Ultraviolet extrapolations in finite oscillator bases

Ultraviolet extrapolations in finite oscillator bases. König, S., Bogner, S. K., Furnstahl, R. J., More, S. N., & Papenbrock, T. Physical Review C - Nuclear Physics, 2014.
doi abstract bibtex

The use of finite harmonic oscillator spaces in many-body calculations introduces both infrared (IR) and ultraviolet (UV) errors. The IR effects are well approximated by imposing a hard-wall boundary condition at a properly identified radius Leff. We show that duality of the oscillator implies that the UV effects are equally well described by imposing a sharp momentum cutoff at a momentum $\Lambda$eff complementary to Leff. By considering two-body systems with separable potentials, we show that the UV energy corrections depend on details of the potential, in contrast to the IR energy corrections, which depend only on the S-matrix. An adaptation of the separable treatment to more general interactions is developed and applied to model potentials as well as to the deuteron with realistic potentials. The previous success with a simple phenomenological form for the UV error is also explained. Possibilities for controlled extrapolations for A>2 based on scaling arguments are discussed.

@article{Konig2014,
abstract = {The use of finite harmonic oscillator spaces in many-body calculations introduces both infrared (IR) and ultraviolet (UV) errors. The IR effects are well approximated by imposing a hard-wall boundary condition at a properly identified radius Leff. We show that duality of the oscillator implies that the UV effects are equally well described by imposing a sharp momentum cutoff at a momentum $\Lambda$eff complementary to Leff. By considering two-body systems with separable potentials, we show that the UV energy corrections depend on details of the potential, in contrast to the IR energy corrections, which depend only on the S-matrix. An adaptation of the separable treatment to more general interactions is developed and applied to model potentials as well as to the deuteron with realistic potentials. The previous success with a simple phenomenological form for the UV error is also explained. Possibilities for controlled extrapolations for A>2 based on scaling arguments are discussed.},
author = {K{\"{o}}nig, S. and Bogner, S. K. and Furnstahl, R. J.B. and More, S. N. and Papenbrock, T.},
doi = {10.1103/PhysRevC.90.064007},
issn = {1089490X},
journal = {Physical Review C - Nuclear Physics},
number = {6},
title = {{Ultraviolet extrapolations in finite oscillator bases}},
volume = {90},
year = {2014}
}

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