Using the harmonic version of the generator coordinate method, and Skyrme interaction, the frequencies of the isoscalar breathing and quadrupole modes are related to the relevant incompressibility coefficients. The possibility of extending this to spin modes is also examined. It is found that a spin incompressibility coefficient is negative for a particular set of Skyrme parameter for4He. Other sets produce low positive values and these in turn could imply a relatively low lyingS=2,T=1 state. The replacement of the three-body term by the density-dependent one, suggested by Chang provides a cure for this pathology.
Volume 96, 2022
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