Abstract
We investigate how isospin affects the geometrical shape and energy of classical soliton solutions of topological charges $B=1--4,8$ in the Skyrme model. The novel approach in our work is that we study classically isospinning Skyrmions beyond the rigid-body approximation; that is, we explicitly allow the soliton solutions to deform and to break the symmetries of the static configurations. Our fully three-dimensional relaxation calculations reveal that the symmetries of isospinning Skyrme solitons can differ significantly from the ones of the static configurations. In particular, isospinning Skyrmion solutions can break up into lower-charge Skyrmions, can deform into new solution types that do not exist at vanishing angular frequency $\ensuremath{\omega}$ or energy degeneracy can be removed. These types of deformations have been largely ignored in previous work on modeling nuclei by quantized Skyrmion solutions.
Highlights
In the SU(2) Skyrme model [1, 2], atomic nuclei of nucleon number B can be identified with soliton solutions of conserved topological charge B which are known as Skyrmions
Recall that in our numerical simulations we do not impose any spatial symmetries on the isospinning Skyrme soliton solutions and we do not assume that the solitons’ shape is independent of the angular frequency ω
We do not observe any breaking of the octahedral symmetry for the minimal-energy B = 4 Skyrmion solution when isospinning the configuration around the K = (0, 0, 1) axis
Summary
In the SU(2) Skyrme model [1, 2], atomic nuclei of nucleon (or baryon) number B can be identified with soliton solutions of conserved topological charge B which are known as Skyrmions. This means that one quantizes just the rotational and isorotational zero modes of each Skyrmion solution of a given B and determines the spin and isospin quantum numbers [6,7,8,9] which are compatible with the symmetries of the static, classical soliton This approach neglects any deformations and symmetry changes due to centrifugal effects. It has been found that allowing for axial deformations drastically reduces the rotational energies and that in order to fit the energies of spinning Skyrmions to the nucleon and delta masses, the pion mass parameter mπ of the Skyrme model has to be chosen much larger than its experimental value [18,19,20] All these studies impose spherical or axial symmetry on the spinning Skyrme solitons to simplify the numerical computations.
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