Microscopic derivation of cranking for nuclear systems with large angular momentum

Abstract

We describe a derivation of a microscopic theory of rotation of a nucleus at large angular momentum, based on a rotationally invariant starting point, the Kerman-Klein approximation to the Heisenberg equations of motion. The cranking model emerges as the first term of a systematic expansion in powers of the ratio of the average single particle angular momentum in the deformed state to the total angular momentum. Various arguments in the literature justifying the cranking approximation at low angular momentum, by contrast, depend on the smallness of the reciprocal of this ratio. The justification for these results are examined within the chosen theoretical framework. The detailed arguments are presented for rotation about a prescribed axis (two-dimensional case).