Some simple angular momentum techniques

Charles P. Friedman, Edwin F. Taylor

The quantization of orbital angular momentum can be introduced simply through the model of the two- and three-dimensional simple harmonic oscillator. Most of the analysis is carried out in the familiar Cartesian coordinate system in which the simple harmonic oscillator Schrödinger equation is separable. Angular momentum eigenfunctions are constructed by superposition, and the resulting functions easily transformed into spherical coordinates. The angle-dependent parts of the solutions are the spherical harmonics, which are the orbital angular momentum eigenfunctions for all central potentials including the Coulomb potential of the hydrogen atom. The method also introduces the separation of variables technique and provides practice in applying the concepts of completeness, orthogonality, superposition of states, and alternative representations.

Maria Kaczmarczyk

Arelatively simple numerical method of summing angular momentum vectors with maintaining space quantization rules of each summed angular momentum has been presented. The method enables the calculation of the values of probability ( p j μ ) of finding a definite angular momentum J μ among all vectors J being the results of quantum summation of n angular momentum vectors j μ (μ=1- n . It may be used, e.g., in the calculations of angular momentum of many-particle states. The significance of the paper is connected with the possibility of taking into account, in a simple way, the angular momentum conservation principle for a system which consists of an arbitrary number of excitons.

James D. Louck

G. Scamps, A. Guilleux, D. Regnier +1 more

The generation of angular momentum (intrinsic spin) in fission fragments has recently attracted renewed attention. While several microscopic approaches reproduce the spin distribution qualitatively using projection techniques, the physical origin of the fragments' angular momentum in density functional theory remains unclear. In this work, we investigate the mechanisms responsible for the spin distribution of fission fragments within a microscopic TDDFT framework. We compare spin distributions obtained from projection operators with those predicted by a simple expression derived from the uncertainty relation between angle and angular momentum, where angular fluctuations are estimated using a Monte Carlo sampling of nucleon positions. We find that a large portion of the spin distribution obtained from projection methods can be explained by the uncertainty principle. Our results thus show that, within microscopic approaches, the spin of fission fragments originates primarily from quantum uncertainty associated with their orientation angle with respect to the fission axis, mainly due to quadrupole deformation and, to a lesser extent, octupole deformation.

James D. Louck