Theory of Pairing Vibration Mode

Abstract

A simple and exactly solvable model is proposed which exhibits all the characteristic features of the pairing vibration model of A. Bohr; the near-harmonic level sequences and the strong enhancements of the (L=O) two-nucleon transfer reaction. This model consists of degenerate many-j single particle levels and degenerate hole levels with an energy-gap between them. The pairing interactions are taken into account, except for those between the particle and hole states. Using the empirical values of the single particle and hole energies together with the strength of the pairing interaction, the model is compared with the experi­ mental data in Ni, Sn and Ph isotopes to get quantitative agreement. This model is further used as the basis states to diagonalize the more realistic case of the non-degenerate model with pairing interactions among all levels. It is found that our pair­ ing vibration mode remains predominantly in the ground state of the non-degenerate model. 1l has been proved to be a convenient way of the classification of o+ states of spherical even nuclei. The essential idea is to view the quanta associating with the particle pair correlation as a boson with energy hw, while the quanta arising from pair correlation of holes is regarded as an another kind of boson with the same energy. Taking these two kinds of boson as building stones, a o+ state can be considered as consisting of w bosons of' the particle pair and w bosons of the hole pair, its energy being given by E= (w+w)hw measured from the (w=w=O) o+ state. This pairing vibrational state will be denoted as ( w, w). Bohr1l and Nathan2l made a systematic survey of this scheme in the regions around Ni66, Sn114 and Pb 208• Since the bosons in this model are related to the pairing correlation, the pairing vibration states will be characterized by the strong enhancement of (L= 0) two-nucleon transfer reaction. After this proposal, many high resolution experiments of the two-nucleon transfer reaction have been performed to test the pairing vibration scheme. Microscopic treatment of the pairing vibration model has been made first by Bes and Broglia8l and later by several authors.4l All these works are based on the formal analogy of the pairing correlation to the conventional random-phase­ approximation treatment of nuclear surface vibration, so that the microscopic foundation of the pairing vibration model seems to be not necessarily clear. In view of the above situation, we shall propose an exactly solvable, but nevertheless, realistic model which exhibits all the characteristic features of the pairing vibration model--near-harmonic level sequences and the strong enhance