  Vortex lines affect the spatial order-parameter distribution in superfluid
3He-B owing to superflow circulating around vortex cores and due to the
interaction of the order parameter in the core and in the bulk as a result of
superfluid coherence over the whole volume. The step-like change of the latter
contribution at 0.6Tc (at a pressure of 29bar) signifies the transition from
axisymmetric cores at higher temperatures to broken-symmetry cores at lower
temperatures. We extended earlier measurements of the core contribution to
temperatures below 0.2Tc, in particular searching for a possible new core
transition to lower symmetries. As a measuring tool we track the energy levels
of magnon condensate states in a trap formed by the order-parameter texture.
