Four-body calculation of the0+-1+binding energy difference in theA=4Λhypernuclei

The coupled, two-variable integral equations that determine the ${}_{\mathrm{\Lambda }}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^4{}_{}{}^{}\mathrm{H}$ ground and first excited states, when the NN and ΛN-ΣN interactions are represented by separable potentials, are solved numerically. We find the spin-isospin suppression of the Λ-Σ conversion due to the composite nature of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ nuclear cores to be a significant factor in understanding the $0^{+\mathrm{-}}$ $1^{+}$ binding energy difference.