Algebraic model for scattering in three-s-cluster systems. I. Theoretical background

Abstract

A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the nuclear many-particle state and its asymptotic behaviour are expanded in terms of oscillator states of the intra-cluster coordinates. The Generating Function technique is used to optimize the calculation of matrix elements. In order to derive the dynamical equations, a multichannel version of the Algebraic Model is presented.

Formation and decay of resonance states in Be9 and B9 nuclei: Microscopic three-cluster model investigations

“…These conditions were thoroughly discussed in Ref. [1]. The completeness relations for hyperspherical harmonics and oscillator functions are…”

“…Each hyperspherical harmonic Y K,l 1 ,l 2 ,LM ( ) (similar to the solid harmonics) predetermines one or several dominant shapes of the three-cluster triangles (see some illustrations for this statement in Refs. [34,35]). …”

“…(see the definition of hyperspherical harmonics, e.g., in [1,33]), then the wave function (1) takes the form…”

“…The microscopic model formulated in Ref. [1] makes use of harmonic oscillator functions to describe the intercluster motion. The model is called AM HHB, which stands for the algebraic three-cluster model with the hyperspherical harmonics basis.…”

Three-body properties of low-lying12Be resonances

“…However, a number of low-lying many-body resonances in light nuclei can still be well described as cluster structures even when they appear in the continuum. Prominent examples are found in stable nuclei such as 12 C and 9 Be [5][6][7][8][9][10][11][12][13], but even ground states like in 6 Be [14][15][16][17] and 10 Li [18][19][20] may appear as resonances.…”