Skyrmions and Nuclei

We review recent work on the modelling of atomic nuclei as quantized Skyrmions, using Skyrme's original model with pion fields only. Skyrmions are topological soliton solutions whose conserved topological charge B is identified with the baryon number of a nucleus. Apart from an energy and length scale, the Skyrme model has just one dimensionless parameter m proportional to the pion mass. It has been found that a good fit to experimental nuclear data requires m to be of order 1. The Skyrmions for B up to 7 have been known for some time, and are qualitatively insensitive to whether m is zero or of order 1. However, for baryon numbers B = 8 and above, the Skyrmions have quite a compact structure for m of order 1, rather than the hollow polyhedral structure found when m = 0. One finds that for baryon numbers which are multiples of four, the Skyrmions are composed of B = 4 sub-units, as in the α-particle model of nuclei.

The rational map ansatz gives a useful approximation to the Skyrmion solutions for all baryon numbers when m = 0. For m of order 1, it gives a good approximation for baryon numbers up to 7, and generalisations of this ansatz are helpful for higher baryon numbers.

We briefly review the work from the 1980s and 90s on the semiclassical rigidbody quantization of Skyrmions for B = 1, 2, 3 and 4. We then discuss more recent work extending this method to B = 6, 7, 8, 10 and 12. We determine the quantum states of the Skyrmions, finding their spins, isospins and parities, and compare with the experimental data on the ground and excited states of nuclei up to mass number 12.