A primary theory for the cold fusion mechanism is proposed early in 1989 by us based on atomic, molecular, nuclear and crystal physics. According to this theory, the cold fusion of deuterons may be raised in crystal with produce of excess heat and fusion products $^4He.$ After this theory, the remarkable effects of excess heat and fusion products $^4He$ were observed during the electrolysis of heavy water with Pd or Ti electrodes in our experimental researches. These results indicate that the prediction in our theory is valid. In order to get more clear understanding for the cold fusion, the further theoretical and experimental research had been studied repeatedly by us in the past twenty years. Through a deep analysis, we find that the cold fusion is arised from the interaction of two adjacent full atoms (contain nucleus and valence electrons) of heavy hydrogen in the interstitial position of crystal. This full atomic theory will be discussed in detail in this paper. According to this theory, we find out that $^3He$ may be made from the cold fusion of heavy hydrogen and hydrogen atoms.