Confrontation between the quasiparticle-phonon nuclear model and the interacting boson model for deformed nuclei

Abstract

The Ks=0 + , 2 + and 4 + states are considered in doubly even deformed nuclei. It is shown that in the quasiparticle-phonon nuclear model (QPNM) and in the interacting boson model (IBM) a vibrational state has one dominating component. The states with + 0Z, 0F, 2+a, 4[ and 4f have a dominating one-phonon component within the QPNM and a two-or three-boson component within the IBM. According to the QPNM the contribution of two-phonon components to the wave functions of these states is less than 10%, i.e. there is a qualitative discrepancy in describing the structure of these states within the QPNM and the IBM. The experimental data indicate the existence in these states of one-phonon or two-quasiparticle components. They are rather well described within the QPNM. These states cannot be described within the IBM. This is due to the fact that the IBM takes into account only a small part of the space of two-quasiparticle states, just the one entering into fi-and 7-vibrational states.

On the coupling between multiphonon configurations in deformed nuclei

“…This indicates that in studying two-phonon states one cannot use only the components with n < 2 in the wave function (7) as has been done in the QPNM [1][2][3]. With increasing [3(41 complex components are suppressed more rapidly than the simple ones.…”

“…For the low-lying collective phonons they may take only non-negative values [10]. Just the large positive value of the function A,, which can be considered as a shift of the strength of the n-phonon configuration towards higher excitation energy due to the violation of the Pauli principle, made it possible to conclude within the QPNM [1][2][3] that low-lying two-phonon states should not exist in deformed nuclei.…”

“…During the last decade much attention has been paid to the multiphonon and, first of all, two-phonon components of the low-lying states in doubly-even deformed nuclei [1][2][3][4][5][6][7][8][9][10]. These components are well known to influence essentially the properties of lowlying states so that the up to date experimental information (see, for instance, [11] and in [8] for 16SEr) can hardly we described without including them into consideration.…”

“…It includes: 1) the RPA description of onephonon excitations, 2) the multiphonon wave function, 3) the coupling between multiphonon configurations that differ from each other by a number of phonons n < 4, 4) the Pauli principle, 5) the phonon correlations in the ground state. Note that in comparison with the SMMM the QPNM [1][2][3] takes into account only one-and two-phonon components of the wave function and disregards the Hamiltonian term ~Q+ Q+ which couples the configurations differing by an even number of phonons. In the MPM [8], in contrast with the SMMM, the TDA description of one-phonon states is used.…”

“…But the available models such as quasiparticle-phonon nuclear model (QPNM) [1][2][3], multiphonon model (MPM) [8], self-consistent collective coordinate method (SCCM) [9] and some others are rather cumbersome and difficult to comprehend. Moreover, these models sometimes give contradictory predictions (see, for example, the discussion on the two-phonon states in [8]).…”