Particle Derivation of Nuclear Rotation Properties Associated with a Surface Wave

Abstract

The dynamical conception of nuclear rotation in terms of a surface wave on a droplet of irrotational fluid has achieved some success in spite of the great differences between nucleons and the particles of a normal classical fluid. As a justification for the simplifying assumption of irrotational fluid flow, the collective rotational energy is here derived from a suitable set of nucleon wave functions in the approximation in which there is a rotating distortion, slow compared with the internal nucleon motions. The wave functions are those of a three-dimensional harmonic oscillator that is made anisotropic by having the force constant along one axis different from those along the other two in a rotating cartesian coordinate system. For the case of steady rotation about a fixed axis, the perturbation problem with first-order wave functions leads to a second-order rotational energy which agrees with the droplet-model result. The observed level spacings appear to lie between this result and that of a rigid rotator, and the discrepancy is probably to be attributed to higher orders. The result is also derived by another method without introducing a steady rotation.