Chapter I. Introduction to Comprehensive Nuclear Structure Study Based on Cluster Correlations and Molecular Viewpoint

Abstract

Contents § 1. Development of the studies based on the viewpoint presented in P. T.P. Supplement No. 52 § 2. Basic viewpoint of molecule-like structure in nuclei § 3. Comprehensive understanding on the structure of a-nuclei from the viewpoint of structure-change § 4. Various aspects of cluster correlations and cluster structure in non-anuclei § 5. Molecule-like structure in highly excited energy region § 6. Interaction between complex nuclei as composite particles § 7. Summary and future problems § 1. Development of the studies based on the viewpoint presented in P. T.P. Supplement No. 52As a basic correlation of the nuclear many-body system there exist cluster correlations by which various kinds of molecule-like structure are realized in wide regions of mass number and excitation energy. Consequently the molecule-like structure constitutes a fundamental form of existence and motion of nuclei, together with the shell-model-like structure. This viewpoint was presented in the Supplement No. 52n of the Progress of Theoretical Physics (abbreviated to P.T.P.).In the course of the progress of the successful studies by the nuclear shell model, the independent-particle picture was founded firmly, but at the same time it was recognized clearly that there exist in light nuclei groups of levels (ground or excited) with anomalous properties which were left outside the success of the shell model interpretations. These levels could not be 2 K. Ikeda, H. Horiuchi and S. Saito easily understood on the basis of the independent-particle picture. Another viewpoint different from the independent-particle one was needed for the understanding of these groups of levels. A basic viewpoint of the cluster correlation and molecule-like structure in nuclear system was formed through the accumulated studies aimed to understand the structure of these groups of levels. In P.T.P. Supplement No. 52, together with the presentation of the molecular viewpoint and with the historical background of investigations, there were reported the results of the theoretical studies which were necessary for the formation of the viewpoint and done under the research project of "Alpha-Like Four Body Correlations and Molecular Aspects in Nuclei" organized by the Research Institute for Fundamental Physics (abbreviated to RIFP) during 1968'" '--' 1971.The prospect 2 l that the molecule-like structure can appear in wide region of nuclei both in mass number and in excitation energy has promoted an extensive development of study of cluster structure in light nuclei. After the presentation of the molecular viewpoint in P.T.P. Supplement No. 52, two research projects were organized by RIFP; one was on "Study of Composite Particle Scattering by Microscopic Model" 3 l during 1972"'1973 and the other was on "Study of 20 Ne Region Nuclei with Transient Character from Shell-Structure to Molecular One"•l during 1973'" '--'1974. The former project aimed to develop the microscopic and semi-microscopic models which treat the relative motion and the interaction between clusters so ...

Impurity Effects in Λ Hypernuclei

“…The core nucleus 20 Ne is a typical sdshell nucleus with various structures within the small excitation energy range [3][4][5]. It is known that the K π = 0 − band has a pronounced α+ 16 O clustering, while the ground-state band shows mixture of deformed shell structure and α + 16 O cluster structure.…”

“…Furthermore, in 21 Λ Ne, we also discuss the dependence of impurity effects on structures, namely their difference between mean-filed like and α + 16 O + Λ cluster states. In 20 Ne [3][4][5], it is known that the K π = 0 − band has a pronounced α+ 16 O clustering, while the ground-state band has a mixture of deformed shell structure and α + 16 O cluster structure. Another aim is a rather challenging: to show the possibility of using a Λ particle as a probe to investigate structure of the core nuclei.…”

Few-Body Problem in Nuclear Reactions:Beyond the horizon of the three-body Faddeev equations

“…The present approach is different from the method used for heavy nuclei. Especially, the molecular structure with several alpha-clusters is well developed in light nuclei [1]. Beside the alpha-particle, realistic nuclei are constructed by the proton, neutron, d, t, 3 He, 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S, and so on.…”

“…2) The path a : from the two-body free Hamiltonian and the system energy: {H (2) 0 , E (2) } to the onebody set: {H (1) 0 , E (1) } is replaced with the path b to ensure the analytic continuation to the set {H (2) 0 , E (2) cm }, where H (1) 0 is the one-body kinetic operator for the center-of-mass motion, and finally {H (2) 0 , E (2) cm } arrives at {H (1) 0 , E (1) } via the path c . These paths are illustrated by,…”

“…Because the one-body Hamiltonian H (1) 0 (→ H (1) 0 ) will vanish due to the zero relative energy and no "one-body potential", then the "eigenenergy" E (1) should be zero. Therefore, we obtain the three-body eigenenergy E = − B − ζ, where ζ is the separation energy from the three-body bound state (see Figure 4).…”