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

Abstract

Fw 21.60.Cs Keywords:Perturbation and fractional calculus methods Nuclear shell models Ground state properties of nuclei a b s t r a c t Based on the Riemann and Caputo definitions of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higherdimensional 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.

Properties of the single-particle spectrum generated by the mixed fractional rotation group

“…The qualities that recommend the ECRRSR model as a suitable alternative for the description of nuclear single-particle levels were presented in [10]. The similitude of the energy levels (2.2) with the single-nucleon spectrum becomes obvious when…”

“…To this end, extensions of the spherical shell model magic numbers based on some physical or mathematical symmetries were at some point considered [6][7][8][9]. A group theoretical interpretation for the emergence of both HO and SO magic numbers was recently forwarded [10], without considering an explicit mean-field potential. It was shown that an energy spectrum with naturally included nuclear magic numbers can be generated by a multidimensional rotational group constructed on mixed fractional derivative definitions.…”

“…A thorough comparison to experimental single-particle levels of spherical nuclei will be used to obtain a microscopic parametrization of the model. Following the example of [10], the model's performance will be tested by calculating the microscopic shell and pairing contribution to the ground state properties of experimentally observed even-even nuclei. The theoretical approach for the calculation of the microscopic correction is based on a simultaneous treatment of shell and pairing effects.…”

Infrared Spectroscopy of Diatomic Molecules — A Fractional Calculus Approach

“…Thus the additional symmetry may be imposed as a geometric constraint by fixing the rotation axis in space setting e.g. M = +L, see also [26], [27].…”

Common aspects of -deformed Lie algebras and fractional calculus

“…Since then the investigation of the fractional rotation group within the framework of fractional group theory has lead to a vast amount of interestening results, e.g. a theoretical foundation of magic numbers in atomic nuclei [20] and metallic clusters [21].…”