It is shown that the energy-weighted and inversely-energy-weighted (IEW) random-phase-approximation sum rules may be obtained simultaneously by a doubly constrained self-consistent field calculation. Applications of the IEW sum rule are made to the quadrupole-force Hamiltonian, including a case when zero-frequency modes occur. The relevance to certain higher-order sum rules is noted and discrepancies in some calculations of centrifugal stretching effects in spherical and deformed nuclei are pointed out.

• Received 5 December 1972

DOI:https://doi.org/10.1103/PhysRevC.7.2281