U(6)-Phonon model of nuclear collective motion

Abstract

The U(6)-phonon model of nuclear collective motion with the semi-direct product structure [HW(21)]U(6) is obtained as a hydrodynamic (macroscopic) limit of the fully microscopic proton–neutron symplectic model (PNSM) with Sp(12, R) dynamical group. The phonon structure of the [HW(21)]U(6) model enables it to simultaneously include the giant monopole and quadrupole, as well as dipole resonances and their coupling to the low-lying collective states. The U(6) intrinsic structure of the [HW(21)]U(6) model, from the other side, gives a framework for the simultaneous shell-model interpretation of the ground state band and the other excited low-lying collective bands. It follows then that the states of the whole nuclear Hilbert space which can be put into one-to-one correspondence with those of a 21-dimensional oscillator with an intrinsic (base) U(6) structure. The latter can be determined in such a way that it is compatible with the proton–neutron structure of the nucleus. The macroscopic limit of the Sp(12, R) algebra, therefore, provides a rigorous mechanism for implementing the unified model ideas of coupling the valence particles to the core collective degrees of freedom within a fully microscopic framework without introducing redundant variables or violating the Pauli principle.