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The goal of the present work is to revisit the cranking formula of thevibrational parameters, especially its well known drawbacks. The latter can besummarized as spurious resonances or singularities in the behavior of the massparameters in the limit of unpaired systems. It is found that these problemsare simply induced by the presence of two derivatives in the formula. Ineffect, this formula is based on the hypothesis of contributions of excitedstates due only to two quasiparticles. But it turns out that this is not thecase for the derivatives. We deduce therefore that the derivatives are not wellfounded in the formula. We propose then simply to suppress these terms from theformula. Although this solution seems to be simplistic, it solves definitivelyall its inherent problems.

The Inglis-Belyaev formula and the hypothesis of the two-quasiparticle excitations (version 2012)