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Description
The carbon isotopes, with $Z$=6 being the first spin-orbit shell gap originating from the splitting of the $1p_{1/2}$–$1p_{3/2}$ orbitals, provide an excellent ground to study changes in proton spin-orbit splitting from stability to the dripline. Neutron-rich carbon isotopes have been intensively investigated over the last decade. Transition probabilities, $B(E2;2^+\rightarrow0^+)$, have been measured up to $^{20}$C [1,2], revealing an increase from $^{16}$C to $^{20}$C. These $B(E2)$ values have been interpreted in terms of the mixing of unperturbed neutron and proton $2^+$ excitations, with the observed increase in collectivity explained by an enhanced contribution of proton excitations. This enhancement is likely due to a reduction of the proton $1p_{1/2}$–$1p_{3/2}$ spin-orbit splitting toward the dripline [3].
In a more recent experiment [4], neutron-rich carbon isotopes $^{16,18,20}$C were studied via proton removal reactions from nitrogen isotopes. Cross sections populating the ground and $2^+_1$ states were measured in each case. The results showed an increase in the proton component of the $2^+_1$ state, supporting a moderate reduction of the proton $1p_{1/2}$–$1p_{3/2}$ splitting towards the neutron dripline [4]. This study, as well as [3], further suggested that a mixed-symmetry $2^+$ state with an excitation energy around 7 MeV should be strongly populated in proton removal reactions from nitrogen isotopes. This state, lying above the neutron separation energy and therefore unbound, likely decays via neutron emission. Investigating this unbound $2^+$ state in carbon isotopes will provide critical experimental data to shed light on the evolution of the $Z$=6 spin-orbit splitting and benchmark theoretical models.
We present the investigation of the unbound states in $^{20}$C, populated via proton removal from $^{21}$N. The radioactive $^{21}$N beam was produced by the BigRIPS separator at RIBF and induced a proton removal reaction on a carbon target. The unbound states in $^{20}$C were analyzed using the SAMURAI spectrometer via invariant mass spectroscopy. In this report, the experimental setup, the data analysis as well as the preliminary results will be presented.
[1] M. Petri et al., Phys. Rev. Lett. 107, 102501 (2011).
[2] M. Petri et al., Phys. Rev. C 86, 044329 (2012).
[3] A.O. Macchiavelli et al., Phys. Rev. C 90, 067305 (2014).
[4] I. Syndikus et al., Phys. Lett. B 809, 135748 (2020).