Nuclear Vibrations and Effective Interactions

Abstract

We derive separable interactions which are equivalent to the zero-range Skyrme forces in the random phase approximation. The isoscalar and the isovector tl-pole-tl-pole forces proposed by Bohr and Mottelson are obtained as a special case of the separable interactions. Spin- and isospin-dependent separable forces are also discussed. 3 ) reproduces very well static properties of the nuclear ground states in the broad region of the mass table. The same interaction has been shown by many authors 4)~6) to explain very well the gross structure of the dynamic properties of nuclei like giant multipole resonances. It is well known that the separable Q-Q force developed by Bohr and Mottelson et al.7),8) has played an important role in comprehensive description of nuclear low-lying collective excitations. The introduction of the separable force makes it possible to perform the calculations of many-body correlation problems in a simple and intuitive manner and to analyze experimental data systematically throughout the periodic table. Moreover, Bohr and Mottelson et a1. 7 ),9) have extended their idea of the separable-force to the study of giant multipole resonances by using the sum-rules and the self-consistent condition between the vibrating potential and density. Their model has been Quite successful in the calculation of the excitation energies of the isoscalar and isovector giant resonances and, also, in the estimate of the core polarization effects. Up till now, some authors10),11J discussed the connection between the separable A-pole-A-pole interaction and the more sophisticated interaction, that is, the Skyrme force related with the isoscalar and the isovector giant resonances. 'l Present address: Division de Physique Theorique, Intitut de Physique Nucleaire, 91406 Orsay-Cedex, France.