Static Properties of Nucleons in the Skyrme Model

The geometrical construction of rational maps using a cubic grid has led to many new Skyrmion solutions, with baryon numbers up to 108. Energy spectra of some of the new Skyrmions are calculated here by semi-classical quantization. Quantization of the B = 20 T d -symmetric Skyrmion, which is one of the newly found Skyrmions, is considered, and this leads to the development of a new approach to solving Finkelstein-Rubinstein (F-R) constraints. Matrix equations are simplified by introducing a Cartesian version of angular momentum basis states, and the computations are easier. The quantum states of all T d -symmetric Skyrmions, constructed from the cubic grid, are classified into three classes, depending on the contribution of vertex points of the cubic grid to the rational maps. The analysis is extended to the larger symmetry group O h . Quantum states of O h -symmetric Skyrmions, constructed from the cubic grid, form a subset of the T d -symmetric quantum states.

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“…The Skyrmion is restricted to have rotational and isorotational degrees of freedom only [10,11] and is parametrized as…”

Section: Semi-classical Skyrmion Quantizationmentioning

confidence: 99%

“…The rotational spectra of Skyrmions can be calculated using semi-classical quantization [10,11]. The spectra of isospin excitations can also be calculated.…”

Section: Introductionmentioning

confidence: 99%

Quantization ofTd- andOh-symmetric Skyrmions

Lau

Manton

2014

Phys. Rev. D

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“…where R µ = (∂ µ U )U † is a current taking values in the Lie algebra of SU (2). For a static field U (x), the energy is…”

Section: The Skyrme Model and Skyrmionsmentioning

confidence: 99%

“…Its quantised states of spin 1 2 and isospin 1 2 represent the nucleons [2,1]. Figure 2: B = 1 Skyrmion (two different views), illustrating the field colouring scheme.…”

Section: The Skyrme Model and Skyrmionsmentioning

confidence: 99%

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Classical Skyrmions—static solutions and dynamics

Manton

2012

Math Methods in App Sciences

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Skyrmions with a realistic value of the pion mass parameter are expected to be quite compact structures, but beyond baryon number B = 8 only a few examples are known. The largest of these is the cubically symmetric B = 32 Skyrmion which is a truncated piece of the Skyrme crystal. Here it is proposed that many more such Skyrmions could be found, without any restriction on the baryon number, as pieces of the Skyrme crystal. Particular attention is given to the possibility of reducing B by 1 by chopping a corner off a cubic crystal chunk.Nuclei are modelled by Skyrmions with quantised spin and isospin. Here it is argued that these quantised states can be approximated by classically spinning Skyrmions. The orientations of the spinning Skyrmions corresponding to polarised protons, neutrons and deuterons are identified. Nuclear collisions and the nuclear spin-orbit force are discussed in terms of classically spinning Skyrmions. Going beyond the rigid collective motions of Skyrmions, there are spatially modulated collective motions, which are oscillatory in time. They are argued to describe not just vibrational excitations of nuclei, but also giant resonance states.

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Interactions of B = 4 Skyrmions

Feist

2012

J. High Energ. Phys.

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It is known that the interactions of single Skyrmions are asymptotically described by a Yukawa dipole potential. Less is known about the interactions of solutions of the Skyrme model with higher baryon number. In this paper, it is shown that Yukawa multipole theory can be more generally applied to Skyrmion interactions, and in particular to the long-range dominant interactions of the B = 4 solution of the Skyrme model, which models the α-particle. A method that gives the quadrupole nature of the interaction a more intuitive meaning in the pion field colour picture is demonstrated. Numerical methods are employed to find the precise strength of quadrupole and octupole interactions. The results are applied to the B = 8 and B = 12 solutions and to the Skyrme crystal. * D. Feist@damtp.cam.ac.uk

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Static Properties of Nucleons in the Skyrme Model

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Quantization ofTd- andOh-symmetric Skyrmions

Quantization ofTd- andOh-symmetric Skyrmions

Classical Skyrmions—static solutions and dynamics

Interactions of B = 4 Skyrmions

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