Abstract
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.
Highlights
The Skyrme model is a nonlinear theory of pions that admits topologically nontrivial configurations called Skyrmions, labeled by a topological charge B
If we can “factor out” these symmetries, only five coordinates, describing the relative interaction between clusters, will remain. This type of reduction is common in the study of comets, many of which are described by twocluster systems bound together by the gravitational force
The system is invariant under a simultaneous increase in both γ0 and ψ, as these coordinates rotate the B 1⁄4 1 Skyrmion around the z axis in opposite directions
Summary
The Skyrme model is a nonlinear theory of pions that admits topologically nontrivial configurations called Skyrmions, labeled by a topological charge B. This is a formidable number of d.o.f. the system transforms under overall rotations and isorotations. If we can “factor out” these symmetries, only five coordinates, describing the relative interaction between clusters, will remain This type of reduction is common in the study of comets, many of which are described by twocluster systems bound together by the gravitational force. As these are body-fixed momenta, they will satisfy the anomalous commutation relations when quantized. We consider both the Uð1Þ symmetry and the discrete symmetries carefully
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