Chapter III. Study of Non-Alpha-Nuclei Based on the Viewpoint of Cluster Correlations

Abstract

Contents § 1. Introduction and summary 1.1. Viewpoint of cluster correlations in non-alpha-nuclei 1.2. Interactions between few-nucleon clusters 1.3. Motion of individual nucleons in molecule-like nuclei 1.4. Multi-cluster model for non-alpha-nuclei 1.5. Alpha and three-nucleon cluster states in lightest sd-shell and A=15 nuclei § 2. Interactions between few-nucleon clusters 2.1. Realistic effective nuclear potentials 2.2. N-a interaction 2.3. d-a interaction and distortion effect of deuteron 2.4. Excited states in A=4 system with 3N+N cluster model § 3. Molecular structure in the 8 Be-core region 3.1. Motion of a nucleon around a 8 Be·core 3.2. Molecular orbital model . Structure of 9 Be nucleus 3.4. Structure of 10 B nucleus 3.5. Structure of neutron-rich Be-and B-isotopes § 4. Three-cluster model of the A=lO and 11 nuclei 4.1. Orthogonality condition model § 5. 4.2. 2a + t cluster model of 11 B nucleus 4.3. 2a+d cluster model of 10 B and 10 Be nuclei 4.4. Effect of the complete antisymmetrization Alpha and three-nucleon cluster states in lightest nuclei 5.1. Structure of A=19 nuclei 5.2. Structure of A=l8 nuclei 5.3. Structure of A=l7 nuclei 5.4. Structure of A=l5 nuclei § 1. Introduction and summary sd-shell 1.1. Viewpoint of cluster correlations in non-alpha-nuclei and A=151.1.1. The light nuclei (we consider in this chapter the P-shell and lightest sd-shell nuclei) have a relatively small number of nucleons, and their characters vary remarkably from nucleus to nucleus, showing strong individuality. Even in these light nuclei we see the persistency of saturation property which is considered a fundamental property of overall nuclei. In light nuclei, the saturation property emerges through formation of the acluster as a saturating subunit. This is the fundamental aspect prescribing the characteristics of light nuclei. The basic viewpoint of a-cluster structure in light nuclei has been presented in Ref. 1). As stated in detail in the previous chapter, 2 l recent investigations on light a-nuclei 3 l~el exhibit a remarkable success of the a-cluster model, which provides us with a comprehensive understanding of nuclear structure including quite high excited states, where coexistence of the shell and cluster structures and structure change between them can be understood in a unified way. Now we naturally proceed to an extensive investigation of non-a-nuclei from the cluster-model viewpoint. 1.1.2.The structure of light nuclei has been explained mostly in terms of the intermediate-coupling shell model or the deformed shell model, like the Nilsson model and the deformed Hartree-Fock method. They assume the formation of a static one-center single-particle field. The 9 Be nucleus, on the other hand, has long been considered a prototype of the molecule-like structure of nuclei, in which two a-particles constitute a stable dumbbell-like core and a remaining (valence) neutron moves on a single-particle orbital at NERL on May 26, 2015 http://ptps.oxfordjournals.org/ Downloaded from tion, which is an "elementary interaction...

Molecular orbital structures in10Be

“…This is a rather large binding energy, since 8 Be does not have a bound state of ␣-␣ and 9 Be is bound from the ␣ϩ␣ϩn threshold by only 1.67 MeV. Thus, the binding of 8.38 MeV from the four-body threshold in 10 Be is larger than twice the neutron binding energy in 9 Be by 5 MeV. This is a problem which we are going to discuss.…”

“…As a result, the ratio of the contributions of the spinorbit interaction for the two states is very different from the ratio of Ϫ1:2 expected from a simple shell model. The spinorbit components in 3/2 Ϫ and 1/2 Ϫ were calculated to be Ϫ3.1 MeV and 1.1 MeV in 9 Be. This change of ratio from the simple shell model is one of the characteristic properties of a weakly bound ͑or unbound͒ system.…”

“…In 10 Be, the microscopic ␣-cluster model has also been applied ͓9,10͔, and a developed cluster structure in the excited states was considered. According to this analysis of 9 Be, the ␣-␣ cluster structure of the core can reproduce not only natural parity states, but also the famous anomalous parity 1/2 ϩ state at low energy ͓7,8͔. It has been shown that the density of the 1/2 ϩ state is polarized along the ␣-␣ axis, so that there is a strong mixing of the s-wave and the d-wave components.…”

“…This model is an important candidate for explaining shellstructure anomalies. In the Be and B region, the ␣-␣ structure is well established, and especially in 9 Be, where a microscopic ␣ϩ␣ϩn model has reproduced the properties of low-lying states ͓7,8͔. In 10 Be, the microscopic ␣-cluster model has also been applied ͓9,10͔, and a developed cluster structure in the excited states was considered.…”

“…Their positions are determined variationally. Using this model, we reanalyze the structure of 9 Be and show that this extension enables us to use the original two-body spin-orbit interaction determined from a scattering phase-shift analysis of ␣-n. In 10 Be, all of the observed positive-parity bands and the negative-parity bands are described within the model.…”