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Hartree-Fock theory of nuclear deformations and high spin states

Hartree-Fock theory of nuclear deformations and high spin states

Hartree-Fock theory of nuclear deformations and high spin

Prama!)a - J. P~ys., Vol. 32, No.4, April 1989, pp. 351-365. (hJ Printed in India. .7 , Hartree-Fock theory of nuclear deformations and high spin states C R PRAHARAJ Institute of Physics, Bhubaneswar 751005, India Abstract. A brief review of the Hartree-Fock approximation to nuclear shapes and nuclear spectra is presented. Various aspects of rotation-alignment eITectand high spin states are illustrated in the Hartree-Fock model. Kcywords. Nuclear deformation; self-consistent field; nuclear rotation; high spin states; bandcrossing; electromagnetic transitions. PACS:".'os 21'65; 21'10; 23-20 l. Introduction As an interacting many-fermion system, a nucleus possesses some unique features. The number of particles and the associated shell model configurations are large enough;lO preclude a straightforward diagonalization scheme for a meaningful description of the complex nuclei. At the same time the simplicities of an infinite system are absent in a nucleus. The nuclei show certain features which are describable in macroscopic terms. Many nuclei have multipole deformations, making it possible to visualize their shapes and to study the rotational bands associated with such deformation (Bohr 1952; Bohr and Mottelson 1975). The Hartree-Fock (HF) theory is able to provide a microscopic description of such nuclei. It starts at the fundamental levelwith a shell structure and two-body interaction among nucleons and describes the nucleons as moving in an average deformed field (the Hartree-Fock field). It assigns a deformed orbit to each nucleon (Nilsson 1955) and provides an intuitively simple description of the many-body system. In this paper we review the HF theory of deformed nuclei and present some results of HF and angular momentum projection studies of band-crossings and high spin states in nuclei. As will be seen in these discussions, this deformed HF model provides a useful basis for a simple deformed configuration mixing scheme for studying the ground and excited bands in nuclei and the high spin states. In §2we review the HF description of the structure of nuclei in various mass regions. The high spin states and the application of Hartree-Fock and angular momentum projection methods for their description are given in §3 and the concluding remarks in §4. 2. 2.1 Hartree-Fock theory and nuclear shapes For many nucleons interacting among themselves via two-body force we have the 351

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