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

TL;DR

This paper investigates the rotational properties of $^{8}$Be in the continuum using a two-alpha cluster model, revealing that continuum resonances exhibit collective rotational features despite deviations in static and transition probabilities.

Contribution

It introduces a detailed analysis of rotational bands in the continuum, including complex energy scaling and the division of transition probabilities into various contributing components.

Findings

Reproduction of rotational energy sequence with complex scaling.

Continuum resonances show strong collective rotational character.

Discussion of properties of higher $6^+$ and $8^+$ resonances.

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.