The structure of neutron-rich carbon isotopes continues to be a subject of interest in nuclear physics, particularly the nucleus ¹⁶C. One of the key unresolved issues is the variation in measured B(E2) values for the transition from the first-excited 2⁺₁ state to the ground state, with reported values spanning nearly an order of magnitude. Traditional interpretations assume a
simple model in which two valence neutrons couple to a ¹⁴C core, requiring the introduction of a large effective charge to match experimental data. However, this approach does not fully capture the complexity of ¹⁶C’s nuclear structure.

This talk presents results from a large-scale  (2 + 4)ℏω no-core shell-model calculation of ¹⁶C, incorporating six major shells and employing the Zheng et al [1] interaction within the OXBASH [2] framework. The analysis of the wave functions indicates significant mixing of higher-order configurations, challenging the validity of the simple two-neutron model. The theoretical predictions are further validated by comparing the computed excitation spectrum and intermediate-energy elastic proton scattering cross-sections with experimental data. Notably, the results demonstrate that a smaller, or even negligible, effective charge is sufficient to reproduce the accepted B(E2) value, resolving discrepancies observed in previous studies.

References
[1] D. C. Zheng, B. R. Barrett, J. P. Vary, W. C. Haxton, and C.-L.Song, Phys. Rev. C 52, 2488 (1995).
[2] OXBASH-MSU (the Oxford-Buenos-Aries-Michigan State University shell model code). A.Etchegoyen, W. D. M. Rae, and N. S. Godwin (MSU version by B. A. Brown, 1986); B.A.Brown, A. Etchegoyen, and W. D. M. Rae, MSUCL Report Number 524 (1986).