Magnetic moments of spherical nuclei: Status of the problem and unsolved issues
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CLEI Theory
Magnetic Moments of Spherical Nuclei: Status of the Problem and Unsolved Issues I. N. Borzov1), E. E. Saperstein2)* , and S. V. Tolokonnikov2) Received September 6, 2007
Abstract—Dipole magnetic moments of more than 100 odd spherical nuclei are calculated within the theory of finite Fermi systems. For the effective interaction of nucleons within the theory of finite Fermi systems, use is made of a version that takes into account nuclear-medium-modified amplitudes for the exchange of one pion and one rho meson. A new tensor local charge ζt is incorporated in the theory of finite Fermi systems in addition to the known orbital (ζl ) and spin (ζs ) local charges. Good agreement with experimental data, at a level of 0.1 to 0.2µN , is obtained for the overwhelming majority of the nuclei considered here. Several cases of a significant discrepancy with experimental data, at a level of 0.3 to 0.5µN , are revealed. Possibilities for removing these discrepancies are discussed. A detailed comparison with known results obtained within the multiparticle shell model is performed for 2p- to 1f -shell nuclei. Cases where the standard theory of finite Fermi systems must be extended by taking into account multiparticle configurations are found. Magnetic moments are analyzed for a number of long isotopic chains. Several new experimental values of magnetic moments for copper isotopes far from the beta-stability valleys are known. For the example of the copper-isotope chain, it is shown how the emergence of a deformation in the ground state of a nucleus can be revealed on the basis of a systematic analysis of magnetic moments. PACS numbers: 21.10.Ky, 21.60.-n, 21.65.+f DOI: 10.1134/S1063778808030095
1. INTRODUCTION Magnetic dipole moments are one of the fundamental nuclear features. Their description played an important role in the development of basic approaches in the theory of the nucleus, including the shell model [1] and the theory of finite Fermi systems [2]. Indeed, a qualitatively correct prediction of magnetic-moment values for odd nuclei on the basis of Schmidt’s single-particle formulas was one of the main arguments in support of the shell model at the early stage of its development, while the explanation of deviations from Schmidt’s formulas was the first nuclear-physics problem considered within the theory of finite Fermi systems [3]. However, no systematic theoretical analysis of experimental data on magnetic moments has been performed since the 1960s, despite the fact that these data have become ever more diverse and detailed. Advances made in recent years owing to radioactive-ion accelerators, which provide various spectroscopic information for nuclei far off the beta-stability boundary, are especially impressive. An overview of experimental data obtained in recent 1)
Institute of Physics and Power Engineering, pl. Bondarenko 1, Obninsk, Kaluga oblast, 249020 Russia. 2) Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia. * E-mail: [email protected]
years can be found in [4, 5]. Dat
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