SEMICLASSICAL TREATMENT OF QUADRUPOLE BOSON HAMILTONIANS - NEW RESULTS FOR SMALL AND LARGE-AMPLITUDE REGIMES

A fourth order quadrupole boson hamiltonian is semiclassically treated through a time dependent variational principle (TDVP), the variationa l states being of coherent type for boson operators b20+, (1/square-ro ot2) (b22+ + b2+-2). The static ground state is studied as a function of the parameters involved in the model hamiltonian. Linearizing the c lassical equations of motion one obtains the RPA approach for the many boson correlations. There are two RPA roots which describe the beta a nd gamma vibrations, respectively. Several quantization procedures for both small and large amplitude regimes are discussed. The quantized h amiltonians are compared with some others which were previously obtain ed by using different methods. A special attention is paid to the quan tal states associated to some of the peaks appearing in the Fourier sp ectrum of the classical action density. Some of the quantal states exh ibit a pronounced anharmonic structure. Therefore the procedure may be used for a unified description of small and large amplitude regimes.