dorsal/arxiv
View SchemaConvergence of the Born Series with Low-Momentum Interactions
| Authors | S. K. Bogner, R. J. Furnstahl, S. Ramanan, A. Schwenk |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0602060 |
| URL | https://arxiv.org/abs/nucl-th/0602060 |
| DOI | 10.1016/j.nuclphysa.2006.05.004 |
| Journal | Nucl.Phys. A773 (2006) 203-220 |
Abstract
The nonperturbative nature of nucleon-nucleon interactions as a function of a momentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This investigation extends an earlier study of the perturbative convergence of the Born series to partial waves beyond the 3S1-3D1 channel and to positive energies. As the cutoff is lowered using renormalization-group or model-space techniques, the evolution of nonperturbative features at large cutoffs from strong short-range repulsion and the iterated tensor interaction are monitored via the complex Weinberg eigenvalues. When all eigenvalues lie within the unit circle, the expansion of the scattering amplitude in terms of the interaction is perturbative, with the magnitude of the largest eigenvalue setting the rate of convergence. Major decreases in the magnitudes of repulsive eigenvalues are observed as the Argonne v18, CD-Bonn or Nijmegen potentials are evolved to low momentum, even though two-body observables are unchanged. For chiral EFT potentials, running the cutoff lower tames the impact of the tensor force and of new nonperturbative features entering at N3LO. The efficacy of separable approximations to nuclear interactions derived from the Weinberg analysis is studied as a function of cutoff, and the connection to inverse scattering is demonstrated.
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"abstract": "The nonperturbative nature of nucleon-nucleon interactions as a function of a\nmomentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This\ninvestigation extends an earlier study of the perturbative convergence of the\nBorn series to partial waves beyond the 3S1-3D1 channel and to positive\nenergies. As the cutoff is lowered using renormalization-group or model-space\ntechniques, the evolution of nonperturbative features at large cutoffs from\nstrong short-range repulsion and the iterated tensor interaction are monitored\nvia the complex Weinberg eigenvalues. When all eigenvalues lie within the unit\ncircle, the expansion of the scattering amplitude in terms of the interaction\nis perturbative, with the magnitude of the largest eigenvalue setting the rate\nof convergence. Major decreases in the magnitudes of repulsive eigenvalues are\nobserved as the Argonne v18, CD-Bonn or Nijmegen potentials are evolved to low\nmomentum, even though two-body observables are unchanged. For chiral EFT\npotentials, running the cutoff lower tames the impact of the tensor force and\nof new nonperturbative features entering at N3LO. The efficacy of separable\napproximations to nuclear interactions derived from the Weinberg analysis is\nstudied as a function of cutoff, and the connection to inverse scattering is\ndemonstrated.",
"arxiv_id": "nucl-th/0602060",
"authors": [
"S. K. Bogner",
"R. J. Furnstahl",
"S. Ramanan",
"A. Schwenk"
],
"categories": [
"nucl-th",
"cond-mat.other",
"hep-ph"
],
"doi": "10.1016/j.nuclphysa.2006.05.004",
"journal_ref": "Nucl.Phys. A773 (2006) 203-220",
"title": "Convergence of the Born Series with Low-Momentum Interactions",
"url": "https://arxiv.org/abs/nucl-th/0602060"
},
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