Theoretical Studies of α Condensates in Heavy Self-conjugate Nuclei

α condensates are exotic states in nuclear many-body systems, and can be viewed as the generalization of the Bose-Einstein condensate in nuclear physics. It is widely believed that, α condensates exist not only in ¹²C, but also in heavier self-conjugate nuclei such as ¹⁶O, ²⁰Ne, ²⁴Mg, ²⁸Si, etc. It is important to understand the physical properties of these α condensates in heavy self-conjugate nuclei from the theoretical perspective, and the theoretical results could be a useful reference for the experimental studies. This work reviews the basic frameworks to study α condensates, including the Tohsaki-Horiuchi-Schuck-Röpke wave function, the Yamada-Schuck model, and the recently proposed semi-analytic approximation. The impacts of the four-body interactions of α particles on the physical properties of α condensates are reported. The breakup of α condensates and the one-dimensional α condensates are discussed briefly as the possible future directions in this field.