An effective field theory approach to two trapped particles

I. Stetcu; J. Rotureau; B. R. Barrett; U. van Kolck

doi:10.1016/j.aop.2010.02.008

An effective field theory approach to two trapped particles

I. Stetcu, J. Rotureau, B. R. Barrett, U. van Kolck

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50 Scopus citations

Abstract

We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.

Original language	English (US)
Pages (from-to)	1644-1666
Number of pages	23
Journal	Annals of Physics
Volume	325
Issue number	8
DOIs	https://doi.org/10.1016/j.aop.2010.02.008
State	Published - Aug 2010
Externally published	Yes

Keywords

Effective field theory
Few-body systems
Trapped atoms

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.aop.2010.02.008

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title = "An effective field theory approach to two trapped particles",

abstract = "We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.",

keywords = "Effective field theory, Few-body systems, Trapped atoms",

author = "I. Stetcu and J. Rotureau and Barrett, {B. R.} and {van Kolck}, U.",

note = "Funding Information: We thank Thomas Papenbrock for pointing out some useful references and Mike Birse for interesting discussions. The work reported here benefited from hospitality extended to its authors by the National Institute for Nuclear Theory at the University of Washington during the Program on Effective Field Theories and the Many-Body Problem (INT-09-01), and to UvK by the Kernfysisch Versneller Instituut at the Rijksuniversiteit Groningen. This research was supported in part by NSF grants PHY-0555396 and PHY-0854912 (BRB, JR), and by US DOE grants DE-FC02-07ER41457 (IS) and DE-FG02-04ER41338 (JR, UvK). ",

year = "2010",

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doi = "10.1016/j.aop.2010.02.008",

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AU - Stetcu, I.

AU - Rotureau, J.

AU - Barrett, B. R.

AU - van Kolck, U.

N1 - Funding Information: We thank Thomas Papenbrock for pointing out some useful references and Mike Birse for interesting discussions. The work reported here benefited from hospitality extended to its authors by the National Institute for Nuclear Theory at the University of Washington during the Program on Effective Field Theories and the Many-Body Problem (INT-09-01), and to UvK by the Kernfysisch Versneller Instituut at the Rijksuniversiteit Groningen. This research was supported in part by NSF grants PHY-0555396 and PHY-0854912 (BRB, JR), and by US DOE grants DE-FC02-07ER41457 (IS) and DE-FG02-04ER41338 (JR, UvK).

PY - 2010/8

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N2 - We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.

AB - We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.

KW - Effective field theory

KW - Few-body systems

KW - Trapped atoms

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JO - Annals of Physics

JF - Annals of Physics

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An effective field theory approach to two trapped particles

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Keywords

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