Hypertriton with S-prime State and the Lambda-N Interaction
Jan 28, 196610 pages
Published in:
- Phys.Rev. 141 (1966) 1387-1397
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Abstract: (APS)
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, rs≈3.6 F), acceptable agreement with σexp can be obtained with only a modest increase of |at| (at≈−1.3 F, rt≈2.9 F) above the value obtained from hypernuclei. (The maximum value consistent with the hypernuclear results is at≈−0.9 F together with rt≈3.3 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.References(23)
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