Theory of elementary excitations in closed shell nuclei
Jul, 197732 pages
Published in:
- Nucl.Phys.A 284 (1977) 429-460
- Published: 1977
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Abstract: (Elsevier)
We discuss a theoretical approach which allows the calculation of both ground and excited state properties of nuclei in the same framework. The energy of the nucleus, calculated with effective density dependent interactions, is considered as a functional of the one-body density matrix. Starting from this functional, we derive the Hartree-Fock equations for the ground state and the random phase approximation for the excited states. Thus the same effective nucleon-nucleon interaction is used for the ground state and for the excited states: this yields self-consistent effects which are shown to be very important for the properties of the collective states. This approach may be viewed as a microscopic basis for the unified model. A method is developed to solve the RPA equations in the self-consistent basis. It allows the use of any phenomenological form of interaction, in particular finite range ones. We analyse the spinisospin components in the particle-hole channel of some effective interactions used up to now in ground state calculations; we show that they are well-behaved except for the σ·σ part which has the wrong sign. Sum rules which connect the static properties of the nucleus to moments of the strength function are calculated and used to check the accuracy of our results. It is shown that it is necessary to use a large configuration space in order to get reliable values of the transition probabilities B ( Eλ ). Due to the fact that the only parameters are those of the effective interaction, correlations appear between the calculated values of various quantities, e.g. the value of the B ( Eλ ) of low-lying collective states is strongly related to the single particle gap. Some results are presented in order to show the importance of self-consistency.References(25)
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