Microscopic approach to coupled modes in nuclei

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Abstract
A microscopic theory of low-lying collective states in even-even nuclei is developed. It treats rotations, vibrations and their coupling on the same footing. It is based on elementary transition operators, which are an extension of the phonon concept, on a density-matrix expansion in terms of these operators, and on equations of motion for the density matrix. The example of ground, beta and gamma rotational bands is treated up to second order of the density-matrix expansion. The cranking-model results for rotations and the random-phase approximation results for vibrations are reproduced, both for energies and E2 transition rates, by the same formalism in first order. For E2 transition rates the effects of rotation-quasiparticle, rotation-vibration and vibration-quasiparticle coupling are described in second order. This covers non-adiabatic corrections to the Alaga rules inside the bands and between the ground, beta and gamma bands, deviations in the intrinsic moments of the beta and gamma bands, and the beta-gamma transitional moment.