#### Abstract

The hypertriton ${}_{\Lambda}{}^{}{}_{}{}^{}\mathrm{He}_{}^{3}{}_{}{}^{}$ is considered with the inclusion of an ${S}^{\prime}$ state ${\Psi}_{{S}^{\prime}}$ in the total wave function. For ${\Psi}_{{S}^{\prime}}$ 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 $\Lambda -N$ interaction can give a nonzero admixture of ${\Psi}_{{S}^{\prime}}$ to the dominant component ${\Psi}_{S}$, 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 ${\Psi}_{S}$ has the same 6-parameter form as used by Downs and Dalitz and ${\Psi}_{{S}^{\prime}}$ has a corresponding flexibility. In particular, for an intrinsic range $b=1.5\mathrm{}$ F (corresponding to a Yukawa interaction appropriate to two-pion exchange), the effect of ${\Psi}_{{S}^{\prime}}$ 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 ($b=0.84\mathrm{}$ F), the effect of ${\Psi}_{{S}^{\prime}}$ is considerably less. With inclusion of ${\Psi}_{{S}^{\prime}}$ (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 ${B}_{\Lambda}\left({}_{\Lambda}{}^{}{}_{}{}^{}\mathrm{H}_{}^{3}{}_{}{}^{}\right)$. The resulting total $\Lambda -N$ cross sections at low energies (≲20 MeV) are compared with the experimental values ${\sigma}_{\mathrm{exp}}$. If it is assumed that the singlet scattering length ${a}_{s}$ and effective range ${r}_{s}$ are most reliably determined from hypernuclei, then for $b=1.5\mathrm{}$ F (for which the estimated values with a hard core of radius 0.42 F are ${a}_{s}\approx -2.3\mathrm{}$ F, ${r}_{s}\approx 3.6$ F), acceptable agreement with ${\sigma}_{\mathrm{exp}}$ can be obtained with only a modest increase of $\left|{a}_{t}\right|$ (${a}_{t}\approx -1.3\mathrm{}$ F, ${r}_{t}\approx 2.9$ F) above the value obtained from hypernuclei. (The maximum value consistent with the hypernuclear results is ${a}_{t}\approx -0.9\mathrm{}$ F together with ${r}_{t}\approx 3.3$ F.) It is shown that an increase of this order of magnitude could be obtained through suppression of the coupling with the $\Sigma N$ channel in ${}_{\Lambda}{}^{}{}_{}{}^{}\mathrm{He}_{}^{5}{}_{}{}^{}$. Results are also given for a Yukawa potential with $b=2.07\mathrm{}$ 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 $3{m}_{\pi}$. Finally, it is argued that there is a tentative indication for the existence of a repulsive core in the $\Lambda -N$ 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