The Three-Boson System at Next-to-Next-to-Leading Order

Platter, Lucas; Phillips, Daniel R.

doi:10.1007/s00601-006-0165-z

Cited by 64 publications

(117 citation statements)

References 43 publications

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“…A formalism which employs a partial resummation of range effects was developed in Refs. [9,10,11] and observables were calculated up to nextto-next-to-leading order (N2LO) in the l/a expansion. Hyperradial coordinates and the Wilsonian renormalization group were used to re-derive the leading-order amplitude and develop a power counting for sub-leading effects in Ref.…”

Section: Introductionmentioning

confidence: 99%

Range corrections to three-body observables near a Feshbach resonance

2009

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A non-relativistic system of three identical particles will display a rich set of universal features known as Efimov physics if the scattering length a is much larger than the range l of the underlying two-body interaction. An appropriate effective theory facilitates the derivation of both results in the |a| → ∞ limit and finite-l/a corrections to observables of interest. Here we use such an effectivetheory treatment to consider the impact of corrections linear in the two-body effective range, r s on the three-boson bound-state spectrum and recombination rate for |a| |r s |. We do this by first deriving results appropriate to the strict limit |a| → ∞ in coordinate space. We then extend these results to finite a using once-subtracted momentum-space integral equations. We also discuss the implications of our results for experiments that probe three-body recombination in Bose-Einstein condensates near a Feshbach resonance.

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Section: Introductionmentioning

confidence: 99%

Range corrections to three-body observables near a Feshbach resonance

2009

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“…The calculations of [40] were based on the adiabatic hyperspherical expansion in three-body configuration space, while the hard-core version of the twodimensional Faddeev differential equations has been used in [33]. References [41,42,43,44,45,46,47,48] suggest that the 4 He 3 ground state itself may be considered as an Efimov state since, given the 4 He- 4 He atom-atom scattering length, both the 4 He 3 ground-state and excited-state energies lye on the same universal scaling curve (for details, see, e.g., [49,Sections 6.7 and 6.8]). …”

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The 4He Trimer as an Efimov System

Kolganova¹,

Мотовилов²,

Sandhas

2011

Few-Body Syst

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“…[28,29] showed that if the cutoff is taken to infinity in Eq. (10) with t 2B 0 replaced by t 2B 0 + t 2B 1 + t 2B 2 , then a second three-body datum is not needed for renormalization.…”

Section: Some Results At Nnlomentioning

confidence: 99%

Universality and Beyond

Phillips

2010

EPJ Web of Conferences

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Abstract. I discuss the impact of a finite effective range, r, on systems with a large two-body scattering length, a. In particular, I show how observables can be written as an expansion around the "universal", or large-scatteringlength limit. The parameter governing this expansion is the ratio r/a. In few-nucleon systems the ratio r/a has a value of about 1/3, and so such corrections are essential in producing good agreement between theory and data. Hence, I first show how these effects range play a key role in making the so-called "pionless" effective field theory a successful descriptor of low-energy processes in the NN system. I then move to the NNN system, and review predictions for the energy-dependence of observables there. However, the beautiful Efimov physics associated with the presence of a large scattering length is not fully revealed in the NNN system, precisely because r/a corrections are large. I therefore turn to cold atomic gases and show that there are some important recent experiments where physics "beyond universality" affects the data. In the process I demonstrate that an additional piece of short-distance physics is necessary to renormalize scattering-length-dependent observables in the three-body system once corrections ∼ r are considered. Finally, I discuss recent initial efforts to compute r/a corrections to the predictions of universality for the four-body system.

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The Three-Boson System at Next-to-Next-to-Leading Order

Cited by 64 publications

References 43 publications

Range corrections to three-body observables near a Feshbach resonance

Range corrections to three-body observables near a Feshbach resonance

The 4He Trimer as an Efimov System

Universality and Beyond

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