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PROJECTED SHELL MODEL AND HIGH-SPIN SPECTROSCOPY
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1995
Year
EngineeringNuclear PhysicsNuclear DataSpin SystemsMagnetic ResonanceSpin DynamicShell ModelMagic NumbersHigh-energy Nuclear ReactionPhysicsNuclear TheoryAtomic PhysicsExperimental Nuclear PhysicsShell Model ConfigurationNatural SciencesSpectroscopyParticle PhysicsNuclear Many-body PhysicsDynamic Nuclear PolarizationNeutron Scattering
Most nuclei are deformed, making them difficult to treat with the standard spherical shell model, and the growing need for a proper quantum‑mechanical description of high‑spin states has arisen as modern experiments can resolve fine details of these states. This review presents an angular‑momentum‑projection approach, originally developed in the late 1970s, to enable efficient shell‑model configuration‑mixing calculations for high‑spin states. The method employs angular‑momentum projection to mix shell‑model configurations, illustrated with numerous examples and physical interpretations, and can be executed on workstations or modern PCs. Applying the technique to an axially symmetric rare‑earth nucleus, the full spectrum up to spin ≈ 40 is computed in only a few minutes on a mainframe, and similarly fast on a PC, demonstrating its computational efficiency. Appendix A provides detailed technical information useful for programming the method.
Most of the nuclei in the nuclear chart are deformed except for those in the vicinity of the magic numbers. It is difficult to treat such nuclei within the framework of the standard (spherical) shell model. On the other hand, the necessity for a proper quantum mechanical treatment of high-spin states has been steadily growing ever since modern experimental techniques made it possible to measure the fine details of the high-spin states of heavy nuclei. The present article reviews an approach based on the angular momentum projection technique which was initiated in the late seventies for the purpose of carrying out shell model configuration mixing calculations efficiently. A large number of examples is presented with an emphasis on the physical interpretation of the numerical results. Computing time for the whole spectrum up to spin ≈ 40 of an axially symmetric rare-earth nucleus takes only a few minutes on a Mainframe, showing the efficiency of the method. Most of the present calculations were carried out on a Workstation, but computation on a modern PC also presents no problem, so that one can enjoy a genuine quantum mechanical analysis of high-spin data using a facility available everywhere. Detailed technical information which may be useful for programming purposes is given in an Appendix.