Level densities of J pi=2+ and 2- states extracted from high-resolution studies of E2 and M2 giant resonances in 58Ni and 90Zr are used to test recent predictions of a possible parity dependence. The experimental results are compared to a combinatorial approach based on the Hartree-Fock-Bogoliubov model and to shell-model Monte Carlo calculations including both spin and parity projection. No parity dependence is observed experimentally, which is in agreement for 90Zr but in contrast with the model predictions for 58Ni.
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