The reaction dynamics of ¹²C$+{}^{52}$Cr reaction induced via a cluster-structured projectile (¹²C) is examined theoretically using the dynamical cluster decay model (DCM) with respect to the recent experimental data available at wide span of center-of-mass energies ($E_{c.m.}=$41.84-71.20 MeV). In view of the cluster-structured projectile, a systematic analysis is carried out for both complete fusion (CF) and incomplete fusion (ICF) channel. The calculations are done by including the quadrupole (${\beta }_2$) deformations and optimum (${\theta }_i^{opt.}$) orientation criteria of the decaying fragments. With an aim to have comprehensive analysis of the decay of compound nuclei formed via CF and ICF processes, the role of center-of-mass energy ($E_{c.m.}$) and angular momentum (ℓ) is explored in terms of various parameters of DCM such as fragmentation potential, preformation probability, penetrability and barrier modification. Further, the role of diffuseness parameter is also studied for ¹²C$+{}^{52}$Cr reaction. For the given reaction, the contribution of light particles (LPs), and energetically favored intermediate mass fragments (IMFs) constitutes the decay cross sections. Therefore, the contribution of emitted LPs and IMFs is estimated for the decay of both compound nuclei formed via CF and ICF channels. Furthermore, the comparative analysis of different proximity potentials is also worked out for ICF. Finally, the effect of $E_{c.m.}$ on the contribution of ICF cross sections is studied and compared with the experimental data.

¹² C的反应动力学$+{}^{52}$使用动态团簇衰减模型 (DCM) 从理论上检查通过团簇结构射弹 ( ¹² C)诱导的 Cr 反应，该模型关于最近在宽质心能量范围内可用的实验数据 (${乙}_{C.米.}=$41.84-71.20 兆电子伏）。针对团簇结构弹丸，对完全融合（CF）和不完全融合（ICF）通道进行了系统分析。计算是通过包括四极杆 (${\beta }_2$) 变形和最佳 (${\theta }_{\mathrm{一世}}^{○磷吨.}$) 衰变碎片的取向标准。为了综合分析CF和ICF过程形成的复合核的衰变，质心能量的作用（${乙}_{C.米.}$) 和角动量 ( ℓ ) 根据 DCM 的各种参数进行探索，例如碎裂潜力、预成形概率、穿透性和障碍修改。此外，还研究了扩散参数对¹² C 的作用$+{}^{52}$铬反应。对于给定的反应，轻粒子 (LP) 和能量有利的中间质量碎片 (IMF) 的贡献构成了衰变截面。因此，发射的 LP 和 IMF 的贡献估计为通过 CF 和 ICF 通道形成的复合核的衰变。此外，还对ICF进行了不同邻近电位的比较分析。最后是效果${乙}_{C.米.}$ 对 ICF 横截面的贡献进行了研究，并与实验数据进行了比较。