Applications of Pionless EFT in Atomic and Nuclear Theory

Author

Samuel Bryan Emmons, University of TennesseeFollow

Date of Award

12-2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Physics

Major Professor

Lucas Platter

Committee Members

Katherine Grzywacz-Jones, Lawrence Heilbronn, Thomas Papenbrock

Abstract

Effective Field Theory (EFT) is a useful approach in situations where the physical system in question exhibits a separation of scales that can be used to form a perturbative expansion in a ratio of elementary parameters of the system. In a low-energy EFT such as the so-called pionless EFT, such an expansion may be carried out in the ratio of the effective range to the scattering length. It is referred to as pionless EFT because of its origins in nuclear physics, where it is used to describe nuclear interactions with effective degrees of freedom without explicitly including the strong nuclear force, which is mediated by pion exchange. However, it may also be referred to as short-range EFT in non-nuclear contexts. In atomic physics, this theory is applicable when the scattering length between atoms is much larger than the underlying range of the interaction, such as in a cold atomic gas of ⁴He. Nuclear physics applications range from describing the properties of weakly bound nuclei like deuterium to halo nuclei such as ¹¹Be. In this dissertation, we have applied pionless EFT to a homogeneous, balanced fermionic gas to determine universal relations that describe various parameters for any such system regardless of the short-range details of the underlying interaction. Additionally, we have studied a heteronuclear cold-atomic mixture and the interesting phenomena that occur when the interspecies scattering length is large compared to either the short range interaction distance, or any intraspecies scattering lengths. We calculated three-body recombination and relaxation rates at finite temperatures and compared our results with available experimental data. In nuclear physics, we have calculated the polarization corrections to the Lamb shift in muonic deuterium to next-to-leading order in the deuteron effective range, ρ_d. These examples comprise a small sample of the possible range of applications of pionless EFT, and another goal of this dissertation is to make accessible the basic principles of the theory for its further use.

Recommended Citation

Emmons, Samuel Bryan, "Applications of Pionless EFT in Atomic and Nuclear Theory. " PhD diss., University of Tennessee, 2018.
https://trace.tennessee.edu/utk_graddiss/5288