Three-body problem with short-range forces: Renormalized equations and regulator-independent results

Afnan, I. R.; Phillips, Daniel R.

doi:10.1103/physrevc.69.034010

Cited by 60 publications

(74 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work we have extended the subtraction formalism developed previously [13,32] to higher orders in the R/a 2 expansion. Using analytical and numerical arguments we have shown that the three-body system at NNLO can be renormalized without the need for a second three-body datum.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

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

2006

View full text Add to dashboard Cite

We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R ≪ a 2 , with a 2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R 3 /a 3 2 ). Since corrections of O(R/a 2 ) and O(R 2 /a 2 2 ) can be straightforwardly included in the integral equation's kernel, a unique solution for 1+2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with the recent three-dimensional Faddeev calculations of Roudnev and collaborators that used phenomenological inter-atomic potentials.

show abstract

Section: Discussionmentioning

confidence: 99%

“…With Eq. (18) in hand resolvent identities may be used to obtain the subtracted amplitude at any energy [13]: (19) where the second inhomogeneous term is given by…”

Section: Three-body Scattering At Leading Ordermentioning

confidence: 99%

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

2006

View full text Add to dashboard Cite

show abstract

“…κ * 1/|a|. The hyperradial formalism is particularly well-suited to the analysis of that limit, as the hyperradial potential is a power law (or, more generally, sum of powers of r s /R) for all values of R. In this section we use a momentum-space formalism [20] to obtain the corrections to the Efimov spectrum for arbitrary values of 1/(aκ * ). Numerical calculation of scattering and bound-state observables is straightforward, and it is easy to compute range correctionsregardless of the value of a [10].…”

Section: The Linear Range Correction For Arbitrary Scattering Lementioning

confidence: 99%

Range corrections to three-body observables near a Feshbach resonance

2009

View full text Add to dashboard Cite

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.

show abstract

“…Ref. [18] showed that this removes this sensitivity of the low-energy amplitude to the choice of Λ. Afnan and Phillips subsequently demonstrated that this result can also be obtained by making a subtraction on the original integral equation, in order to render its kernel better behaved [21].…”

Section: Epj Web Of Conferencesmentioning

confidence: 97%

Universality and Beyond

Phillips

2010

EPJ Web of Conferences

View full text Add to dashboard Cite

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.

show abstract

Three-body problem with short-range forces: Renormalized equations and regulator-independent results

Cited by 60 publications

References 48 publications

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

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

Range corrections to three-body observables near a Feshbach resonance

Universality and Beyond

Contact Info

Product

Resources

About