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Few-Body Systems

, 60:51 | Cite as

Can a \(\varLambda nn\) Resonance Constrain the \(\varLambda n\) Amplitude?

  • Iraj R. AfnanEmail author
  • Benjamin F. Gibson
Article
  • 63 Downloads
Part of the following topical collections:
  1. Ludwig Faddeev Memorial Issue

Abstract

We address the question of constraints on the \(\varLambda n\) amplitude as a result of observing a \(\varLambda nn\) resonance above the \(\varLambda nn\) three-body threshold. To examine this question, we will first demonstrate that by starting with a \(\varLambda n\) interaction based upon the experimental \(\varLambda p\) data and then scaling the \(\varLambda n\) potential by \(\approx 8\%\) one can generate a \(\varLambda nn\) resonance, and with a sufficiently large scaling one can generate a \(\varLambda nn\) bound state. This is achieved using the three-body Faddeev equations with rank one separable potentials for all pairwise interactions. The use of separable potentials is motivated by two factors: (i) the Faddeev equations reduce to a set of one dimensional integral equations that can be analytically continued into the complex energy plane where resonances reside. (ii) The \(\varLambda n\) amplitude can be defined in terms of the effective range parameters. As a result we can explore the question: What constraint can be placed on the \(\varLambda n\) effective range parameters by the \(\varLambda nn\) resonance parameters?

Notes

Acknowledgements

The work of BFG was performed under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396.

Supplementary material

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Science and EngineeringFlinders UniversityAdelaideAustralia
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

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