The criterion of appearance of unstable thermonuclear reaction in the helium burning shell of AGB stars *

A criterion of the appearance of unstable thermonuclear reaction in the helium burning shell of thermal pulsating AGB (TP-AGB) star is established. The new criterion contains abundant physical information. It involves not only the geometric parameters of the helium burning shell, but also its mechanical, thermal and chemical parameters.The following mechanism of the occurrence and disappearance of unstable thermonuclear reaction in the helium burning shell of TP-AGB star is proposed: The appearance of a region of unstable convection in the helium burning shell of the TP-AGB star triggers unstable thermonuclear reaction which will promote a rapid expansion and a rapid geometric deformation of the shell, thereby removing the unstable thermonuclear reaction.Using the improved program of stellar evolution of Kippenhahn, the evolution of a 5Mo star is followed from the main sequence to the TP-AGB stage. The results show that the new criterion can well reflect the status of the thermonuclear reaction in the helium burning shell of the star. Besides, it is revealed that in the sixth period of thermal pulsation of the star the elements that are dredged up to the surface of the star, are synthesized mainly by thermonuclear reaction under the conditions, temperature lgT2/K < 8.155 and density 4.0 < lg P2 /9 . CM-3 < 4.6.