Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator

Abstract

Based on the Riemann and Caputo definitions of the fractional derivative we use the fractional extensions of the standard rotation group S O ( 3 ) to construct a higher-dimensional representation of a fractional rotation group with mixed derivative types. An extended symmetric rotor model is derived, which predicts the sequence of magic proton and neutron numbers accurately. The ground state properties of nuclei are correctly reproduced within the framework of this model.