Quasiparticle-Shell-Model Calculations of So-Called Two-Phonon States in Cd and Sn Isotopes

Abstract

The anharmonicity effect due to the couplings between pamng vibrational modes and quadrupole correlation modes is investigated in the cases of Cd and Sn isotopes by carrying out the quasiparticle-shell-model calculations. It is clarified that the effect is so large in the first excited o+ state in Sn isotopes that its energy drops down dramatically in 114• 116• 11 '• 120Sn. In Cd isotopes, the coupling effect is indispensable for formation of roughly degenerate two­ phonon triplet. The static quadrupole moments and B(E2) values in Cd isotopes are also calculated and the results do not contradict with experiment. §I. Introduction The mechanism of the spherical-cleformecl transition in medium and heavy nuclei 1s considered to be governed by mutual interweaving of two different types of cor­ relation, i.e., the pairing correlation and the quadrupole correlation. Therefore, it is natural to consider that the elementary modes of excitation in these nuclei are pairing vibrational mode and quadrupole phonon mode under the random-phase ap­ proximation (RPA) and that the anharmonicity effects which manifest themselves as couplings between these elementary modes of excitation play an essential role in structure of low-lying states of transitional nuclei. The existence of hidden regu­ larities in the anharmonicity effects has been suggested by the quasi-band structure 1) and there have been a number of theoretical attempts to elucidate the microscopic structure of the anharmonicity effects in transitional nuclei. It has been pointed out in our previous papers 2>.a> that the anharmonicity effects clue to the couplings between pairing vibrational mode and quadrupole phonon mode play so important a role that the so-called two-phonon o+ state and the pairing vibra­ tional state couple with each other and the energy of the first excited o+ state drops do·wn in the transitional nuclei, for example, in Se and Mo isotopes. A similar situation may be expected in Cd and Te isotopes, because the neutron-single­ particle-level structure fairly resembles that in Se region. On the other hand, Cd isotopes have so far been referred to as typical examples of appearance of two­ phonon-triplet states. Standing on the viewpoint of usual phonon (boson) picture, we find no structural difference between the members of the two-phonon triplet. However, if the excited o+ state is strongly affected by the pairing vibrational mode,