  Evolution and coexistence of shape and the related collective states of
even-even Te isotopes are investigated within the quadrupole collective model
that is based on the nuclear density functional theory. By means of the
constrained self-consistent mean-field calculations performed within the
relativistic Hartree-Bogoliubov method with a choice of an energy density
functional and a pairing force, parameters of the triaxial quadrupole
collective Hamiltonian are completely determines. The collective model produces
for the near mid-shell nuclei, e.g., $^{116}$Te and $^{118}$Te, low-energy and
low-spin excited states, including the $0^+_2$ state, that can be interpreted
as the intruder states associated with the strongly deformed prolate minimum in
the potential energy surface, along with the $0^+_1$ ground state that is
attributed to the normal state based on a weakly oblate deformed global
minimum. The collective model calculation suggests the lowering of the $0^+_2$
energy level toward neutron mid-shell, as observed experimentally. The
sensitivity of the mean-field and spectroscopic results to the choice of the
pairing strength is also analyzed, and it is shown that by increasing the
pairing strength description of the low-lying states of the near mid-shell
nuclei is improved.
