title: Structure and breakup reactions of neutron halo nuclei
Creators: name: Göbel, Matthias
Publisher: name: UNSPECIFIED
Year: 2024

description: Although there are only two building blocks for nuclear matter, protons and neutrons, there are plenty of nuclear systems and phenomena that emerge from the interaction between these two building blocks. The great number of systems is manifested in the nuclear chart containing thousands of bound nuclear systems. This thesis focuses on a special type of exotic nuclear systems, the two-neutron halo nuclei. Halo nuclei are systems displaying a significant spatial separation between a more tightly bound core and some additional nucleons which are more loosely bound. The latter are called halo nucleons. Two-neutron halos are those halo systems that have two neutrons as halo nucleons. Prominent examples are ¹¹Li and ⁶He. Halo nuclei are highly non-classical systems requiring a quantum mechanical description. The halo nucleons spend most of the time outside of the range of interaction.

In this thesis, these nuclei will be investigated using the framework of halo effective field theory (halo EFT). Halo EFT is an EFT with the core and the halo nucleons as degrees of freedom. It makes use of the separation of scales and offers a systematic expansion of the results in the low-momentum scale over the high-momentum scale. Thereby, it also provides robust uncertainty estimates.

The aim of this work is to advance the understanding of these systems by calculating different observables allowing for comparison with experiments and, thereby, validation of our understanding of these systems. Concretely, the E1 strength distribution of ¹¹Li is calculated based on a description of the ground state in the Faddeev formalism and the evaluation of the E1 operator in a partial-wave basis. The role of the core spin in the description of the ground state is investigated in detail, and results that are also applicable to other two-neutron halo nuclei with s-wave interactions are derived. In the calculation of the E1 strength, also final-state interactions (FSIs), interactions subsequent to the breakup distorting the final spectrum, are taken into account. A perturbative scheme for including multiple different interactions that preserves unitarity (isometry) is developed. It is based on the Møller distortion operators. It is found that neutron-neutron FSI is here the most important FSI. The results for the E1 strength are also compared to experimental data from RIKEN. Agreement within the EFT's uncertainty bands is found. Also, a detailed comparison with the calculations from Hongo and Son, who constructed an EFT without an explicit neutron-core interaction and applied it to ¹¹Li, is done. This comparison confirms the expectation of Hongo and Son that ¹¹Li is not the ideal playground for their EFT.

Another observable that is experimentally well accessible is the neutron-neutron relative-energy distribution measured subsequent to the knockout of the halo's core. In addition to testing the current understanding of halo nuclei, this observable can also be used to measure the strength of the neutron-neutron interaction since it is heavily influenced by the neutron-neutron FSI. If this interaction is parameterized in terms of the effective-range expansion for the real part of the on-shell t-matrix's denominator, the leading-order parameter is the neutron-neutron scattering length. In order to extract this scattering length from a measured relative-energy distribution following a knockout reaction, one needs theoretical predictions for the distribution parameterized by this scattering length. Then the theory prediction can be fitted to the experimental data. The aim of this part of this work is to provide the theoretical distribution for the reaction ⁶He(p,p'α)nn, i.e., the knockout of the α particle out of ⁶He. For this purpose, the ground state of ⁶He is calculated in halo EFT and thoroughly benchmarked against well-established three-body model calculations. These comparisons show the robustness of the EFT results and also highlight the EFT's advantage of providing uncertainty estimates. In the next step, the final-state interactions are taken into account. The approximative approach of so-called FSI enhancement factors is investigated in detail and benchmarked against the exact calculation. The final result shows that this distribution displays a significant dependence on the scattering length via its shape in the region of relative energies up to 1 MeV. Varying the scattering length by 2 fm results in a change of a characteristic shape parameter by approximately 10 %. The main result was obtained using the most important partial-wave component. In addition to that, also the contributions from other partial waves are investigated. It is found that these are not relevant in the low-energy region of this distribution.

The research on neutron-neutron relative-energy distributions is continued by investigating the universality of the distributions of different two-neutron s-wave halo nuclei. It is found that the distributions of the halo nuclei ¹¹Li, ¹⁴Be, ¹⁷B, ¹⁹B, and ²²C are quite similar if plotted as a function of relative energy over two-neutron separation energy and if the normalization is adjusted. Moreover, we show that an approximate description can be obtained by putting the neutron-neutron interaction as well as the neutron-core interaction into the unitarity limit. The effects of neutron-neutron final-state interactions can be incorporated into this universal description using enhancement factors. It is found that for the final distribution with neutron-neutron FSI for these nuclei, the deviation of the actual curve from the universal prediction is typically below 20 % for relative energies up to four times the two-neutron separation energy of the respective nucleus.

Finally, the formalism and derivations for a computer code that can calculate the ground state of two-neutron halos in momentum space with arbitrary many separable interactions in arbitrary partial waves are presented. This computer code might simplify future investigations of other two-neutron halos in halo EFT.