Search for $^{21}$C and constraints on $^{22}$C
S. Mosby, N. S. Badger, T. Baumann, D. Bazin, M. Bennett, J. Brown, G., Christian, P. A. DeYoung, J. E. Finck, M. Gardner, J. D. Hinnefeld, E. A., Hook, E. M. Lunderberg, B. Luther, D. A. Meyer, M. Mosby, G. F. Peaslee, W., F. Rogers, J. K. Smith, J. Snyder, A. Spyrou

TL;DR
This study searched for the unbound nucleus $^{21}$C and constrained properties of $^{22}$C, finding no low-lying states for $^{21}$C and suggesting $^{22}$C is very weakly bound, with implications for nuclear structure models.
Contribution
The paper provides experimental limits on $^{21}$C and $^{22}$C, offering new insights into their binding energies and structure near the neutron dripline.
Findings
No low-lying state observed in $^{21}$C.
$^{22}$C is bound by less than 70 keV.
Constraints on $^{21}$C's scattering length.
Abstract
A search for the neutron-unbound nucleus C was performed via the single proton removal reaction from a beam of 22 N at 68 MeV/u. Neutrons were detected with the Modular Neutron Array (MoNA) in coincidence with C fragments. No evidence for a low-lying state was found, and the reconstructed C+n decay energy spectrum could be described with an s-wave line shape with a scattering length limit of |as| < 2.8 fm, consistent with shell model predictions. A comparison with a renormalized zero-range three-body model suggests that C is bound by less than 70 keV.
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