THE PHASE TRANSITION FROM THE "ROTATION" TO VIBRATION SPECTRA IN THE LIPKIN SU(2) MODEL

The collective monopole excitation spectra of the Lipkin SU(2) model aresolveaexactly in the truncated monopole phonon representation and also approximately in the continuous variable representation. The transition from the "rotation" to vibration spectra for lowly-lying exclted states with the increase of the particle number in the upper level and the disappearance of the monopole "deformation" with the increase of the excitation energy are exhibited. The origin of these phase transitions is explained and the shape transition of real nuclei with the number of valence nucleons i s briefly discussed.