  It has become clear in recent years that the configuration space of the
nuclear Skyrme model has, in each topological class, many almost degenerate
local energy minima and that the number of such minima grows with the degree
(or baryon number) $B$. Rigid body quantization, in which one quantizes motion
on the spin-isospin orbit of just one minimum, is thus an ill-justified
approximation. Instead, one should identify a (finite-dimensional) moduli space
of configurations containing all local minima (for a given $B$) as well as
fields interpolating smoothly between them. This paper proposes a systematic
computational scheme for generating such a moduli space: one constructs an
energy minimizing path between each pair of local minima, then defines the
moduli space to be the union of spin-isospin orbits of points on the union of
these curves, a principal bundle over a graph. The energy minimizing curves may
be constructed in practice using the nudged elastic band method, a standard
tool in mathematical chemistry for analyzing reaction paths and computing
activation energies. To illustrate, we apply this scheme to the lightly bound
Skyrme 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 the
graph has two vertices and a single edge. The low-lying quantum states with
isospin $1/2$ do not strongly localize around either of the local energy minima
(the vertices). Their energies rise monotonically with spin, conflicting with
experimental data for Lithium-7.
