Quantising the B = 2 and B = 3 Skyrmion systems

We examine the quantisation of a collective Hamiltonian for the two-baryon system derived by us in a previous paper. We show that by increasing the sophistication of the approximations we can obtain a bound state or a resonance not too far removed from the threshold with the quantum numbers of the deuteron. The energy of this state is shown to depend very sensitively on the parameters of the model. Subsequently we construct part of a collective Hamiltonian for the three baryon system. Large-amplitude quantum fluctuations play an important rôle in the intrinsic wave function of the ground-state, changing its symmetry from octahedral to cubic. Apart from the tetrahedron describing the minimum of the potential, we identify a “doughnut” and a “pretzel” as the most important saddle points in the potential energy surface. We show that it is likely that inclusion of fluctuations through these saddle points lead to an energy close to the triton’s value.