightly and the lattice spacing is small enough.Secondly, I perform an analysis of 2N, 3N and 4N systems for three different lattice spacings at leading, next-to-leading and next-to-next-to-leading order. I show that the continuum correlation between 3N and 4N systems is reproduced once the lattice spacing is chosen fine enough.Lastly, I examine the few-body boson system in one dimension. Such a system does have an exact solution and hence, lattice artifacts can be observed in a very transparent way. I show that we can absorb lattice spacing artifacts systematically by adding additional operators due to a consistent power counting scheme. Finally, we can do robust continuum extrapolations. We examine systems up to and including five bosons and the remaining errors scale linearly, as the third and fourth power of the lattice spacing at leading, next-to-leading and next-to-next-to-leading order. |

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