Heiko Hergert

Atomic nuclei are among nature's most fascinating, and at the same time, most confounding objects. This is mainly due to the complicated nature of the strong interaction. Its fundamental theory in the Standard Model is Quantum Chromodynamics (QCD), which describes interactions of quarks and gluons. While deceptively easy to write down, QCD is very hard to solve. Describing nuclei based on QCD is even more challenging, because nucleons are composite objects that have a complicated quark and gluon substructure themselves.

The interplay of complicated nuclear interactions and quantum-mechanical many-body effects gives rise to a rich variety of nuclear phenomena, especially in exotic nuclei that are the focus of the experimental program at NSCL/FRIB. A reliable theoretical framework is required to support the experimental efforts, e.g., in the analysis of data or the planning of future experiments.

Ab initio (i.e., first-principles) nuclear many-body theory seeks to provide such a framework, by combining

• nuclear interactions from chiral effective field theory (EFT), which are formulated in terms of nucleons instead of quarks, but maintain a stringent link with QCD,
• renormalization group (RG) methods to tune the resolution scale and facilitate the practical aspects of a many-body calculation, and
• efficient techniques to solve the many-body Schrödinger equation.

An important feature of this approach is that we control the theoretical uncertainties of each aspect of a calculation, and are able to make systematic improvements to reduce the theoretical error bar. While open issues remain, this provides us with a natural road map towards a predictive model of nuclei.

My own work focuses on the aforementioned RG and many-body techniques. By developing efficient new methods, my colleagues and I have extended the range of accessible nuclei from light isotopes like carbon (atomic number 6) to tin (atomic number 50). After achieving this for isolated "magic" nuclei, the counterpart to chemistry's noble gases, I am now developing tools to calculate the properties of entire chains of so-called open-shell nuclei, and increase the number of accessible isotopes more than tenfold.

My research program offers many opportunities for collaboration with experimental colleagues at NSCL/FRIB. The confrontation of our calculations with new experimental data will also allow us to diagnose and resolve issues of the chiral interactions, in collaboration with EFT practitioners.

Computation is an important aspect of my work. Calculations are performed on systems ranging from mid-size computing clusters to massively parallel supercomputers. Ensuring  the good use of high-performance computing resources despite the continuously changing architectures is a challenge, and relying on the hardware alone for performance is not enough. For instance, one of the biggest practical obstacles we face are the massive memory requirements of three-nucleon interactions, which cannot be met by even the largest supercomputers. To overcome such limitations and increase efficiency, I am also working on improving the algorithms and numerical techniques used by ab initio practitioners.

Collaborations with computer scientists, e.g., at MSU's new Department of Computational Mathematics, Science, and Engineering, are essential to achieve these goals, and provide opportunities to obtain a dual degree for interested  Ph. D. students. Moreover, I am a member of the NUCLEI project, a national collaborative effort between nuclear theorists, computer scientists, and  mathematicians that is supported  by the Department of Energy's SciDAC (Scientific Discovery Through Advanced Computing) program.

Ground-state energies of oxygen isotopes from chiral two- plus three-nucleon interactions, calculated with a variety of ab initio many-body methods. The calculations consistently predict  that ²⁴O is the most neutron-rich bound oxygen isotope in nature, marking the position of the so-called neutron drip line (cf. PRL 110, 242501).