Unified Treatment of Rotation, Surface Vibration and Pairing Vibration of Atomic Nucleus

Abstract

Using the quadrupole deformation parameters, fi and r, and the gap parameters, .dn and .dP, as generator coordinates, the trial wave function is generated by superposing the projected wave functions with various values of the generator coordinates. Such a choice of the generator coordinates enables us to treat the rotation, the surface vibration and the pairing vibration in a unified way. The generator function, which serves as a weight function, is obtained by solving an integral equation derived through the variational principle. It is shown that our projected wave functions have the same symmetry properties as those of wave functions given by the Bohr model. It is well known that in the nuclei far from the doubly closed shell the low-lying excited states have collective nature. We restrict ourselves to the doubly even nuclei in this article. In the spherical region, the energy spectra and the electromagnetic properties of the low-lying excited states are at least qualitatively well described as the quadrupole harmonic vibration of the nuclear surface in the framework of the Bohr model.lJ.-!) The microscopic treatment based on linearization approximation of the equation 5 ), 6 ) of motion has been proved to be successful to the same extent. There are, however, observed many deviations from the predicted harmonic vibration such as unequidistant level spacings of one- and two-phonon states, splitting of the two-phonon triplet states, missing of one or two members of the triplet, cross-over transitions from the two-phonon state to the ground state and so on. All of these experimental results show that there are strong anharmonic effects in the so-called spherical vibrational nuclei. Therefore it is desirable to develop a more rigorous theory which is not based on the harmonic vibration. More direct evidence for anharmonic effects would be the quadrupole moment of the first excited z+ state (Q2+). Unfortunately the experimental evidence 1s