  Background : Recently, Bijker et al. [Phys. Rev. Lett. 122, 162501 (2019)]
explained the rotation-vibration spectrum of 13C by assuming triangular nuclear
shape with D'3h symmetry. Purpose : The purpose of this work is to test the
shape and symmetry of 13C based on a microscopic nuclear model without
assumption of nuclear shape. Method : We have applied the real-time evolution
method to 13C. By using the equation-of-motion of clusters, the model describes
the 3alpha+n system without any assumption of symmetry. Results : REM described
the low-lying states more accurately than the previous cluster model studies.
The analysis of the wave functions showed that the ground band has approximate
triangular symmetry, while the excited bands deviate from it. Conclusion : This
work confirmed that the ground band has the intrinsic structure with the
triangular arrangement of three alpha particles.
