  It is shown that recently observed $\alpha$ cluster states a few MeV above
the $\alpha$ threshold energy in $^{52}$Ti correspond to the higher nodal band
states with the $\alpha$+$^{48}$Ca cluster structure, i.e. a vibrational mode
in which the intercluster relative motion is excited. The existence of the
higher nodal states in the $^{48}$Ca core region in addition to the well-known
higher nodal states in $^{20}$Ne and $^{44}$Ti reinforces the importance of the
concept of vibrational motion due to clustering even in medium-weight nuclei
with a $jj$-shell closed core. The higher nodal band and the shell-like ground
band in $^{52}$Ti are described in a unified way by a Luneburg lens-like deep
local potential due to the Pauli principle, which explains the emergence of
backward angle anomaly (anomalous large angle scattering (ALAS)) at low
energies, prerainbows at intermediate energies and nuclear rainbows at high
energies in $\alpha$+$^{48}$Ca scattering. The existence of a $K=0^-$ $\alpha$
cluster band analog to $^{44}$Ti midway between the ground band and the higher
nodal band is inevitably predicted.
