Normal-ordering approximations and translational (non)invariance
Journal article, 2021

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 He-4 and O-16 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 He-4, it is also shown to be much smaller for O-16 although full convergence is not reached. These tools can be easily implemented in studies using other many-body frameworks and bases.


Tor Djärv

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

Andreas Ekström

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

Christian Forssén

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

G. R. Jansen

Oak Ridge National Laboratory


2469-9985 (ISSN) 2469-9993 (eISSN)

Vol. 104 2 024324

Strong interactions for precision nuclear physics (PrecisionNuclei)

European Commission (EC) (758027), 2018-02-01 -- 2023-01-31.

Weak and rare nuclear processes: nuclear probes of fundamental symmetries and dark matter

Swedish Research Council (VR) (2017-04234), 2018-01-01 -- 2021-12-31.

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9/3/2021 1