Derivation of microscopic uni-axial unified adiabatic Bohr-Mottelson rotational model

摘要

For a rotational motion about a single axis, we derive a microscopic, quantum version of the phenomenological Bohr-Mottelson unified adiabatic rotational model without using redundant coordinates, imposing constraints on the intrinsic state or the particle coordinates, or assuming explicitly a deformed intrinsic state. The model Schrodinger equation is derived from the direct action of the multi-particle Hamiltonian operator on the rotational-model wavefunction. We show that the Coriolis-coupling terms in the derived Schrodinger equation vanish exactly only for a choice of the Euler angle that is consistent with the rotational model requirement that the intrinsic wavefunction be invariant under rotation. For this angle, which also satisfies the conjugate commutation relation, the kinematic moment-of-inertia tensor, collective-rotation velocity field, and flow vorticity have the rigid-flow characteristics. Pairing interaction and fluctuations in the rigid-flow moment of inertia are shown to reduce the rigid-flow value of the kinematic moment of inertia in closer agreement with the experimental value. The derivation shows that a multi-fermion system with unpaired or paired (quasi) particles rotates nearly rigidly and a single-particle system rotates irrotationally if the intrinsic system is rotationally invariant, regardless of the value of the moment of inertia and the nature of the rotationally-invariant momentum-independent interaction.