Collective degrees of freedom of the two-component nuclear system

Abstract

A microscopic proton-neutron symplectic model of collective motions, based on the non-compact symplectic group Sp(12, R) , is introduced by considering the symplectic geometry of the two-component many-particle nuclear system. The dynamical group of the whole many-particle system allows the separation of the nuclear variables into kinematical (internal) and dynamical (collective) ones. Then, the number and type of collective degrees of freedom, related to the dynamical variables, are determined properly by the group-theoretical consideration of the coordinate transformation of the microscopic configuration space, spanned by the \( m = A-1\) translationally invariant Jacobi vectors, to the collective and intrinsic submanifolds. As a result the nuclear wave functions are represented as a product of collective and intrinsic parts. Dynamical content of the \( Sp(12,R)\) model is revealed by considering its \( GCM(6)\) submodel, which appears as an irrotational flow collective model of the two-component nuclear system augmented by the \( SO(6)\) intrinsic vortex degrees of freedom. Consequently, the \( Sp(12,R)\) model appears therefore as a hydrodynamic collective model of the proton-neutron nuclear system which include 21 collective irrotational flow degrees of freedom and an \( U(6)\) intrinsic structure associated with the vortex degrees of freedom. The latter play an important role in the construction of the microscopic wave functions because they allow to ensure the full antisymmetry of the total wave function and are responsible for the appearance of the low-lying collective bands.