Physics introduction and developments in the first funding period

The SFB 1245 “Nuclei: From Fundamental Interactions to Structure and Stars” investigates the strong and electroweak interaction physics from nuclei to stars. The strong interaction described by quantum chromody- namics (QCD) is responsible for binding neutrons and protons into nuclei and for the many facets of nuclear structure physics. Combined with the electroweak interaction, it determines the structure of all nuclei in the nuclear chart in a similar way as quantum electrodynamics shapes the periodic table of elements. While the latter is well understood, it is still unclear how the nuclear chart emerges from the underlying forces.

Nuclear structure theory has evolved into a field with a systematic theoretical foundation, with nuclear forces based on QCD and advanced methods to solve the nuclear many-body problem with controlled uncertainties. Effective field theories (EFT), first proposed in the pioneering work by Steven Weinberg, have played a guiding role in this process, as they reduce the complexity of the underlying QCD theory to the relevant degrees of freedom in a systematic way. While this was first demonstrated for light nuclei, we have shown in the first funding period that this approach can be successfully extended to medium-mass and heavy nuclei. Research performed in this direction has the ultimate goal to understand the nuclear chart from first principles. Since the properties of nuclei, their existence, excitations and decays are all encoded in the nuclear chart, it represents the boundary condition for the complete evolution of known matter from the Big Bang to today.

The CRC builds on the exciting connections between the experimental and theoretical nuclear structure fron- tiers based on EFTs of the strong interaction. At low energies, chiral EFT offers a systematic basis for nuclear forces, built on the symmetries of QCD, with controlled expansions of the interactions in powers of the inverse chiral-symmetry breaking scale. This is shown in the left panel of Fig. 2, where the second column represents nucleon-nucleon interactions at different orders. The interaction between the nucleons (solid lines) is medi- ated by the exchange of pions (dashed lines), the Goldstone bosons of QCD, which are responsible for the long-range part of strong interactions. Three-nucleon (3N) forces, which emerge naturally in EFTs, enter at next-to-next-to-leading order (N2LO). Moreover, EFTs lead to a hierarchy among many-body interactions, with 4N forces at next-to-next-to-next-to-leading order (N3LO). Combining EFTs with powerful many-body methods is opening up a systematic path to investigate nuclear forces and their impact on nuclei and nuclear matter. The CRC has pioneered calculations including all 3N forces up to N3LO and ab initio advances up to 100 Sn (see Fig. 2). We have also taken a lead in exploring EFT and many-body uncertainties in ab initio calculations, which has become a major effort in the field.

Figure 1 Figure 1: Left panel: Nuclei in the nuclear chart, with the CRC highlight calculation of 100 Sn marked with a star. The blue squares represent all known nuclei, with stable nuclei in darker blue. More than half of the nuclear chart is unknown1. Right panel: Chiral EFT for nuclear forces, where the different contributions at successive orders are shown diagrammatically. Nucleons and pions are represented by solid and dashed lines, respectively. Many-body forces are highlighted in orange including the year they were derived. In the first funding period, we achieved the first ab initio calculations of nuclei including all 3N forces up to N3LO.

In strongly interacting systems three-body forces are especially important and have been the target of recent theoretical and experimental work. They also play a key role in universal properties of halo nuclei, which are explored in Halo EFT, and their connection to the Efimov effect in ultracold atoms. Three-nucleon forces are a frontier in the physics of nuclei, for shell structure and the evolution to the limits, the drip lines. Exotic nuclei become increasingly sensitive to 3N forces and other subtle components of nuclear forces, so that experiments with rare-isotope beams in this CRC provide unique insights into strong interactions. Calculations based on chiral EFT interactions also provide systematic constraints for the properties of nuclear matter in neutron stars, supernovae, and mergers. The physics of nuclear forces therefore connects nuclear structure physics with nuclear astrophysics. The exploration of next generation nuclear forces is particularly exciting, because all N3LO many-body forces are predicted with many new structures. They are only now being applied beyond the lightest nuclei and must still pass experimental precision tests. These developments come in time with the establishment of major rare isotope beam facilities like the Facility for Antiproton and Ion Research (FAIR) in Darmstadt and other new facilities and upgrades worldwide, including the Radioactive Ion Beam Facility (RIBF) at RIKEN in Japan, the Facility for Rare Isotope Beams (FRIB) in the US, the ARIEL facility at TRIUMF in Canada, and the HIE-ISOLDE upgrade at CERN, which will give great access to the unexplored regions of the nuclear chart. New initiatives in the second funding period will include all-optical charge radius measure- ments of light elements, precision studies of few-neutron correlations in nuclear reactions, and exploring shell structure towards the neutron drip line by extending the reach of gamma spectroscopy.

The electroweak interaction plays a crucial role in nuclear physics. Gauge symmetry allows using the same EFT expansion to derive electroweak operators that are consistent with the strong interaction. The couplings in nuclear forces thus largely determine also electroweak processes, and EFTs predict consistent electroweak one- and two-body currents. In chiral EFT, two-body currents, also known as meson-exchange currents, natu- rally enter at higher order, just like 3N forces. In the first funding period, we have shown that two-body currents play a crucial role in understanding the quenching puzzle of beta decays and for the S-DALINAC precision measurement of the 6Li M1 transition.

The exploration of electroweak interactions in nuclei and nuclear matter is therefore continuing as an emerging area of EFT research. Experimentally, this opens up exciting opportunities for an electron-beam machine. The superconducting Darmstadt electron linear accelerator S-DALINAC is unique worldwide to study electromagnetic processes in the energy regime of chiral EFT. We will investigate new collective excitations and use electromagnetic probes to explore forbidden transitions and the nuclear structure involved in neutrino- nucleus reactions. Another particular focus will be on the electric dipole response, which constrains the neutron matter equation of state. This will include new theory developments and novel measurements of photoabsorp- tion of nuclei.

The strong and electroweak interactions describe all reactions for the synthesis of the elements in the Uni- verse and all the microphysics relevant for how stars shine and explode in supernovae. Electroweak neutrino processes play a pivotal role in the explosion mechanism and the nucleosynthesis in core-collapse super- novae. The electroweak reactions developed in this CRC, combined with novel calculations of the nuclear matter equation of state from low to high densities and finite temperature, will provide a systematic basis for astrophysical applications. In the second funding period, we will expand our efforts to explore the nuclear physics involved in neutron star mergers, the gravitational wave signal, and the associated kilonova, where we have made pioneering contributions. Combining the advances for the nuclear matter equation of state and consistent neutrino-matter interactions with simulations of core-collapse supernovae and neutron star mergers will lead to an understanding of how nuclei, neutrinos and the equation of state impact the nucleosynthe- sis of elements in these explosive events. This will connect to questions in neutrino physics, to forefront astronomical observations of the oldest stars, which shed light on the chemical history of the elements in the Universe, and to gravitational wave detection in the new multimessenger era.

In summary, the physics of nucleonic matter ranges from universal properties at low densities to the densest matter we know to exist in neutron stars. Chiral EFT provides a link between nuclear structure and matter in stars with the underlying theory of QCD. The pioneering work in this CRC, accessing the medium-mass region within the first funding period, provides the basis for the ultimate goal of a consistent description of nuclear structure across the nuclear chart into the heavy mass region and for matter in stars. Additionally, strong and electroweak processes are key to understanding the chemical contribution from supernovae and neutron star mergers to the Universe, and will provide systematic uncertainties for nuclear matrix elements required to test fundamental symmetries. The reach of this CRC thus extends well beyond nuclear physics with a demonstrated impact on neutrino physics, astroparticle physics, and astrophysics.

1 J. Erler, N. Birge, M. Kortelainen, W. Nazarewicz, W. Olsen, A.M. Perhac, and M. Stoitsov, The limits of the nuclear landscape, Nature 468, 509 (2012).
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