  In this paper, we have calculated the energy spectrum of 12C isotope by
cluster model. The experimental results show that the "Hoyle" state at 7.65 MeV
in 12C isotope has a well-developed three-alpha structure. Hence, we select a
three-body system and for interaction between the clusters we use modified
Yukawa potential plus coulomb potential. Then, we solve the relativistic
Klein-Gordon equation using Nikiforov-Uvarov method to calculate the energy
spectrum. Finally, the calculated results are compared with the experimental
data. The results show that the isotope 12C should be considered as consisting
of three-alpha cluster and the modified Yukawa potential is adaptable for
cluster interactions.
