Resolution of the spin paradox in the Nilsson model
Faculty of Physics, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran
2 Institute of Nuclear and Particle Physics, National Centre for Scientific Research “Demokritos”, 15310, Attiki, Aghia Paraskevi, Greece
Accepted: 6 March 2021
Published online: 15 April 2021
In the well-known Nilsson diagrams, depicting the dependence of the nuclear single-particle energy levels on quadrupole deformation, a spin paradox appears as the deformation sets in, leading from spherical shapes to prolate deformed shapes with cylindrical symmetry. Bunches of levels corresponding to a spherical shell model orbital, sharing the same orbital angular momentum and the same total angular momentum, appear to correspond to Nilsson energy levels, labeled by asymptotic quantum numbers in cylindrical coordinates, some of which have spin-up, while some others have spin-down. Furthermore, for some orbitals the correspondence between spherical shell model quantum numbers and Nilsson asymptotic quantum numbers is not the same for protons and for neutrons. Introducing a new rule of correspondence between the two sets of quantum numbers, we show that the spin paradox is resolved and full agreement between the proton and neutron Nilsson diagrams is established. The form of the Nilsson diagrams as a function of the quadrupole deformation remains unchanged, the only difference between the new diagrams and the traditional ones being the mutual exchange of the Nilsson labels for certain pairs of single-particle energy levels.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021