Normal-ordering approximations and translational (non) invariance
| Autor: | Djärv, T., Ekström, A., Forssén, C., Jansen, G. R. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. C 104, 024324 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevC.104.024324 |
| Popis: | 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 work 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 $^4\rm{He}$ and $^{16}\rm{O}$ 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 $^4\rm{He}$, it is also shown to be much smaller for $^{16}\rm{O}$ although full convergence is not reached. These tools can be easily implemented in studies using other many-body frameworks and bases. Comment: 13 pages, 10 figures |
| Databáze: | arXiv |
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