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| Dissertation / PhD Thesis | GSI-2026-00165 |
2025
Please use a persistent id in citations: urn:nbn:de:hebis:30:3-909607
Abstract: Nearly the entire matter in the universe consists of atoms. The electron shell occupies almost the whole volume of the atom, but the vast majority of the atomic mass is concentrated in the tiny nucleus at the center. In the nucleus, protons and neutrons are held together by the strong interaction. The fundamental theory of the strong interaction is quantum chromodynamics, but it cannot yet be solved directly for nuclear matter.To understand nuclear matter, we must draw conclusions from experimental observations. In addition to measurements of atomic nuclei, astrophysical observations provide valuable insights into nuclear matter. Neutron stars are composed of nuclear matter. By measuring the masses and radii of neutron stars, we can place constraints on the properties of nuclear matter. The equation of state (EoS) relates thermodynamic state variables, and thus encapsulates information about the behavior of the considered matter. The Tolman-Oppenheimer-Volkoff equations allow us to link the EoS and the proportions of neutron stars, allowing for inference on the EoS.The recent detection of gravitational waves, emitted during the merger of two neutron stars, was not only a breakthrough in astrophysics, but provided valuable input on the EoS of nuclear matter. Constraints on the EoS derived from neutron star observations are particularly insightful, because nuclear matter is probed at much higher density than present in atomic nuclei.Such densities can, in terrestrial measurements, only be reached through collisions of heavy atomic nuclei. During heavy-ion collisions, the nuclei are heavily compressed, enabling the study of the high-density EoS. Measurements of heavy-ion collisions are provided with excellent accuracy thanks to tremendous experimental efforts. However, conclusions about the dense stage of the collision can only be drawn using theoretical models, because only the final state of the collision can be observed experimentally.Heavy-ion collisions are highly dynamic processes. To model the evolution of the non-equilibrium system, transport calculations are performed. These calculations bridge the early stage, where the EoS can be probed at high densities, and the final state, where experimental data is available. The EoS enters the transport calculation through nuclear potentials, which are known to strongly influence the azimuthal anisotropy of the proton distribution in the final state. Flow coefficients quantify this anisotropy, meaning they provide an excellent observable for studying the EoS.In this thesis, the sensitivity of flow coefficients to the EoS is verified in collisions of gold nuclei, as performed at the HADES experiment. Due to the high precision of the measurement, flow coefficients are available, subdivided into small regions in phase-space. A sensitivity study is performed, aiming to identify the regions in phase-space, where information about the EoS can be obtained cleanly. For this purpose, the impact of light nuclei formation is estimated by comparing two different models for light nuclei treatment. This is crucial, as a significant fraction of protons are bound in nuclei. A region is identified where the flow coefficients are sensitive to the EoS but not to the formation mechanism for light nuclei. In this region, robust conclusions about the EoS can be drawn.For a quantitative determination of the EoS, realistic potentials must be employed. To achieve this, a momentum-dependent term is added to the nuclear potential in the transport model. Along with the inclusion of the Coulomb potential, the model is well-suited for a quantitative study of the EoS. To carry out this study in a controlled manner, a Bayesian analysis is performed within the scope of this thesis. This way, a systematic estimate of the EoS is obtained with statistical uncertainties. The posterior distribution is found through Markov-Chain-Monte-Carlo sampling, for which the model must be evaluated numerous times. To reduce computational costs, the transport model is emulated using a Gaussian Process, making this approach feasible. The posterior distribution favors a relatively stiff EoS, with a small statistical uncertainty. This small uncertainty suggests that the experimental data contains sufficient information about the EoS for this study. However, the uncertainty does not account for systematic contributions arising from choices made in the model's implementation. Given that different modeling choices can affect the extracted EoS, it will be important to address these differences in future work. To learn more about the density dependence of the EoS, transport calculations are compared with measurements from the FOPI experiment. This dataset has the advantage that a broader range in collision energy is covered. As higher collision energies translate to greater compression, the density-dependence of the EoS can be accessed more directly. By calculating the chi-squared, the agreement of both a soft and stiff EoS to the measurement is quantified. One observes that overall a soft EoS is preferred. Examining the data more differentially, one observes that there may be a stiffening in the EoS towards higher densities.Finally, the formation of light nuclei is studied at collision energies in the range of the Beam Energy Scan program. This program aims to identify structures in the phase diagram, such as the possible existence of a critical point. Near a critical point, fluctuations of the baryon number are significantly enhanced, which should reflect in the yield of light nuclei, as they are composite particles of protons and neutrons, both of which are baryons.In the later stages of heavy-ion collisions, the formation of light nuclei is dynamically modeled through the creation of nuclei in multiparticle reactions within a transport calculation. By examining the scattering rates of nuclei, it is shown that the later stage of the hybrid model plays a crucial role, particularly in the dynamics of light nuclei. Furthermore, ratios of light nuclei, which are sensitive to fluctuations, are calculated. However, the model does not account for critical fluctuations, meaning that not all ratios can be described.
Note: Dissertation, GU Frankfurt, 2025
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