  To discuss a possible observation of large-amplitude nuclear shape mixing by
nuclear reaction, we employ a simple collective model and evaluate transition
densities, with which the differential cross sections are obtained through the
microscopic coupled-channel calculation. Assuming the spherical-to-prolate
shape transition, we focus on large-amplitude shape mixing associated with the
softness of the collective potential in the $\beta$ direction. We introduce a
simple model based on the five-dimensional quadrupole collective Hamiltonian,
which simulates a chain of isotopes that exhibit spherical-to-prolate shape
phase transition. Taking $^{154}$Sm as an example and controlling the model
parameters, we study how the large-amplitude shape mixing affects the elastic
and inelastic proton scatterings. The calculated results suggest that the
inelastic cross section of the $2_2^+$ state tells us an important role of the
quadrupole shape mixing.
