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Universality in Systems of up to Four Particles — From Nuclei to Ultracold Atoms

Christiane H. Schmickler

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Universal physics manifests in low-energy phenomena over a large array of different systems from nuclear to atomic physics. Here, two interesting aspects of universality are studied using the Gaussian Expansion Method (GEM). This is a variational method that uses products of Gaussians as basis functions. Gaussian potentials are used as a short-range potential. The first aspect is the behaviour close to the dimer + atom breakup threshold of Efimov states and associated universal tetramers in ultra-cold mixtures of alkali atoms. These can be treated as bosons here. It is shown that trimer and tetramer vanish into the threshold at almost the same point. The predictions of effective Efimov states in the vicinity of the dimer + atom breakup threshold are addressed, but the results are inconclusive. The second aspect is the interplay between universal states of up to four bosons and the Coulomb interaction. This is interesting because it opens up nuclear physics to the investigation. First, the effect of the Coulomb interaction on universal states is studied in natural units. This introduces a scale for the Coulomb potential's strength relative to the strength of the short-range Gaussian potential. A generalised Efimov plot of the binding energies of states of charged bosons versus the Coulomb-modified scattering length is shown. This plot illustrates the impact of different relative strengths of the Coulomb potential on universal states. To complement this analysis, the structure is also calculated via root mean square (rms) radius calculations and contour plots. The results are then applied to the excited state of 17 F, which has a proton halo. The binding energy of this state can be reproduced after fixing the effective range of the potential to the physical value. The N α system proved more problematic. It was found that the ground state of 12 C was too deep to be described within the framework used and the highest excited state of 16 O below the 4α breakup threshold proved difficult to describe. I discuss possible reasons for this. In the last part I studied the zero-range limit in the presence of the Coulomb interaction. I show that my results for the dimer and trimer can be rescaled to coincide with the zero-range result. An extrapolation towards the zero-range limit for the tetramer ground state is also presented.

DOI
10.25534/tuprints-00011780

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Universal physics manifests in low-energy phenomena over a large array of different systems from nuclear to atomic physics. Here, two interesting aspects of universality are studied using the Gaussian Expansion Method (GEM). This is a variational method that uses products of Gaussians as basis functions. Gaussian potentials are used as a short-range potential. The first aspect is the behaviour close to the dimer + atom breakup threshold of Efimov states and associated universal tetramers in ultra-cold mixtures of alkali atoms. These can be treated as bosons here. It is shown that trimer and tetramer vanish into the threshold at almost the same point. The predictions of effective Efimov states in the vicinity of the dimer + atom breakup threshold are addressed, but the results are inconclusive. The second aspect is the interplay between universal states of up to four bosons and the Coulomb interaction. This is interesting because it opens up nuclear physics to the investigation. First, the effect of the Coulomb interaction on universal states is studied in natural units. This introduces a scale for the Coulomb potential's strength relative to the strength of the short-range Gaussian potential. A generalised Efimov plot of the binding energies of states of charged bosons versus the Coulomb-modified scattering length is shown. This plot illustrates the impact of different relative strengths of the Coulomb potential on universal states. To complement this analysis, the structure is also calculated via root mean square (rms) radius calculations and contour plots. The results are then applied to the excited state of 17 F, which has a proton halo. The binding energy of this state can be reproduced after fixing the effective range of the potential to the physical value. The N α system proved more problematic. It was found that the ground state of 12 C was too deep to be described within the framework used and the highest excited state of 16 O below the 4α breakup threshold proved difficult to describe. I discuss possible reasons for this. In the last part I studied the zero-range limit in the presence of the Coulomb interaction. I show that my results for the dimer and trimer can be rescaled to coincide with the zero-range result. An extrapolation towards the zero-range limit for the tetramer ground state is also presented.
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