Soft-core hyperon-nucleon potentials

A new Nijmegen soft-core OBE potential model is presented for the low-energy $\mathrm{YN}$ interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. The potentials are generated by the exchange of nonets of pseudoscalar, vector, and scalar mesons. As is standard in the Nijmegen soft-core models, we also include the $J=0\mathrm{}$ contributions from the tensor $f_2{,f}_2^{\prime }{,a}_2,$ and pomeron Regge trajectories, and use Gaussian form factors to guarantee that the potentials have a soft behavior near the origin. An important innovation with respect to the original soft-core potential is the assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices in accordance with broken $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_F,$ which serves to connect the $\mathrm{NN}$ and the $\mathrm{YN}$ channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the ${}^3{P}_0$ model with a Gell-Mann–Okubo hypercharge breaking for the BBM coupling. Charge-symmetry breaking in the $\Lambda p$ and $\Lambda n$ channels is included as well. We present six hyperon-nucleon potentials which describe the available $\mathrm{YN}$ cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\Sigma N$ and $\Lambda N$ channels. In all cases, we obtained ${\chi }^2{/N}_{\mathrm{data}}\approx 0.55$ for 35 $\mathrm{YN}$ data. In particular, we were able to fit the precise experimental datum $r_R=0.468\mathrm{}\pm 0.010$ for the inelastic capture ratio at rest. For the scalar-meson mixing angle we obtained values ${\theta }_S=37\mathrm{}°–40°,$ which points to almost ideal mixing angles for the scalar $q\overline{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\Lambda$ hypernuclei.