Cometary globules, dense molecular gas structures exposed to the UV radiation, are found inside HII regions. Understanding the nature and origin of these structures through a kinematic study of the molecular gas is useful to advance in our knowledge of the interplay between radiation and molecular gas. Using ASTE we carried out molecular observations towards two cometary globules (Sim129 and Sim130) in the HII region Sh2-236. We mapped two regions with the 12CO J=3-2 and HCO+ J=4-3 lines. Additionally, two single pointings of C2H (N=4-3), HNC and HCN J=4-3 were observed. We combined our observations with public infrared and optical data to analyse the distribution and kinematics of the gas. We found kinematic signatures of infalling gas in the 12CO J=3-2 and C2H J=4-3 spectra towards Sim129 . We detected HCO+, HCN, and HNC J=4-3 only towards Sim130. The HCN/HNC integrated ratio of about 3 found in Sim130 suggests that the possible star formation activity within the globule has not yet ionized the gas. The location of NVSS 052255+33315, which peaks towards the brightest border of the globule, supports this scenario. The non-detection of these molecules towards Sim129 could be due to the radiation arising from the star formation activity inside this globule. The ubiquitous presence of the C2H molecule towards both globules shows the action of nearby O-B stars irradiating their external layers. Based on mid-infrared emission, we identified two new structures: a region of diffuse emission (R1) located, in projection, in front of the head of Sim129, and a pillar-like feature (P1) placed besides Sim130. Based on 12CO J=3-2, we found molecular gas associated with Sim129, Sim130, R1 and P1 at radial velocities of -1.5, -11, +10, and +4 km/s, respectively. Therefore, while Sim129 and P1 are located at the far side of the shell, Sim130 is placed at the near side, consistent with earlier results.
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