A Theory of Anharmonic Vibrations in Spherical Even-Even Nuclei

概要

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Unexpectedly large quadrupole moments of the first 2^+ states of the vibrational nuclei force us to treat those states as collective states of anharmonic vibrations. The time dependent perturbation theory using the adiabatic approximation is applied to obtain the phonon Hamiltonian for the anharmonic motion. Advantages of this treatment are; i) the collective vibration with a low frequency can be well described, ii) it is easy to derive higher order anharmonic terms and iii) the connection with the static deformation becomes evident. We introduce the generalized collective coordinate for the treatment of anharmonic terms. In our theory, it is defined by adopting the principle of the linked cluster expansion. The Hamiltonian is obtained so that it has the form of a rapidly converging expansion series in terms of the generalized collective coordinate and its conjugate momentum. Finally quantization is performed, which leads us to the phonon picture. Typical features of the resulting Hamiltonian for the anharmonic vibration are discussed.
理論物理学刊行会の論文
1968-09-25