Hypertriton with S State and the Λ-N Interaction

Phys. Rev. 141, 1387 – Published 28 January 1966
A. R. Bodmer


The hypertriton He3Λ is considered with the inclusion of an S state ΨS in the total wave function. For ΨS the nucleons are in a singlet spin state and the space part is correspondingly antisymmetric with respect to exchange of the nucleons. Only a spin dependence of the Λ-N interaction can give a nonzero admixture of ΨS to the dominant component ΨS, which is space-symmetric under exchange of the nucleons and which is the only component that has been considered in previous investigations. Central, spin-dependent Yukawa potentials were used. The most flexible trial function used was one with 16 parameters for which ΨS has the same 6-parameter form as used by Downs and Dalitz and ΨS has a corresponding flexibility. In particular, for an intrinsic range b=1.5 F (corresponding to a Yukawa interaction appropriate to two-pion exchange), the effect of ΨS is quite appreciable; the singlet strength is reduced, the triplet strength slightly increased, and the spin dependence reduced by about a third. For a range corresponding to K-meson exchange (b=0.84 F), the effect of ΨS is considerably less. With inclusion of ΨS (for a given b), the singlet strength is found to be quite insensitive to the value of the triplet strength and is therefore almost entirely determined by BΛ(H3Λ). The resulting total Λ-N cross sections at low energies (≲20 MeV) are compared with the experimental values σexp. If it is assumed that the singlet scattering length as and effective range rs are most reliably determined from hypernuclei, then for b=1.5 F (for which the estimated values with a hard core of radius 0.42 F are as-2.3 F, rs3.6 F), acceptable agreement with σexp can be obtained with only a modest increase of |at| (at-1.3 F, rt2.9 F) above the value obtained from hypernuclei. (The maximum value consistent with the hypernuclear results is at-0.9 F together with rt3.3 F.) It is shown that an increase of this order of magnitude could be obtained through suppression of the coupling with the ΣN channel in He5Λ. Results are also given for a Yukawa potential with b=2.07 F, which is the intrinsic range for an interaction with a hard core of radius 0.42 F and an attractive Yukawa tail appropriate to an exchanged boson with mass 3mπ. Finally, it is argued that there is a tentative indication for the existence of a repulsive core in the Λ-N interaction.

DOI: http://dx.doi.org/10.1103/PhysRev.141.1387

  • Received 21 July 1965
  • Published in the issue dated January 1966

© 1966 The American Physical Society

Authors & Affiliations

A. R. Bodmer

  • Argonne National Laboratory, Argonne, Illinois

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