The hypertriton is considered with the inclusion of an state in the total wave function. For 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 interaction can give a nonzero admixture of to the dominant component , 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 has the same 6-parameter form as used by Downs and Dalitz and has a corresponding flexibility. In particular, for an intrinsic range F (corresponding to a Yukawa interaction appropriate to two-pion exchange), the effect of 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 -meson exchange ( F), the effect of is considerably less. With inclusion of (for a given ), the singlet strength is found to be quite insensitive to the value of the triplet strength and is therefore almost entirely determined by . The resulting total cross sections at low energies (≲20 MeV) are compared with the experimental values . If it is assumed that the singlet scattering length and effective range are most reliably determined from hypernuclei, then for F (for which the estimated values with a hard core of radius 0.42 F are F, F), acceptable agreement with can be obtained with only a modest increase of ( F, F) above the value obtained from hypernuclei. (The maximum value consistent with the hypernuclear results is F together with F.) It is shown that an increase of this order of magnitude could be obtained through suppression of the coupling with the channel in . Results are also given for a Yukawa potential with 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 . Finally, it is argued that there is a tentative indication for the existence of a repulsive core in the interaction.
- Received 21 July 1965
- Published in the issue dated January 1966
© 1966 The American Physical Society