  The resonances in $^{12}$C+$^{12}$C system described earlier using long range
Morse potential determined from resonance data itself, are reexamined in the
light of the recent development of the two new methods for identification of
resonances in the scattering theory, namely Imaginary Test Potential and
Imaginary Phase-shift methods. The high lying resonances are found to be not
genuine as pointed out by Kato and Abe, and as such are discarded. This
discomfiture is due to the (i) shallow behavior of the Morse potential at the
outer edge and (ii) inappropriate insertion of Coulomb tail used in that work.
These two deficiencies are now removed in the present study by finding a
modified Morse potential with steep rise in the outer edge, and joining
smoothly to it a term approximating the Coulomb tail. Calculation of the
resonances for this modified Morse potential using the above two methods of
identification of resonances in our study, yields more than 25 states with
angular momenta $0^{+}$ - $12^{+}$ in the relevant energy regions. This
reaffirms the diatomic-like rotational and vibrational picture of the nuclear
molecular resonances in $^{12}$C+$^{12}$C system proposed earlier, and shows
close resemblance with the physics of diatomic molecules, a phenomenon
belonging to altogether a different area. It is revealing that the similarity
extends right upto the level of potential which is Morse type in both the
cases. This study also reveals new features of heavy ion potential.
