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It has become clear in recent years that the configuration space of thenuclear Skyrme model has, in each topological class, many almost degeneratelocal energy minima and that the number of such minima grows with the degree(or baryon number) $B$. Rigid body quantization, in which one quantizes motionon the spin-isospin orbit of just one minimum, is thus an ill-justifiedapproximation. Instead, one should identify a (finite-dimensional) moduli spaceof configurations containing all local minima (for a given $B$) as well asfields interpolating smoothly between them. This paper proposes a systematiccomputational scheme for generating such a moduli space: one constructs anenergy minimizing path between each pair of local minima, then defines themoduli space to be the union of spin-isospin orbits of points on the union ofthese curves, a principal bundle over a graph. The energy minimizing curves maybe constructed in practice using the nudged elastic band method, a standardtool in mathematical chemistry for analyzing reaction paths and computingactivation energies. To illustrate, we apply this scheme to the lightly boundSkyrme model in the point particle approximation, constructing the graphs for$5\leq B\leq 10$. We go on to complete the quantization for $B=7$, in which thegraph has two vertices and a single edge. The low-lying quantum states withisospin $1/2$ do not strongly localize around either of the local energy minima(the vertices). Their energies rise monotonically with spin, conflicting withexperimental data for Lithium-7.

Nudged Elastic Bands and Lightly Bound Skyrmions