Abstract
We have examined the hypothesis by Bijker and Iachello who asserted that \(^{12}\textrm{C}\) has an internal structure with three \(\alpha \) particles arranged in a triangular shape, leading to the formation of the ground rotational band consisting of \(0^+\), \(2^+\), \(3^-\), \(4^\pm \) and \(5^-\) states. Following this idea, we reconstructed the intrinsic shape of \(^{12}\textrm{C}\) using experimental electron scattering data with minimal theoretical assumption. Our sole assumption was that the observed \(0^+_1\), \(2^+_1\), \(3^-_1\), and \(4^+_2\) states share a common internal structure, forming a rotational spectrum. The reconstructed intrinsic density showed a beautiful triangular shape with three peaks implying \(\alpha \) cluster formation in the ground band.
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Notes
Note that to convert the plots in Fig. 4 to densities, you need to multiply by spherical harmonics according to Eq. (1). For example, the central density of \(L=0\) component is approximately \(0.25/\sqrt{4\pi }\simeq 0.07\ \mathrm fm^{-3}\). Thus, combined with the neutron density, the central matter density is about \(0.14\ \mathrm fm^{-3}\), slightly lower than the normal density.
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Acknowledgements
The authors acknowledge the fruitful discussions with Dr. Q. Zhao, Dr. B. Zhou and Dr. Y. Funaki. They also thank to Dr. T. Neff and Dr. P. von Neumann-Cossel for the discussion and providing us the latest form factor data. We dedicate this work to Prof. Peter Schuck, whose pioneering study of \(\alpha \) particle condensation ignited our interest in nuclear cluster physics. One of the authors fondly remembers the discussion with him on the results presented here. It was just before the onset of COVID-19, marking our last conversation in person. Although he might not have fully endorsed this idea, it felt like a fitting topic to pay tribute to his lasting impact on our community.
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Kimura, M., Taniguchi, Y. Shape of \(^{12}\textrm{C}\). Eur. Phys. J. A 60, 77 (2024). https://doi.org/10.1140/epja/s10050-024-01302-w
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DOI: https://doi.org/10.1140/epja/s10050-024-01302-w