Abstract
Normal ordering provides an approach to approximate three-body forces as effective two-body operators and it is therefore an important tool in many-body calculations with realistic nuclear interactions. The corresponding neglect of certain three-body terms in the normal-ordered Hamiltonian is known to influence translational invariance, although the magnitude of this effect has not yet been systematically quantified. In this paper we study in particular the normal-ordering two-body approximation applied to a single harmonic-oscillator reference state. We explicate the breaking of translational invariance and demonstrate the magnitude of the approximation error as a function of model space parameters for He4 and O16 by performing full no-core shell-model calculations with and without three-nucleon forces. We combine two different diagnostics to better monitor the breaking of translational invariance. While the center-of-mass effect is shown to become potentially very large for He4, it is also shown to be much smaller for O16 although full convergence is not reached. These tools can be easily implemented in studies using other many-body frameworks and bases.
| Original language | English |
|---|---|
| Article number | 024324 |
| Journal | Physical Review C |
| Volume | 104 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 2021 |
Funding
We thank S. R. Stroberg for useful discussions and suggestions. We thank P. Navrátil for useful discussions and for support in the use of the ncsd code. This work was supported by the Swedish Research Council (Grant No. 2017-04234) and the European Research Council (ERC) under the European Unions Horizon 2020 Research and Innovation Programme (Grant No. 758027). The computations were enabled by resources provided by the Swedish National Infrastructure for Computing at Chalmers Centre for Computational Science and Engineering, the National Supercomputer Centre, partially funded by the Swedish Research Council. G.R.J. acknowledges support by the U.S. Department of Energy under Grant No. desc0018223 (NUCLEI SciDAC-4 collaboration). This research used resources of the Oak Ridge Leadership Computing Facility located at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan .
| Funders | Funder number |
|---|---|
| U.S. Department of Energy | desc0018223 |
| Office of Science | DE-AC05-00OR22725 |
| Oak Ridge National Laboratory | |
| Horizon 2020 Framework Programme | |
| European Research Council | |
| Vetenskapsrådet | 2017-04234 |
| Horizon 2020 | 758027 |