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arXiv · 1409.5997

Ultraviolet extrapolations in finite oscillator bases

S. König·S. K. Bogner·R. J. Furnstahl·S. N. More·T. Papenbrock
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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 L_eff. 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 L_eff. 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.

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S. König, S. K. Bogner, R. J. Furnstahl, S. N. More, T. Papenbrock. 2014-12-29. Ultraviolet extrapolations in finite oscillator bases. https://doi.org/10.1103/physrevc.90.064007

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