Rotational bands in the continuum illustrated by ${}^8$Be results

Abstract

We use the two-alpha cluster model to describe the properties of ${}^8$Be. The rotational energy sequence of the $(0^{+},2^{+},4^{+})$ resonances are reproduced with the complex energy scaling technique for Ali-Bodmer and Buck-potentials. However, both static and transition probabilities are far from the rotational values. We trace this observation to the prominent continuum properties of the $2^{+}$ and $4^{+}$ resonances. They resemble free continuum solutions although still exhibiting strong collective rotational character. We compare with cluster models and discuss concepts of rotations in the continuum in connection with central quantities as transition probabilities, inelastic cross sections and resonance widths. We compute the $6^{+}$ and $8^{+}$ $S$-matrix poles and discuss properties of this possible continuation of the band beyond the known $4^{+}$ state. Regularization of diverging quantities are discussed in order to extract observable continuum properties. We formulate division of electromagnetic transition probabilities into interfering contributions from resonance-resonance, continuum-resonance, resonance-continuum, and continuum-continuum transitions.

To be published in Physical Review C

References in corpus (4)

• Radioactive decays at limits of nuclear stability
• Momentum distributions of $\alpha$-particles from decaying low-lying ${}^{12}$C-resonances
• Binary reaction decays from 24Mg+12C
• Inelastic cross sections and continuum transitions illustrated by ${}^8$Be results

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• Nuclear rotation in the continuum
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• Effects of rotation and valence nucleons in molecular-like $\alpha$-chain nuclei
• Resonant and Scattering States in the $\alpha +\alpha$ System from the Non-Localized Cluster Model
• Techniques to treat the continuum applied to electromagnetictransitions in ${}^8$Be
• Three-body bremsstrahlung and the rotational character of the 12C-spectrum
• Rotational bands beyond the Elliott model
• Broad resonances and beta-decay
• Borromean structures in medium-heavy nuclei
• A Vision for the Science of Rare Isotopes
• Calculation of expectation values of operators in the Complex Scaling method