Nature of excited0+states inGd158described by the projected shell model

Abstract

Excited 0 + states are studied in the framework of the projected shell model, aiming at understanding the nature of these states in deformed nuclei in general, and the recently observed 13 excited 0 + states in 158 Gd in particular. The model, which contains projected two-and four-quasiparticle states as building blocks in the basis, is able to reproduce reasonably well the energies for all the observed 0 + states. The obtained B(E2) values however tend to suggest that these 0 + states might have a mixed nature of quasiparticle excitations coupled to collective vibrations.PACS numbers: 21.60. Cs, 23.20.Lv, 27.70.+q Dynamic perturbations of nuclear shapes around the equilibrium can give rise to physical states at low to moderate excitation energies. Classical examples of such motion are β and γ vibrations [1,2], in which nucleons undergo vibrations in a collective manner. Traditionally, the first excited K π = 0 + states and the first excited 2 + states are interpreted, respectively, as the β and γ vibrational states. While the 2 + collective excitations are better understood theoretically, the nature of the lowest 0 + excitation of deformed nuclei still remains under debate [3,4,5,6,7]. The physics of higher 0 + states is even more complex because, on one side, they can predominantly be multi-phonon states based on the single-phonons [8], and on the other side, they can be quasiparticle (qp) excitations in nature. The real situation is, perhaps, that the two aspects, collective excitations and qp states, are mixed by residual interactions.Data on K π = 0 + states have been relatively sparse. In a very recent work by Lesher et. al.[9], a remarkable (p, t) experiment revealed a total of 13 excited 0 + states in 158 Gd, below an excitation energy of approximately 3.1 MeV. This abundance of 0 + states in a single nucleus provides significant new information on the poorly understood phenomenon, which has immediately sparked off theoretical interest. For this energy range, one may think about an explanation through collective modes. In fact, Zamfir, Zhang, and Casten [10] suggested that many of the observed 0 + states may be of two-phonon octupole character. Nevertheless, these authors warned also that, although the mechanism was excluded in their collective models, many of the 0 + states in this excitation energy range may be predominantly two-qp in character.The purpose of the present paper is to investigate whether one can explain the nature of the observed 0 + states in terms of qp excitations. In contrast to Ref.[10], our calculation here does not emphasize the aspect of collective excitation. Although, similar to the work of Zamfir, Zhang, and Casten [10], we may provide only a partial image, our results may shed light on the importance of considering the qp aspects in understanding the nature of these 0 + states.Our study is based on the projected shell model (PSM)[11]. The PSM is the spherical shell model built on a deformed basis. The PSM calculation usually begins with the deformed Nilsson single-particle...

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