Abstract
We study the vibrational modes of Skyrmions with baryon numbers one through eight in the standard Skyrme model. The vibrational modes are found in the harmonic approximation around the classical soliton solution and the real parts of the frequencies of the modes are extracted. We further classify the vibrational modes into representations of the symmetries possessed by the Skyrmion solutions. We find that there are approximately 7B low-lying modes for a Skyrmion with baryon number B, in addition to an infinite continuum of scattering modes. This result suggests that the instanton moduli space, which is 8B-dimensional, does not accurately describe the deformation space of Skyrmions as previously conjectured.
Highlights
In the Skyrme model [1], nuclei are described as topological solitons known as Skyrmions
We study the vibrational modes of Skyrmions with baryon numbers one through eight in the standard Skyrme model
We find that the question is illposed and that low lying quasinormal modes should be included in the counting
Summary
In the Skyrme model [1], nuclei are described as topological solitons known as Skyrmions. The simplest and most widely applied truncation is to only include the zero modes, those transformations which leave the Skyrmion’s energy unchanged: translations, rotations and isorotations. This procedure has some successes, such as the reproduction of the energy spectra and static properties of some small-B nuclei [2,3]. The result can be understood as follows: as well as its six zero modes, translations and rotations, a single Skyrmion can increase and decrease its size radially. This is known as the breathing mode. These are available online accompanied by animations of each mode at http://www1.maths.leeds.ac .uk/pure/geometry/SkyrmionVibrations/
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
