Transition from Vibrational to Rotational Regimes in the Pairing Phase

An approximate solution at the critical point of the pairing transition from harmonic vibration (normal nuclear behavior) to deformed rotation (superconducting behavior) in gauge space is found by analytic solution of a collective pairing Hamiltonian. The eigenvalues are expressed in terms of the zeros of Bessel functions of integer order. Comparison of the results to the pairing bands based on the Pb isotopes suggests that this description may provide a simple approach to explaining the observed anharmonicities of the pairing vibrational structure around 208Pb. The validity of the model is reinforced by comparing the results to an exact treatment of the pairing-phase transition in a two-level model.