Alpha-chain States Research Articles

Cluster Approach to Atomic Nuclei: Alpha-Chain States in 12C

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Alpha-Chain Structure of 12C

Alpha-chain states in 12C are studied via an analysis of underlying quantum mechanical symmetry. It is pointed out that the linear chain band exists undoubting in 12C. However, the pure linear chain structure does not exist in 12C. All possible linear chain states are mixture with triangle structures.

Alpha-chain states in 12C.

Alpha-chain states in $^{12}\mathrm{C}$ are studied by employing the isomorphic shell model. Where possible \ensuremath{\alpha} particles and their spatial distribution are derived, instead of being assumed as usual in \ensuremath{\alpha}-cluster models. It has been found that the average forms of both the ground state and the first ${0}^{+}$ excited state can be associated with an \ensuremath{\alpha} chain composed of three \ensuremath{\alpha} particles in a row. The ground state and the first ${0}^{+}$ excited state energies and their rotational bands, together with their charge radii and intrinsic quadrupole moments, have been computed and compared with the predictions of \ensuremath{\alpha}-particle models. With reference to experimental data, all quantities examined lend support to the present approach.

Alpha chain states in 4N-nuclei

Alpha chain states in 4N-nuclei

Systematics of some 3-dimensional α-cluster configurations in 4 N nuclei from 16O to 44Ti

The predicted systematics of alpha chain states (one-dimensional alpha-cluster configurations) and two-dimensional alpha-cluster configurations calculated using the Bloch-Brink (BB) alpha-cluster model have recently been presented. Here we present systematics for other alpha-cluster states which arise from three-dimensional configurations predicted by the BB model. Many of the three-dimensional alpha-cluster configurations can be classed into families which are found to extend over a wide range of nuclei. We consider mostly sd-shell nuclei but present a few results for 44Ti as well.

Systematics of 2-dimensional α-cluster configurations in 4 N nuclei from 12C to 44Ti

The recent discovery of the six-alpha chain state in 24Mg suggests that alpha-cluster configurations may extend to much higher excitation energies and have much larger deformations than has previously been believed possible. The systematics of alpha chain states (one-dimensional alpha-cluster states) have recently been published. Here we present systematics of a second class of highly deformed alpha-cluster states which arise from two-dimensional configurations.

Alpha-chain states in 4N-nuclei from 20Ne to 32S.

A 6\ensuremath{\alpha}-chain state has recently been discovered in $^{24}\mathrm{Mg}$ which is some 16--17 MeV above the 6\ensuremath{\alpha}-breakup threshold and yet paradoxically only 4--5 MeV wide. This surprising discovery raises the question of the possible existence of N\ensuremath{\alpha}-chain states in other 4N-nuclei. The excitation energy of this 6\ensuremath{\alpha}-chain state is very close to the value predicted by the Bloch-Brink cluster model. Therefore, to aid the experimental search for similar states in other nuclei, we present here predictions of the excitation energies of the N\ensuremath{\alpha}-chain state bandheads in the 4N-nuclei from $^{20}\mathrm{Ne}$ to $^{32}\mathrm{S}$ obtained using the Bloch-Brink cranked cluster model with the Brink-Boeker effective interaction and free variation of all parameters.

Systematics of alpha-chain states in 4 N-nuclei

Recently a six-alpha chain state has been discovered in 24Mg. The Bloch-Brink cranked cluster model shows that linear chains of alpha particles are associated with stable minima in the potential-energy surface for all 4 N-nuclei. Experimental candidates in 8Be, 12C and 16O have already been identified. Using a Brink-Boeker effective interaction, and allowing free variation of all parameters, we calculate the geometric arrangements and energies of the lowest alpha-chain states. These configurations are then cranked to predict the maximum angular momenta and the excitation energies that they can sustain. We conclude that states similar to that in 24Mg should also be accessible to experimental investigation in other nuclei.

Comparison of the Nilsson and Skyrme Hartree-Fock results for the properties of highly deformed states in nuclei

A Comparison of the Nilsson model and the Skyrme Hartree-Fock model for studying highly deformed states in nuclei is made. The states constructed are the 4-particle, 4-hole and 8-particle, 8-hole states in 40Ca and the linear alpha chain states in 12C and 16O. The deformations obtained in the two approaches are remarkably similar. The change in the radius of the np-nh state in 40Ca relative to the ground state is smaller in the Skyrme Hartree-Fock model than in the Nilsson model, indicating monopole shrinkage in the former approach, hence volume non-conservation. Whereas the energies of the 4 p−4 h states are nearly the same in the two approaches, the 8 p−8 h is at too high an energy in the Nilsson model. For the linear chain states in 12C and 16O, the Skyrme 3 Hartree-Fock approach gets the energies of the projected J π = 0 + states a factor of two too high while the results of the Nilsson model are in surprisingly good agreement with experiments. The quadrupole moment in momentum space ( Q p ) for the ground state and the metastable highly deformed states is discussed.