Indirect Measurement For The Astrophysicai Reaction Rates Of ²⁵Mg（p,γ）²⁶ Al

The evolution of the universe began with the Big Bang that formed the elementary particles, through original nuleosynthesis,cohesion phase of the Galaxies, and evolution of the stellar, a vast deep sky and colorful world appeared. From ancient times, the universe has been attracting people to explore the mysteries of itself. Since the 20 th century, a new period for exploration of the universe began with the development of the society and the technology.The discovery of interstellar gamma rays that E=1.809 MeV lead to many researches about the source of large volumes of 26 Al in the Galaxy. The 26 Al and 26 Mg mainly came from the proton capture reaction ²⁵Mg（p,γ）²⁶Al that which one is the critical reaction of the Mg-Al circle in explosive hydrogen burning, it is very important for the research of nuleosynthesis in massive stars, the related research can also explain the reason for the source of large volumes of 26 Al in the Galaxy.At the Gamow peak,the reaction rate of ²⁵Mg（p,γ）²⁶Al consists of 58 keV, 92 keV, 190 keV resonance level. Since the cross section near the Gamow peak is very small, it is very difficult for the direct measurement of 58 keV energy level, so indirect method is the only way in current time. There are three experiments done in the world. They had measured the angulardistribution of 6.364 MeV excited state in 26 Al, then they obtained the spectroscopic factor through fitting data of measurement and theoretical calculation,and further obtained the astrophysical reaction rates of the ²⁵Mg（p,γ）²⁶Al reaction via calculations.The 58 keV resonance state of 25Mg（3He,d）²⁶Al reaction has two components that of l=0 and l=2, but they can’t been distinguished by experimental measurement. The three experiments done in the world obtained the spectroscopic factor via fitting the data of measurement and the two components of l=0 and l=2, therefor error of the result will be large. Moreover, the experimental measurement had a strong interference so that they only got several data points, thus the error of the result is relatively large. The spectroscopic factor of l = 0 component obtained by the three experiments have almost twice the error, so the proton width that mainly depending on the l = 0 component also have almost the same error.This work obtained the ratio between the components of l=0 and l=2 by using the code Nushell@MSU firstly, then calculated the angulardistribution of the two components by using a new program TWOFNR. Next we obtained the spectroscopic factor of 26 Al by fitting the angulardistribution of experimental measurement and theoretical calculation, and then we get the astrophysical reaction rates of the ²⁵Mg（p,γ）²⁶Al reaction.