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.
A microscopic model for three-cluster configurations in light nuclei is presented. It uses an expansion in terms of Faddeev components for which the dynamic equations are derived. The model is designed to investigate binary channel processes in a compound system. Gaussian and oscillator bases are used to expand the wave function and to represent appropriate boundary conditions. We study the effect of cluster polarization on ground and resonance states of 7 Be, and on the astrophysical S-factor of the reaction 6 Li(p, 3 He) 4 He.
The resonance states embedded in the three-cluster continuum of 6 He and 6 Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.
We study the nature of the low-lying resonance states in mirror nuclei 9 Be and 9 B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides a convenient description of the three-cluster continuum. The dominant three-cluster configurations α + α + n and α + α + p in 9 Be and 9 B, respectively, are taken into account. Dominant decay channels for all resonance states in 9 Be and 9 B are explored. Much attention is paid to the controversial 1/2 + resonance states in both nuclei. We study effects of the Coulomb interaction on the energy and width of three-cluster resonances in the mirror nuclei 9 Be and 9 B. We also search for the Hoyle-analog state, which is a key step for alternative ways to synthesize 9 Be and 9 B in triple collisions of clusters in a stellar environment.
The resonance structure of 5H is investigated within a three-cluster microscopic model. Hyperspherical harmonics are used to characterize the channels of the three-cluster continuum and to implement the appropriate boundary conditions. The model reveals the energy and width of the 5H resonance states and allows for a detailed channel analysis. These results are verified against the available experimental data and compare qualitatively favorably with some other theoretical calculations.
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