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Detailed $\gamma$-ray spectroscopy of the exotic neon isotope $^{28}$Ne hasbeen performed for the first time using the one-neutron removal reaction from$^{29}$Ne on a liquid hydrogen target at 240~MeV/nucleon. Based on an analysisof parallel momentum distributions, a level scheme with spin-parity assignmentshas been constructed for $^{28}$Ne and the negative-parity states areidentified for the first time. The measured partial cross sections and momentumdistributions reveal a significant intruder $p$-wave strength providingevidence of the breakdown of the $N=20$ and $N=28$ shell gaps. Only a weak,possible $f$-wave strength was observed to bound final states. Large-scaleshell-model calculations with different effective interactions do not reproducethe large $p$-wave and small $f$-wave strength observed experimentally,indicating an ongoing challenge for a complete theoretical description of thetransition into the island of inversion along the Ne isotopic chain.

Intruder configurations in $^{29}$Ne at the transition into the island of inversion: Detailed structure study of $^{28}$Ne