Energy-weighted RPA sum rules for isoscalar giant resonances |
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| Affiliation: | 1. Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singapore;2. Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UK;3. Smith School of Enterprise and the Environment, University of Oxford, South Parks Road, Oxford OX1 3QY, UK;4. Centre for Environmental Policy, Imperial College London, South Kensington, London SW7 2AZ, UK;1. State Key Laboratory of Pollution Control and Resource Reuse, Key Laboratory of Yangtze River Water Environment, Ministry of Education, College of Environmental Science and Engineering, Tongji University, Shanghai 200092, PR China;2. College of Architecture and Urban Planning, Tongji University, Shanghai 200092, PR China;3. Department of Chemical Engineering, Royal Institute of Technology (KTH), Sweden;4. Department of Energy, Building and Environment, Mälardalen University (MDH), Sweden |
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| Abstract: | ![]()
Explicit analytic expressions are derived for the cubic energy-weighted sum rule in RPA and for Skyrme interactions. From these and the once energy-weighted sum rule an average energy for the giant resonance is estimated. The contributions from the deformation of the Fermi sea, and also from the Coulomb, surface and effective mass terms in the interaction are explicitly evaluated. The limited validity of estimates based on the assumption of a uniform density distribution is stressed. The important role of the surface for modes of high multipolarity is shown quantitatively. Using a leptodermous expansion the true volume, surface and higher order terms are obtained. |
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