  We investigate the behavior of eigenvalues for a magnetic Aharonov-Bohm
operator with half-integer circulation and Dirichlet boundary conditions in a
planar domain. We provide sharp asymptotics for eigenvalues as the pole is
moving in the interior of the domain, approaching a zero of an eigenfunction of
the limiting problem along a nodal line. As a consequence, we verify
theoretically some conjectures arising from numerical evidences in preexisting
literature. The proof relies on an Almgren-type monotonicity argument for
magnetic operators together with a sharp blow-up analysis.
