Background: The pairing correlation in weakly bound nuclei causes a mixing among bound and unbound configurations. A remarkable consequence is the emergence of the quasiparticle resonance, which has been predicted with the coordinate space Hartree-Fock-Bogoliubov (HFB) theory, but not yet observed experimentally.

Purpose: We discuss possible observation of quasiparticle resonances in decay spectrum of unbound nuclei near the neutron drip-line. We deal with an example of unbound nucleus ${}^{21}\mathrm{C}$ which disintegrates to ${}^{20}\mathrm{C}$ and a neutron.

Method: We describe a scattering state consisting of ${}^{20}\mathrm{C}$ and a neutron in the framework of the HFB formalism. We assume that a nucleon knockout reaction produces a doorway state of the decay, and we evaluate the decay spectrum by taking an overlap of the doorway state and the scattering state of ${}^{20}\mathrm{C}+n$. A numerical calculation was performed with the Woods-Saxon potential and a density-dependent effective pairing interaction.

Results: We show that the quasiparticle resonance appears as low-lying peaks in the decay spectrum of ${}^{21}\mathrm{C}$. They originate from the weakly bound single-neutron orbits $2s_{1/2}$ and $1d_{5/2}$, but emerge as unbound resonant quasiparticle states under the influence of the neutron pairing correlation. The resonance energy and the width of the calculated quasiparticle resonances are consistent with an experimental observation whereas they are sensitive to the neutron pairing correlation.

Conclusion: The results suggest that nucleon knockout reactions populating the unbound nucleus ${}^{21}\mathrm{C}$ provide realistic opportunity of experimentally observing the quasiparticle resonance and of disclosing the pairing correlation in neutron-rich nuclei.

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• Nuclear density functional theory
• Nuclear structure & decays
• Resonance reactions
• 20 ≤ A ≤ 38