Hypernuclear Spectroscopy for A=6
Abstract
The hypernuclei _{ΛΛ}He^{6} and _{Λ}He^{6} are studied using the method of Dawson, Talmi, and Walecka. As a check on the calculation, He^{6} is also studied using a pure central force for the neutronneutron interaction. By working within a harmonicoscillator frame work, the BetheGoldstone equation is transformed to relative coordinates and solved using the variational procedure developed by Dawson and Walecka. Assuming a pure central potential with a Yukawa shape for the ΛΛ interaction, the strengths of the potential yielding the observed binding energy are found for three different ranges. As a check, the binding energy of He^{6} is estimated assuming central potentials of the BrucknerGammelThaler type and of the Hamada type. The spinorbit and tensor parts of the potentials are neglected, because the neutrons interact most strongly in a relative singlet s state. Too much binding is found, presumably because of our use of harmonicoscillator singleparticle potentials. A 15% reduction in the attractive part of the central Hamadatype potential gives reasonable binding for the neutrons. The energy levels of the ground state and excited states of _{Λ}He^{6} are estimated using the potentials given by Shemsher Ali, Grypeos, and Kok. A 20 to 25% reduction in the potential yields the observed binding energy of the ground state. In addition to the ground state, which is 1^{}, a 2^{} excited state is also found, which may not be bound against breakup into _{Λ}He^{5}+n.
 Publication:

Physical Review
 Pub Date:
 November 1967
 DOI:
 10.1103/PhysRev.163.985
 Bibcode:
 1967PhRv..163..985A