Using a simple density-dependent interaction -αδ(r1-r2)+γρσ( 1 2(r1+r2))δ(r1-r2), with the parameters α and γ adjusted to give the correct binding energy and the correct radius, we show that the energy of the giant quadrupole state is √2. This is the same result obtained by Mottelson, Hamamoto and Suzuki, using, however, different methods. We then consider finite-range terms in the interaction, such as those considered by Vautherin and Brink, and obtain a fairly simple modification of the above result. In contrast to the above quadrupole result the energy of the giant monopole state is not unique but depends linearly on σ, the power of the density. The Inglis cranking model is used to get the relevant mass parameters. This model appears to work very well for high frequency vibrations.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics