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A renormalized equation for the three-body system with short-range interactions

Publication ,  Journal Article
Hammer, HW; Mehen, T
Published in: Nuclear Physics A
July 30, 2001

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained. © 2001 Elsevier Science B.V.

Duke Scholars

Published In

Nuclear Physics A

DOI

ISSN

0375-9474

Publication Date

July 30, 2001

Volume

690

Issue

4

Start / End Page

535 / 546

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5106 Nuclear and plasma physics
  • 5101 Astronomical sciences
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0201 Astronomical and Space Sciences
 

Citation

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Hammer, H. W., & Mehen, T. (2001). A renormalized equation for the three-body system with short-range interactions. Nuclear Physics A, 690(4), 535–546. https://doi.org/10.1016/S0375-9474(00)00710-7
Hammer, H. W., and T. Mehen. “A renormalized equation for the three-body system with short-range interactions.” Nuclear Physics A 690, no. 4 (July 30, 2001): 535–46. https://doi.org/10.1016/S0375-9474(00)00710-7.
Hammer HW, Mehen T. A renormalized equation for the three-body system with short-range interactions. Nuclear Physics A. 2001 Jul 30;690(4):535–46.
Hammer, H. W., and T. Mehen. “A renormalized equation for the three-body system with short-range interactions.” Nuclear Physics A, vol. 690, no. 4, July 2001, pp. 535–46. Scopus, doi:10.1016/S0375-9474(00)00710-7.
Hammer HW, Mehen T. A renormalized equation for the three-body system with short-range interactions. Nuclear Physics A. 2001 Jul 30;690(4):535–546.
Journal cover image

Published In

Nuclear Physics A

DOI

ISSN

0375-9474

Publication Date

July 30, 2001

Volume

690

Issue

4

Start / End Page

535 / 546

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5106 Nuclear and plasma physics
  • 5101 Astronomical sciences
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0201 Astronomical and Space Sciences