  In the semiclassical domain the exponent of vortex quantum tunneling is
dominated by a volume which is associated with the path the vortex line traces
out during its escape from the metastable well. We explicitly show the
influence of geometrical quantities on this volume by describing point vortex
motion in the presence of an ellipse. It is argued that for the semiclassical
description to hold the introduction of an additional geometric constraint, the
distance of closest approach, is required. This constraint implies that the
semiclassical description of vortex nucleation by tunneling at a boundary is in
general not possible. Geometry dependence of the tunneling volume provides a
means to verify experimental observation of vortex quantum tunneling in the
superfluid Helium II.
