Abstract
The effects of deformation and the change of the nuclear core on the hyperon binding and halo structure in single-$\mathrm{\ensuremath{\Lambda}}$ $p$-shell hypernuclei are studied for the C hyperisotopes and $N=6$ hyperisotones in the framework of the deformed Skyrme-Hartree-Fock approach with combinations of the $NN$ interactions SIII, SGII, SkI4 and the $\mathrm{\ensuremath{\Lambda}}N$ interactions LY1 and SLL4, respectively. Deformation causes more deeply bound states with smaller extension of the density distributions and radii. The possibility of deformed halo structures of $\mathrm{\ensuremath{\Lambda}}$ $1p$ states in hypernuclei up to a mass number $A=15$ is found.
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