Structure of 12C

doi:10.1016/0375-9474(71)90549-5

Nuclear Physics A

Volume 168, Issue 3, 21 June 1971, Pages 593-624

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Abstract

The low-lying states of ¹²C are investigated with the Heitler-London approximation of the clustering wave functions. The distances between α-clusters are determined to make the total energy minimum; they are relatively small in the ground state band but large in the excited band. The l · s force is taken into account in the ground-state band by hybridizing the shell model and the cluster model and is found important to raise the excitation energies of the 2⁺ and 4⁺ states. Even though the clusterization is small in the ground-state band, it has an important effect on the enhanced transition probabilities and the form factors for electron scattering. The clusterization is essential to explain the observed properties of the excited band such as the low excitation energy and the large α-decay width.

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The 3α-cluster structure of excited states in ¹²C is investigated by taking into account the correct boundary condition for three-body resonant states. In this study, we adopt the Complex Scaling Method (CSM), which enables us to obtain the resonant states that can be described as square integrable states with the same boundary conditions as those of the bound states, and calculate not only resonance energies but also the total decay widths of the 3α system. We compare the calculated resonance parameters to the experimental data and also to the previous 3α model results obtained with a bound state approximation. Our results well explain the many observed levels and give an assurance for the presence of the second $2^{+}$ state, which is expected by the 3α model calculations with the approximations of bound state or two-body scattering. As for the negative-parity states, it is considered that the calculated $4^{-}$ state is assigned to the observed $E_{x} = 13.4 MeV$ state. Through the calculation of channel amplitudes, the obtained third $0^{+}$ state is found to have a s-wave dominant and a more dilute structure compared to the second $0^{+}$ state.
Nuclear clusters and nuclear molecules
2006, Physics Reports
Clustering has long been known to be influential in the structure of ground and excited states of $N = Z$ nuclei. States close to the decay thresholds are of particular interest, as clustering becomes dominant. Recent studies of loosely bound light neutron-rich nuclei have focused attention on structures based on clusters and additional valence neutrons, which give rise to covalent molecular binding effects. These nuclear molecules appear only at the extremes of deformation, in the deformed shell model they are referred to as super- and hyper-deformed. The beryllium isotopes provide the first examples of such states in nuclear physics. Further nuclear molecules consisting of unequal cores and also with three centres can be considered. These arise in the isotopes of neon and carbon, respectively. Molecular states in intrinsically asymmetric configurations give rise to parity (inversion) doublets. Examples of recent experiments demonstrating the molecular structure of the rotational bands in beryllium isotopes are presented. Further experimental evidence for bands as parity doublets in nuclei with valence neutrons in molecular orbits is also analysed. Work on chain states (nuclear polymers) in the carbon isotopes is discussed. These are the first examples of hyper-deformed structures in nuclei with an axis ratio of 3:1. Future perspectives are outlined based on a threshold diagram for covalent nuclear molecules with clusters bound via neutrons in covalent molecular configurations.
Angular correlation, spin alignment, and systematics of mis-matched 12C + 12C inelastic scattering resonances
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Particle gamma-ray angular correlation measurements have been used to study the spin alignment and magnetic-substate population parameters for the 2⁺₁ (4.443 MeV) state in ¹²C, populated in the $^{12} C (^{12} C,^{12} C [0^{+}_{2}])^{12} C (2^{+}_{1})$ inelastic scattering reaction in the vicinity of a prominent, narrow peak in the scattering excitation function. The data show a strong alignment of the spin with the orbital angular momentum, and suggest that the cross section peak corresponds to a spin 14⁺ resonance at E_c.m.=28.0 MeV. This energy is close to that where a strong peak is also observed in the 0⁺₁+0⁺₂ excitation function. A comparison between the data for these two channels lends some support to recent theoretical calculations of resonance behavior for angular-momentum-mismatched channels in $^{12} C +^{12} C$ inelastic scattering.
Molecules in nuclei
2003, Comptes Rendus Physique
The possible existence of analogues of atomic molecules within nuclei is considered in the context of the neutron-rich beryllium and carbon isotopes, where the underlying α cluster structure is believed to produce a multi-centred potential in which valence neutrons move. The generation of molecular wave-functions is examined and the link with the deformed harmonic oscillator and the Nilsson single-particle level scheme traced. Experimental evidence for the existence of molecular exotic cluster structures is reviewed particularly the nature of spectroscopic information provided by break-up reaction measurements. To cite this article: M. Freer, C. R. Physique 4 (2003).
Les noyaux riches en neutrons semblent présenter des états analogues aux molécules atomiques. En particulier, une sous-strucuture en particules α de noyaux légers riches en neutrons tels les Bérylium et des Carbones pourrait créer un potentiel à plusieurs centres piègeant des neutrons de valence. Cet article fait le point sur les fonctions d'onde de ces états moléculaires et sur leur lien avec les orbites de Nilson et de l'oscillateur harmonique déformé. Les preuves expérimentales de l'existence d'états nucléaires agréés en molécules est passé en revue avec un point particulier sur les informations spectroscopiques provenant de la mesure de leur canaux de désintégration. Pour citer cet article : M. Freer, C. R. Physique 4 (2003).
Antisymmetrized molecular dynamics: A new insight into the structure of nuclei
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The AMD theory for nuclear structure is explained by showing its actual applications. First the formulation of AMD including various refined versions is briefly presented and its characteristics are discussed, putting a stress on its nature as an ab initio theory. Then we demonstrate fruitful applications to various structure problems in stable nuclei, in order to explicitly verify the ab initio nature of AMD, especially the ability to describe both mean-field-type structure and cluster structure. Finally, we show the results of applications of AMD to unstable nuclei, from which we see that AMD is powerful in elucidating and understanding various types of nuclear structure of unstable nuclei. To cite this article: Y. Kanada-En'yo et al., C. R. Physique 4 (2003).
Cet article présente de la structure de plusieurs noyaux atomiques en utilisant l'approximation de la dynamique moléculaire antisymétrisée (AMD). Après un bref rappel mettant en avant la possibilité de faire des calculs ab initio, nous montrons que cette approche permet de comprendre différents problèmes de structure nucléaire bien connus pour les noyaux stables. En particulier, elle donne une description unifiée des comportements de type champ moyen et de l'apparition d'agrégats de nucléons. Pour finir, nous appliquons AMD aux noyaux instables (exotiques) et nous illustrons qu'une telle approche fournit une explication et une compréhension des différentes structures découvertes avec les noyaux exotiques. Pour citer cet article : Y. Kanada-En'yo et al., C. R. Physique 4 (2003).
Nuclear molecules
2001, Nuclear Physics A

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Nuclear Physics A

Abstract

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Cited by (86)

Spectroscopy of <sup>12</sup>C within the boundary condition for three-body resonant states

Nuclear clusters and nuclear molecules

Angular correlation, spin alignment, and systematics of mis-matched <sup>12</sup>C + <sup>12</sup>C inelastic scattering resonances

Molecules in nuclei

Antisymmetrized molecular dynamics: A new insight into the structure of nuclei

Nuclear molecules