Streamlining the Nuclear Force

An optimized nuclear force model yields a high-precision interaction with an unexpected descriptive power.

Graph of difference between calculated and experimentally measured masses of oxygen isotopes as a function of mass number.
Image courtesy of [source]
Difference between calculated and experimentally measured masses of oxygen isotopes as a function of mass number.  The blue line represents the predictive power of the standard interaction model approach in calculating mass.  The line in red represents the optimized coupled cluster method.  The prediction power of the new optimized method shows less deviation between the calculated and measured mass (the difference hovers around zero), indicating that it is much closer to measured values than those computed with the standard interaction (blue).  See Phys. Rev. Lett. 110, 192502 (2013).

The Science

Theoretical nuclear structure calculations require the development of precision forces that describe how protons and neutrons (nucleons) interact with each other. These interactions are responsible for all nuclear properties that scientists measure in the laboratory. Combining very powerful effective field theory derivations of the nuclear interaction and multidimensional optimization techniques, theorists were able to generate a very precise two-body interaction that reproduces experimental data in neutron rich Oxygen isotopes.

The Impact

Most calculations to date required a three-body interaction to obtain reasonable descriptions of nuclear masses, excitations and radii. However, three-body interactions lead to significant computational cost. The newly derived and optimized interaction reproduces nucleon-nucleon scattering data up to 125 MeV. The new interaction yields very good agreement with binding energies and radii for A=3,4 nuclei, and it captures measurable nuclear properties without resorting to three-nucleon forces. The role of three-nucleon forces has to be revisited in view of the optimized two-body interaction.


“Less pain and more gain” is the optimistic perspective from a new model of the nuclear interaction. This interaction was systematically derived using the powerful tools of effective field theory. Such a description preserves the symmetries of the underlying theory of the strong nuclear force, quantum chromodynamics (QCD), while enabling calculations of the properties of medium mass nuclei. In the past decade, models of the strong force that resulted from this procedure pointed to the need to include three-body forces for an accurate description of nuclear properties. More recently, nuclear physics theoreticians revisited these models and used state-of-the-art optimization methods to construct a high-precision potential with only two-body interactions. They showed that certain key aspects of atomic nuclei might be understood with two-nucleon forces alone. The new model requires less computational resources than the previous models and indeed poses the question whether more scientific gain is possible with less computational pain.


Gaute Hagen
Physics Division, Oak Ridge National Laboratory


This work was supported by the Research Council of Norway under contract ISP-Fysikk/216699;by the Office of Nuclear Physics, U.S. Department of Energy (Oak Ridge National Laboratory), under Grants No. DE-FG02-03ER41270 (University of Idaho), No. DE-FG02-96ER40963 (University of Tennessee), No. DE-AC02-06CH11357 (Argonne), and No. DESC0008499 (NUCLEI SciDAC collaboration); by the Swedish Research Council (dnr 2007-4078), and by the European Research Council (ERC-StG-240603). Computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Oak Ridge Leadership Computing Facility located in the Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under Contract No. DE-AC05-00OR22725, and used computational resources of the National Center for Computational Sciences, the National Institute for Computational Sciences, and the Notur project in Norway.


A. Ekström, G. Baardsen, C. Forssén, G. Hagen, M. Hjorth-Jensen, G. R. Jansen, R. Machleidt, W. Nazarewicz, T. Papenbrock, J. Sarich, and S. M. Wild, “An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order,” Phys. Rev. Lett. 110, 192502 (2013)

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