Chris Halcrow — Page 2

arXiv2018

Vibrational modes of Skyrmions

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.

hep-th↗

arXiv2018

The $B=5$ Skyrmion as a two-cluster system

The classical $B=5$ Skyrmion can be approximated by a two-cluster system where a $B=1$ Skyrmion is attached to a core $B=4$ Skyrmion. We quantise this system, allowing the $B=1$ to freely orbit the core. The configuration space is 11-dimensional but simplifies significantly after factoring out the overall spin and isospin degrees of freedom. We exactly solve the free quantum problem and then include an interaction potential between the Skyrmions numerically. The resulting energy spectrum is compared to the corresponding nuclei -- the Helium-5/Lithium-5 isodoublet. We find approximate parity doubling not seen in the experimental data. In addition, we fail to obtain the correct ground state spin. The framework laid out for this two-cluster system can readily be modified for other clusters and in particular for other $B=4n+1$ nuclei, of which the $B=5$ is the simplest example.

hep-th↗