The α particle as a canonically quantized multiskyrmion

Abstract

The rational map approximation to the solution to the SU(2) Skyrme model with baryon number B = 4 is canonically quantized. The quantization procedure leads to anomalous breaking of the chiral symmetry, and exponential falloff of the energy density of the soliton at large distances. The model is extended to SU(2) representations of arbitrary dimension. These soliton solutions capture the double node feature of the empirical α particle charge form factor, but as expected lead to a too compact matter distribution. Comparison to phenomenology indicates a preference for the fundamental representation. PACS numbers: 12.39Dc, 21.10Dr

Transition between nuclear and quark–gluon descriptions of hadrons and light nuclei

“…Skyrme theory [22] treats baryons as topological solitons of an effective pion theory, justified by the large N c limit in which QCD becomes a theory of mesons [23]. The theory has been applied to baryons, NN interactions [24], the structure of the deuteron-see [25] for a review of and references to earlier work, and more recently even to α particles [26] and neutron stars [27]. Predictions tend to be qualitatively rather than quantitatively correct.…”

Recent Developments in the Skyrme Model

“…The zero-mode quantization is the simplest approximation to the quantum states (also known as rigid rotator approximation). A more sophisticated quantization can lead to better results [14,30,31] There is also an ongoing discussion of how best to fix the three physical parameters (f π , e and m) in the Skyrme model. The original, and most widely used, set of Skyrme parameters has been proposed in [2,3], by matching to the proton and the Delta mass.…”

Transition between nuclear and quark-gluon descriptions of hadrons and light nuclei

“…Skyrme theory [22] treats baryons as topological solitons of an effective pion theory, justified by the large N c limit in which QCD becomes a theory of mesons [23]. The theory has been applied to baryons, N N interactions [24], the structure of the deuteron -see [25] for a review of and references to earlier work, and more recently even to α particles [26] and neutron stars [27]. Predictions tend to be qualitatively rather than quantitatively correct.…”