Microscopic Calculation of the Wobbling Excitations Employing the Woods-Saxon Potential as a Nuclear Mean-Field

Abstract

The wobbling excitations of the triaxial superdeformed (TSD) bands in the Lu and Hf region are studied by the microscopic framework of the cranked mean-field and the randomphase approximation (RPA). In contrast to the previous works, where the Nilsson potential was used, the more realistic Woods-Saxon potential is employed as a nuclear mean-field. It is pointed out that the original formulation should be slightly modified for general meanfield like the Woods-Saxon potential. The wobbling-like RPA solutions have been found systematically in the nuclei studied and their characteristic properties are investigated in detail. This confirms the wobbling phonon excitations in TSD nuclei from the microscopic calculations. The result of B(E2) values indicates that the triaxial deformation is increasing as a function of spin in the observed TSD bands in 163 Lu.Subject Index: 210, 211, 212 §1. IntroductionThe observation of the wobbling excitations 1), 2) (see also Refs. 3) and 4)) renewed the interest in the study of nuclear rotational motions. The nuclear wobbling motion 5) is a quantized motion of the triaxial rotor and appears as a multiple-band structure, in which consecutive rotational bands are connected by strong E2 transitions with each other. Until now, the multiple rotational band structure characteristic to the wobbling phonon excitation has been observed at the high-spin excited states in some Lu isotopes 1)-3), 6)-10) around 163 Lu. Nuclei in the Lu and Hf region, including these Lu isotopes, have been predicted to be strongly deformed with pronounced triaxiality 11)-14) at high-spin states, and the associated rotational bands are called triaxial superdeformed (TSD) bands; i.e., the wobbling structure is composed of these TSD bands. In fact the lifetime measurements in these nuclei 15), 16) revealed that the rotational E2 transition probabilities inside the bands are typically about 500 Weisskopf units, and those between the bands associated with the wobbling phonon excitations are about 100 Weisskopf units. These are one of the largest out-of-band B(E2) and believed to be the evidence of the nuclear wobbling motion. Although several candidates of the TSD bands have been observed in even-even Hf isotopes, 17)-21) there is no definite evidence of the wobbling excitation yet.The nuclear wobbling motion was first predicted by using the simple macroscopic rotor model. 5) The experimental data observed in Lu isotopes are investigated by the particle-rotor model, 22)-25) because a i 13/2 quasiproton exists in the proton-odd Lu nuclei. It is, however, noted that the properties of the observed out-of-band E2 transitions suggest that the triaxial deformation is of the so-called positive-γ by guest on April 13, 2015 http://ptp.oxfordjournals.org/ Downloaded from T. Shoji and Y. R. Shimizu shape in the Lund convention, 26) the sign of which is opposite to that of Ref. 5); namely the moment of inertia about the shortest axis of triaxial deformation is the largest. This conflicts with the irrotational moments of inertia wh...

Wobbling motion in Pr135 within a collective Hamiltonian

“…Therefore, the wobbling bands in the Lu and Ta isotopes are interpreted as transverse wobbling bands. Theoretically, the triaxial particle rotor model (PRM) [1,[15][16][17][18][19][20][21][22] and the cranking model plus random phase approximation (RPA) [23][24][25][26][27][28][29][30][31][32] have been widely used to describe the wobbling motion. Recently, based on the cranking mean field and treating the nuclear orientation as collective degree of freedom, a collective Hamiltonian was constructed and applied for the chiral [33] and wobbling modes [34].…”

Role of deformation in odd-even staggering in reaction cross sections for Ne30,31,32 and Mg36Urata1, Hagino2, Sagawa3 2017Phys. Rev. C200120View full textAdd to dashboardCite

“…We analyze the reaction cross sections for the 30,31,32 Ne and 36,37,38 Mg nuclei. Symbolically, we denote the three isotopes in each element as A, A+1, and A+2 systems, respectively.…”

“…We use the same values for the parameters for the single-particle potential as those listed in Table I in Ref. [32], except for the depth parameter V 0 for the configuration for the valence orbit, for which we adjust the value of V 0 so that the neutron separation energy for the A + 1 nuclei is reproduced. For simplicity, we use the same value for the deformation parameter for all the three isotopes, A, A + 1, and A + 2.…”

“…To this end, we study the odd-even staggering in the 30,31,32 Ne and 36,37,38 Mg isotopes, for which the 31 Ne and 37 Mg nuclei have been suggested to have a deformed halo structure with p wave [6,7,17,[20][21][22][23][24][25][26][27][28].…”

“…Secondly, the deformation may change the level density around the Fermi level, which would result in either an enhancement or a decrease of the pairing correlation, depending on the position of the Fermi surface. This would eventually influence the magnitude of the pairing anti-halo effect, thus the cross sections for 32 Ne and 38 Mg. The primary aim of this paper is to investigate how these two effects interplay with each other in actual cases and how the conclusion obtained in our previous analyses based on spherical symmetry is altered if the deformation is explicitly taken into account.…”