ΛΛ Hypernucleus Be10ΛΛ and the Λ-Λ Interaction

Phys. Rev. 138, B644 – Published 10 May 1965
A. R. Bodmer and Shamsher Ali

Abstract

The ΛΛ hypernucleus Be10ΛΛ has been analyzed by use of a four-body α-α-Λ-Λ model which allows for distortion of the core by the Λ particles. In particular, the dependence of the internal energy of the core on the rms separation of the α particles is required. This was obtained from three-body α-α-Λ calculations for Be9Λ. Several types of α-α potentials, whose s-wave phase shifts had been previously obtained, were considered. Calculations for Be10ΛΛ were made for a singlet Λ-Λ Yukawa potential (I) of intrinsic range b=1.48 F, appropriate to the exchange of two pions, and for a hard-core Yukawa potential (II) with a hard-core radius rc=0.42 F and b=2.66 F, appropriate to a range corresponding to two pion masses for the attractive Yukawa part. Results are also given for a hard-core meson-theory potential (III) which has rc=0.42 F and b=1.48 F. Calculations for III were made for He6ΛΛ, and the results were adapted to Be10ΛΛ. For α-α potentials which give s-wave phase shifts consistent with experiment, it is found that (almost independently of the details of the Λ-Λ potential) the effects of core distortion account for rather more than a third of the experimental additional binding energy of 4.5±0.5 MeV which is obtained after the Λ separation energy of Be9Λ has been allowed for. Slightly more than half the contribution due to core distortion comes from the core energy of Be9Λ. The remainder is due to the further distortion of the core by the second Λ, which causes approximately a 10% decrease in the rms α-α separation relative to the value for Be9Λ. The effects of core distortion weaken the resulting Λ-Λ potential quite appreciably. For b=1.48 F, one obtains the scattering length aΛΛ-1±0.3 F and the effective range r0ΛΛ3.3±0.6 F, approximately independent of the shape of the Λ-Λ potential. For II, one gets aΛΛ=-2.3-0.5+0.8 F and rΛΛ=4.9-0.7+1.1 F. The well-depth parameters are 0.45±0.08, 0.675±0.065, and 0.77±0.04 for I, II, and III, respectively. These values are about 35%, 20%, and 12%, respectively, less than the values obtained for a rigid core with a three-body Be8-Λ-Λ model. The Σ-Λ-π coupling constant, obtained with III, is close to the value obtained from the singlet Λ-N interaction for the same hard-core radius.

DOI: http://dx.doi.org/10.1103/PhysRev.138.B644

  • Received 28 December 1964
  • Published in the issue dated May 1965

© 1965 The American Physical Society

Authors & Affiliations

A. R. Bodmer*

  • Argonne National Laboratory, Argonne, Illinois

Shamsher Ali

  • Department of Theoretical Physics, The University, Manchester, England

  • *On leave of absence from Manchester University, Manchester, England.
  • On leave of absence from the Pakistan Atomic Energy Commission, Karachi, Pakistan.

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