Pairing effects in nuclear collective motion: Generator coordinate method

The generator coordinate method for nuclear collective motion is studied in a simple model in which the dynamics is governed by the pairing interaction alone. A formula is derived for the overlap correlation length which exhibits the correct empirical dependence on nucleus mass number, pairing gap, and quadrupole deformation. The same analysis applied to the quadrupole inertia parameter provides an expression proportional to the square of the pairing gap, the same functional form as obtained from the cranking model. However, the simplified model differs numerically by a factor 2 to 4 from the results of a complete Hartree-Fock BCS calculation. The spectrum is well described by a hopping model based on the Hartree-Fock single-particle properties