THE NUCLEAR BORN–OPPENHEIMER METHOD APPLIED TO NUCLEAR COLLECTIVE MOTION

Abstract

We deal with the application of the nuclear Born–Oppenheimer (NBO) method to the study of nuclear collective motion. In particular, we look at the description of nuclear rotations and vibrations. The collective operators are specified within the NBO method only to the extent of identifying the type of collective degrees of freedom we intend to describe; the operators are then determined from the dynamics of the system. To separate the collective degrees of freedom into rotational and vibrational terms, we transform the collective tensor operator from the lab fixed frame of reference to the frame defined by the principal axes of the system; this transformation diagonalizes the tensor operator. We derive a general expression for the NBO mean energy and show that it contains internal, collective and coupling terms. Then, we specify the approximations that need to be made in order to establish a connection between Bohr's collective model and the NBO method. We show that Bohr's collective Hamiltonian can be recovered from the NBO Hamiltonian only after adopting some rather crude approximations. In addition, we try to understand, in light of the NBO approach, why Bohr's collective model gives the wrong inertial parameters. We show that this is due to two major reasons: the ad hoc selection of the collective degrees of freedom within the context of Bohr's collective model and the unwarranted neglect of several important terms from the Hamiltonian.