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Conference on "Mathematical properties of large quantum systems"
Organizers: Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Robert Seiringer (McGill, Montréal) & Jan Philip Solovej (Copenhagen)


Nick Manton (Cambridge, UK): "Skyrmions as models of nuclei"
Friday 21 June 2013, 11:00 - 11:45
Amphi Hermite


Conventional nuclear physics is a complicated quantum many-body problem involving the interactions of point-like protons and neutrons (nucleons). The Skyrme model treats the nucleons as solitons - Skyrmions - in a pion field theory. This reproduces the long-range inter-nucleon force, and gives internal structure to the nucleons. A nucleus is, to first approximation, a solution of the Skyrme equations with the appropriate nucleon number, which is a topological invariant. In these Skyrmion solutions of higher topological charge, the nucleons partially merge, as is physically reasonable, since at a deeper level nucleons are made of interacting quarks. To next approximation, one needs to quantise the Skyrmion as a rigid body in space and isospin-space. The model has some qualitative success, for example, in seeing the formation of alpha-particle structures in nuclei. The mathematical properties of Skyrmions (investigated by M. Esteban) are clear numerically, but remain to be better understood analytically.