Reaction-matrix calculation of the lambda-particle binding in nuclear matter

1970
38 pages
Published in:
  • Nucl.Phys.A 148 (1970) 97-134
  • Published: 1970

Citations per year

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Abstract: (Elsevier)
The two principal procedures for obtaining the phenomenological Λ well depth D from the experimental separation energies B Λ are discussed. A value D ∼ 30 ± 2 MeV, with an upper limit D ≲ 35 MeV, is consistent with the results obtained from both procedures. A reactionmatrix calculation of D is made for central ΛN potentials. This is exact in the g -matrix approximation which gives the term proportional to the density ρ in an expansion in powers of p . To calculate the g -matrix the reference-spectrum method is used in the Kallio-Day form. The free kinetic energies are used for the unoccupied states. The difference between the singleparticle energies of the bound and excited states of the Λ involves a gap which is identified with the well depth. This leads to a self-consistency condition for the determination of D . The nucleon-spectrum parameters are taken from the calculations of Sprung et al . The angle-average approximation for the exclusion-principle operator, appropriate to a Λ in nuclear matter, is examined and found to be excellent. For hard-core potentials, a perturbation expansion in the strength of the attractive tail is in general inadequate and, especially for potentials of short range, it is necessary to obtain the g -matrix exactly for the complete potentials. For given lowenergy scattering parameters, the presence of a sizable hard core very substantially reduces D , The p-state contribution to D can be quite large, especially for the phenomenological potentials with hard cores and with larger intrinsic ranges. Thus for Herndon and Tang's potentials which fit the binding energies of the A = 3 and 4 hypernuclei as well as the Λp scattering data and which have rather large hard cores, one can get close to the phenomenological value of D by assuming zero p-state interaction. With some p-state interaction — about half of that for the s-state — reasonable suppression of the ΛN-σN coupling in nuclear matter can give agreement with the phenomenological depth. The well depth is found to depend fairly linearly on ρ over a large range and the Λ effective mass can be as small as 0.65 M Λ .
  • hypernucleus: binding energy
  • nuclear properties
  • lambda
  • potential