Periodic Reporting for period 2 - EXOTIC (Emergent Complexity from strong Interactions)
Reporting period: 2023-05-01 to 2024-10-31
The matter that surrounds us and that we are made off consists of atomic nuclei. These are composite particles bound together by the strong force. While we know the fundamental theory of the strong interactions, quantum chromodynamics, nuclei cannot be calculated in this framework. Rather, first principles calculations of these fundamental constituents of matter rely on the observed particles, neutrons and protons, and their interactions given in terms of chiral effective field theory as developed by Nobel laureate Steven Weinberg. However, despite many decades of developing nuclear many-body methods, ab initio calculations along the nuclear chart are not yet possible, except for the framework of nuclear lattice effective field theory (NLEFT) employed here. This rather novel method combines the effective nuclear forces with stochastic methods to solve the many-body problem. Such stochastic methods are often used in particle and condensed matter physics, but so far not in the realm of nuclear structure and reactions.
This projects aims at providing methods to investigate nuclei along the nuclear charts, their structure and reactions
and providing answers to a set of questions. These are: Frist, what are the limits of stability of nuclei? Adding additional protons and neutrons to a given nucleus final leads to the case that stability is lost. The precise location of these drip lines is pertinent to the study of element generation as investigated at radioactive beam facilities worldwide. The second set of questions concerns the third dimension of the nuclear chart, the study of the formation of hyper nuclei, where a neutron is substituted by a Lambda hyperon, which contains one valence strange quark, adding an extra dimension to the light up and down quarks. Our method shows a very mild scaling with atomic number $A$, quite in contrast to the conventional methods. This will allow us to map out the third dimension of the nuclear chart. Related to this is the influence of strangeness on the neutron matter equation of state, that is of prime importance to understanding the generation of gravitational waves in the mergers of two neutron stars. Third, the element generation in the Big Bang and in stars exhibits some fine-tuning, that is so far not understood. In our framework, we can vary the fundamental parameters of the Standard Model like the quark masses or the electromagnetic fine-structure constant, that governs the repulsion between the charged constituents of the nuclei, the protons. While these parameters can not be modified in experiment, our simulations allow to address alternative version of the universe with modified parameters, allowing to eventually address the question of how accidental life on Earth really is?
This projects aims at providing methods to investigate nuclei along the nuclear charts, their structure and reactions
and providing answers to a set of questions. These are: Frist, what are the limits of stability of nuclei? Adding additional protons and neutrons to a given nucleus final leads to the case that stability is lost. The precise location of these drip lines is pertinent to the study of element generation as investigated at radioactive beam facilities worldwide. The second set of questions concerns the third dimension of the nuclear chart, the study of the formation of hyper nuclei, where a neutron is substituted by a Lambda hyperon, which contains one valence strange quark, adding an extra dimension to the light up and down quarks. Our method shows a very mild scaling with atomic number $A$, quite in contrast to the conventional methods. This will allow us to map out the third dimension of the nuclear chart. Related to this is the influence of strangeness on the neutron matter equation of state, that is of prime importance to understanding the generation of gravitational waves in the mergers of two neutron stars. Third, the element generation in the Big Bang and in stars exhibits some fine-tuning, that is so far not understood. In our framework, we can vary the fundamental parameters of the Standard Model like the quark masses or the electromagnetic fine-structure constant, that governs the repulsion between the charged constituents of the nuclei, the protons. While these parameters can not be modified in experiment, our simulations allow to address alternative version of the universe with modified parameters, allowing to eventually address the question of how accidental life on Earth really is?
We have made important progress in achieving the goals outlined above. First, method development is necessary to address nuclear structure and reactions beyond what was possible so far. This is related to the so-called fermion sign problem, that complicates or even hinders simulations at finite matter density. While it is known that the approximate Wigner SU(4) symmetry underlying the nuclear interactions to some extent tames this problem, to perform precision calculations or larger mass numbers beyond the oxygen region, we had to develop novel quantum-many body problems. Of particular importance here is the wave function matching transformation, that enables calculations way beyond what was believed to be possible at the start of this project. Another important new tool that was developed in this project is a model-independent method to map out the tomography of a given nuclear state in terms of its matter distribution and resolving possible cluster structures. These tomographic images have opened the new field of nuclear structure studies in high-energy nuclear collisions at CERN. We have further developed an algorithm, that allows to simulate dense neutron matter as it appears in the interior of neutron stars.
Concerning physics results, we have first further developed the so-called minimal nuclear interaction, that allows to describe light and medium-mass nuclei as well as neutron matter with no more than a few percent deviations in energies and radii. This allowed us to completely describe the carbon spectrum up to excitation energies of about 20 MeV and give the first model-independent description of the duality of alpha-cluster and shell model states. Within this framework, we could also resolve a puzzle posed by data from Mainz on the transition form factor of helium-4. Using wave function matching and going to high orders in the expansion of the underlying expansion of the nuclear forces, we could describe the ground state energies and radii of nuclei form $A=2$ to $A=58$, which was never achieved before. This method was also
employed to make predictions for the charge radii of silicon isotopes measured later using laser spectroscopy as well giving a deeper understanding of the vector- and axial-vector structure functions in neutron matter, that have a large impact on neutrino heating and shock revival in core-collapse supernovae. Based on these precise nucleonic interactions,
precision calculations of hypernuclei into the mid-mass region have been performed and the related appearance of strangeness in neutron stars has been critically examined. In addition, we have set new bounds on the possible
variations of the fundamental parameters of the Standard Model in Big Bang nucleosynthesis, providing for the first time systematic uncertainties in such type of investigation.
Concerning physics results, we have first further developed the so-called minimal nuclear interaction, that allows to describe light and medium-mass nuclei as well as neutron matter with no more than a few percent deviations in energies and radii. This allowed us to completely describe the carbon spectrum up to excitation energies of about 20 MeV and give the first model-independent description of the duality of alpha-cluster and shell model states. Within this framework, we could also resolve a puzzle posed by data from Mainz on the transition form factor of helium-4. Using wave function matching and going to high orders in the expansion of the underlying expansion of the nuclear forces, we could describe the ground state energies and radii of nuclei form $A=2$ to $A=58$, which was never achieved before. This method was also
employed to make predictions for the charge radii of silicon isotopes measured later using laser spectroscopy as well giving a deeper understanding of the vector- and axial-vector structure functions in neutron matter, that have a large impact on neutrino heating and shock revival in core-collapse supernovae. Based on these precise nucleonic interactions,
precision calculations of hypernuclei into the mid-mass region have been performed and the related appearance of strangeness in neutron stars has been critically examined. In addition, we have set new bounds on the possible
variations of the fundamental parameters of the Standard Model in Big Bang nucleosynthesis, providing for the first time systematic uncertainties in such type of investigation.
We have clearly advanced nuclear theory beyond the state of the art in various aspects by providing computational tools that allow for stochastic simulations of strongly interacting systems in areas that have not been possible before, such
as investigating neutron matter at densities pertinent to the inside of neutron stars, that is at densities as high as five times nuclear matter density.
as investigating neutron matter at densities pertinent to the inside of neutron stars, that is at densities as high as five times nuclear matter density.