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• W175193248 abstract "The hypertriton $_{ensuremath{Lambda}}mathrm{He}^{3}$ is considered with the inclusion of an ${S}^{ensuremath{'}}$ state ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ in the total wave function. For ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ 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 $ensuremath{Lambda}ensuremath{-}N$ interaction can give a nonzero admixture of ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ to the dominant component ${ensuremath{Psi}}_{S}$, 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 ${ensuremath{Psi}}_{S}$ has the same 6-parameter form as used by Downs and Dalitz and ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ 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 ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ 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 ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ is considerably less. With inclusion of ${ensuremath{Psi}}_{{S}^{ensuremath{'}}}$ (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 ${B}_{ensuremath{Lambda}}(_{ensuremath{Lambda}}mathrm{H}^{3})$. The resulting total $ensuremath{Lambda}ensuremath{-}N$ cross sections at low energies (ensuremath{lesssim}20 MeV) are compared with the experimental values ${ensuremath{sigma}}_{mathrm{exp}}$. If it is assumed that the singlet scattering length ${a}_{s}$ and effective range ${r}_{s}$ are most reliably determined from hypernuclei, then for $b=1.5$ F (for which the estimated values with a hard core of radius 0.42 F are ${a}_{s}ensuremath{approx}ensuremath{-}2.3$ F, ${r}_{s}ensuremath{approx}3.6$ F), acceptable agreement with ${ensuremath{sigma}}_{mathrm{exp}}$ can be obtained with only a modest increase of $|{a}_{t}|$ (${a}_{t}ensuremath{approx}ensuremath{-}1.3$ F, ${r}_{t}ensuremath{approx}2.9$ F) above the value obtained from hypernuclei. (The maximum value consistent with the hypernuclear results is ${a}_{t}ensuremath{approx}ensuremath{-}0.9$ F together with ${r}_{t}ensuremath{approx}3.3$ F.) It is shown that an increase of this order of magnitude could be obtained through suppression of the coupling with the $ensuremath{Sigma}N$ channel in $_{ensuremath{Lambda}}mathrm{He}^{5}$. 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 $3{m}_{ensuremath{pi}}$. Finally, it is argued that there is a tentative indication for the existence of a repulsive core in the $ensuremath{Lambda}ensuremath{-}N$ interaction." @default.
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• W175193248 date "1966-01-28" @default.
• W175193248 modified "2023-09-23" @default.
• W175193248 title "Hypertriton withS′State and theΛ−NInteraction" @default.
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• W175193248 doi "https://doi.org/10.1103/physrev.141.1387" @default.
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