Tilted Rotation and Wobbling Motion in Nuclei

The self-consistent harmonic oscillator model including the threedimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two– or three–dimensional rotation. PACS numbers: 21.60.Jz, 21.60 Ev Nuclear states grouped into ∆I = 2 sequences are remarkably well described in terms of the principal axis rotation which is the basis of the cranking model [1]. The principal axis cranking rotation was intuitively justified by a classical rigid body rotation which is favorable for a uniform rotation around the long or the short principal axis. However, if the classical body is not rigid, it may also uniformly rotate about an axis which does not coincide with the principal axes of the density distribution. In fact, more than a century ago Riemann [2] pointed out that such a situation could occur in the ellipsoidal self-gravitating fluid. The physical mechanism behind it is the vortex motion in a macroscopic system. Numerous experimental observations implying ∆I = 1 sequences in near spherical nuclei [3] raised the question about a new type of rotation and its physical nature in a finite quantum many body system. For particular nuclei the proton and neutron spin vectors may be oriented along different axes. Consequently, the total angular momentum could lie at an angle different from one of the principal axes, i.e. at a tilted angle. It seems shell effects are the driving forces in this case which can be described within the Tilted Axis Cranking Model [4] which assumes a two–dimensional rotation. Other intriguing examples are the rotational bands observed in Hf , W and Os (Z = 72 − 76) nuclei with A ∼ 180 [5, 6, 7]. These bands are characterized by high K-values, where K is the angular momentum projection on