12 - Fast nuclear rotation – the cranking model

Summary

At very high spin, one expects the Coriolis and centrifugal forces to disturb strongly the wave functions of many nucleons. As discussed in the introduction to the previous chapter, it then becomes desirable to treat all nucleons on the same footing.

In this chapter, we will introduce two models of this kind, namely the cranking model and the rotating liquid-drop model. The cranking model is first applied to the simple harmonic oscillator potential to illustrate some different concepts. Then the Nilsson–Strutinsky cranking approach corresponding to a combination of the two models is introduced. Within this approach, phenomena like band terminations and superdeformed high-spin states are discussed.

The cranking model

In the cranking model, the rotation is treated in the classical sense with the rotation vector coinciding with one of the main axes of the nucleus. It then turns out that, in this system, the nucleons can be described as independent particles moving in a rotating potential. In fact, the rotation degree of freedom enters in very much the same way as the deformation degrees of freedom, which were introduced in chapters 8 and 9. One important shortcoming of the cranking model is that the wave functions are not eigenstates of the angular momentum operator. Instead, the angular momentum is generally identified with the expectation value of its projection on the rotation axis.