This study addresses the following question: is there a difference between the deformation of the nuclei in their ground states and in their high-seniority multi-quasiparticle excitations often observed as isomeric states. The importance of this question is related to the question of the quenching of the pairing correlations in atomic nuclei. The nuclear deformations are present as a parameter in many calculations, which requires that they should be determined experimentally. Prior to this experiment [1], only the quadrupole moments of the high-K isomers in ¹⁸²Os (K^p = 25⁺), ¹⁷⁸Hf (K^p = 16⁺) and ¹⁷⁷Lu (K^p = [23/2]^-) were known. For the latter two isomers the deformation which was deduced is similar to the ground-state deformation. In the case of ¹⁸²Os there is a considerable difference between the ground state and isomeric quadrupole moment.
The spectroscopic quadrupole moment of the high-spin, high-K five-quasiparticle isomer (K^p = [35/2]^-,T_1/2 = 750(80) ns, E_i = 3349 keV) in ¹⁷⁹W has been determined using the Level Mixing Spectroscopy (LEMS) method [1]. A value Q_s = 4.00(^+0.83_-1.06) eb was derived, which corresponds to an intrinsic quadrupole moment Q₀ = 4.73(^+0.98_-1.25) eb and to a quadrupole deformation b₂ = 0.185(^+0.038_-0.049). These values differ significantly from the deduced ground-state quadrupole moments and are in disagreement with the current theoretical predictions in this mass region.
Hartree-Fock-Bogolyubov calculations within the framework of the Tilted Axis Cranking (TAC) theory [2] permit us to take into account possible mixing between bands with different K values. Such effects were found to be small. TAC yields a value for the quadrupole moment of this isomer Q_s = 6.223 eb if pairing is treated with the particle number projection technique [3] and Q_s = 6.343 eb without it (the neutron pairing is zero in this case). These values of the quadrupole moment correspond to an axially symmetric nucleus with deformations e₂ = 0.228 and e₄ = 0.038, which coincide practically with the calculated ground-state deformations for ¹⁷⁹W: e₂ = 0.226 and e₄ = 0.039 but contradict with the measured quadrupole moment for the isomer.
In conclusion, we have measured the quadrupole moment of the K = [35/2], E_i = 3349 keV isomer in ¹⁷⁹W. The deduced deformation of this state is smaller, compared to the systematic trend of the ground-state deformations of the nuclei in the region, and smaller than the theoretically predicted values. Further improvement of the experimental accuracy is probably needed. At the same time the exploration of other theoretical aspects is necessary, since it seems impossible to explain these differences within the well established schemes to calculate nuclear deformations in this mass region.

¹ University of Leuven, IKS, Celestijnenlaan 200 D, Leuven, Belgium
² Faculty of Physics, St. Kliment Ohridski University of Sofia, BG-1164 Sofia, Bulgaria
³ IFU, Sao Paulo, CP 20156, Sao Paulo, Brazil
⁴ Department of Physics, Lund University, S-221 00 Lund, Sweden
⁵ Department of Physics,University of Surrey, Guilford GU2 7XH, UK
⁶ Institut für Physikalische und Theoretische Chemie, Technical University Vienna,
A-1060 Vienna, Austria
⁷ on leave of absence at the Department of Physics, University of Notre Dame, IN 46556, USA

References

[1] D.L. Balabanski et al., Phys. Rev. Lett. 86, 604 (2001)
[2] S. Frauendorf, Nucl. Phys. A 557, 259c (1993)
[3] D. Almehed et al., Phys. Rev. C 63, 044311 (2001)  IKH 06/25/01 © F. Dönau