Structural properties of the 10 Be and 10 C four-cluster nuclei
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CLEI Theory
Structural Properties of the
10
Be and
10
C Four-Cluster Nuclei
B. E. Grinyuk* and I. V. Simenog** Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Metrologicheskaya ul. 14b, Kyiv, 03680 Ukraine Received January 29, 2013
Abstract—The structure functions for the 10 Be and 10 C nuclei are studied in a four-particle approximation (two alpha-particle clusters plus two nucleons). New versions of the αα interaction potential are constructed. Together with the nα, pα, and N N potentials proposed previously, they make it possible to describe the binding energies and radii of the nuclei being considered, along with the S-wave twocluster phase shifts at low energies. General properties of four-particle wave functions are studied, and two basic configurations of the cross and tetrahedron types are revealed in the 10 Be and 10 C nuclei. A detailed analysis of the behavior of the structure functions is performed for these nuclei. The density distributions, form factors, and pair correlation functions are considered. The momentum distributions are obtained for the alpha particles and extra nucleons. The structure functions for the 10 Be and 10 C four-cluster nuclei are compared with those for the 6 He three-cluster nucleus. The bound states of the nuclei are studied within a high-precision variational approach by using Gaussian bases. DOI: 10.1134/S1063778814030090
This study is dedicated to V.B. Belyaev, an outstanding theoretical physicist, on the occasion of the 80th anniversary of his birthday 1. INTRODUCTION By explicitly taking into account the clustering of nuclei in studying their structure, one can obtain deeper insight into the structural features of rather complicated nuclear systems. The treatment of clusters as particles makes it possible to simplify substantially the respective many-body problem without a substantial loss of accuracy. In the ground state, the 10 Be and 10 C mirror nuclei can be represented as four cluster systems formed by two alpha particles and two extra nucleons (neutrons in the case of 10 Be and protons in the case of 10 C). This treatment [1, 2] may compete in accuracy with approaches that take into account nucleon degrees of freedom (see, for example, [3]). In order to describe successfully basic structural properties of nuclei, it is important to construct models of cluster–cluster interactions such that these models would not only describe phase shifts but also faithfully reproduce the binding energy and size of the nucleus being considered. A precise description of the binding energy of a nucleus is important for correctly * **
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reproducing the asymptotic behavior of the respective wave function and, as a consequence, basic structure functions (in particular, density distributions and pair correlation functions), while precise values of the root-mean-square radius and root-mean-square distances between the constituent particles ensure a correct description of form factors at low
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