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Physical Review C

Description of collective spin excitations in deformed nuclei within a projected single-particle basis

Apolodor Aristotel Raduta, Ioan Ursu, Nicola Lo Iudice

Published Nov 1, 1992• 3 citations
Publisher

Abstract

Magnetic dipole spin excitations of deformed nuclei are studied in a schematic random-phase approximation (RPA) approach using a projected single-particle basis. The comparison of the present results with those obtained by conventional but more realistic RPA calculations supports the validity of the approach used here.
DOI
10.1103/physrevc.46.1782

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The subject of the present paper is the theoretical description of collective electronic excitations, i.e., spin waves, in the Hubbard model. Starting with the widely used random-phase approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely, the spectral-density ansatz. Doing so we have to introduce a ``screened'' Coulomb interaction rather than the bare Hubbard interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phase diagrams delivered by the single particle theories.
Effects of ground-state correlations on magnetic dipole excitations in 40^{40}40Ca
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Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.