The strong interaction is the force that binds atomic nuclei.  But this force is not naturally available in a form that is practical to use in calculations of the properties and reactions of nuclei. Methods developed and applied in this project establish this force in a systematic expansion using effective field theory (EFT) and then modify it for practical applications using the similarity renormalization group (SRG) and its in-medium counterpart (IM-SRG).  The growing need for theoretical error bars was addressed with pioneering applications of Bayesian methods to the uncertainty quantification (UQ) of EFT.  New calculations were made of light and medium-mass nuclei, and formal developments were made for EFT. Other research focuses on electron scattering from light nuclei, the reaction mechanism and the investigation of short distance effects.  The problems attacked in this project address central questions in nuclear physics as identified in the NSAC Long Range Plan. Specific contributions are summarized below. The EFT and RG methods for nuclear forces, techniques for finite basis corrections in many-body calculations, and the UQ methods that were developed in this project are being used by many groups in low-energy nuclear physics.  

The training received by students and postdoctoral research associates in carrying out the project has contributed directly to the building of a diverse scientific workforce. The mix of analytical and numerical computation our students and postdocs employed to solve complex problems is excellent preparation for both academic and industrial research. Five graduate students and two postdocs were trained during the project.  Results were disseminated through publications in refereed journals and through talks at conferences/workshops.  A new course for upper-level physics majors was developed on forefront research in all of Nuclear Physics, using the decadal survey and the Long Range Plan as a guide. Outreach efforts have brought interactive science to a wide range of Ohio residents, with particular emphasis on young women in Lima, OH.

Specific accomplishments in this project include:

* The SRG is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. We made benchmark calculations with SRG-evolved interactions in light nuclei and studied the nature of two-body universality.  A new understanding of the RG evolution of deuteron electrodisintegration was obtained, including the impact of resolution on final state interactions and nuclear factorization. New frameworks for computing the SRG evolution of three-nucleon (3N) forces in a plane-wave basis and in hyperspherical momentum representation were developed and applied. 

*  A large-scale IM-SRG code capable of handling arbitrary NN and 3N interactions was developed and applied in an extensive study of medium- to heavy-mass closed-shell nuclei. The IM-SRG was also formulated for open-shell nuclei using a multi-reference formalism based on developments from quantum chemistry, and applied  to perform the first ab initio study of even oxygen isotopes with chiral NN and 3N Hamiltonians.  We presented the first ab initio construction of valence-space Hamiltonians for medium- mass nuclei based on chiral two- and three-nucleon interactions using the IM-SRG, which were successfully applied to spectroscopy in light and medium-mass nuclei. 

* We extended our development of corrections to the ground-state energies and radii of atomic nuclei that result from the limitations of finite harmonic oscillator expansions, with refined estimates generalized to non-zero angular momentum, ultraviolet truncation errors, and a demonstration that the infrared corrections depend only on measurable quantities.

* We have investigated the errors introduced in theoretical modeling of the deuteron cross section due to the input of form factors, wave functions and nucleon-nucleon parametrizations. We were able to identify kinematic regimes suitable for extracting momentum distributions, and we have provided a much-needed theoretical error band. 

* Work applying our expertise in electron scattering from light nuclei to neutrino scattering from the deuteron was initiated, in particular calculations for the neutral current reaction.  

* We made pioneering applications of Bayesian statistics to truncation errors in EFTs and extended the application for chiral EFT, including statistical estimates of the expansion breakdown scale.  A detailed framework for Bayesian parameter estimation for EFTs, including diagnostics, was also developed. 

* Pionless EFT is a robust approach to very low-energy nuclear physics as well as a theoretical laboratory for more general EFT developments.  We developed and applied new expansions around the unitary limit (as in cold atom physics) and included Coulomb effects consistently in light systems. 

* We studied regulator artifacts for chiral EFT, which contribute to the development of improved nuclear forces.  New interactions with reduced artifacts were applied successfully to few-body systems and light nuclei.

* We developed a new implementation of the density matrix expansion for nuclear DFT, which allows the effects of long-distance pion exchange to be incorporated.

* The first complete next-to-next-to-next-to-leading order (N3LO) calculation of the neutron matter energy in chiral EFT was made, with results for astrophysics.

Last Modified: 11/29/2017
Modified by: Richard J Furnstahl