This paper presents the results of studies of long-lived resonance states of the 6Li nucleus and the radiative capture reaction leading to the synthesis of 6Li. In connection with the importance of the lithium problem for the fields of nuclear physics and nuclear astrophysics, the reactions of primary nucleosynthesis are of great interest for studies and consideration using new calculation methods. Cluster models are a powerful tool for theoretical analysis and solution of this problem. One of these models is the microscopic cluster model, or a method known as the algebraic version of the resonant group method (AVRGM), which will allow us to investigate this problem from a new angle and obtain data on resonance states. For this task, a modified Hasegawa-Nagata potential was chosen, which has its own unique characteristics and exchange parameters. The obtained data were compared with experimental data and it was shown that they showed good agreement, and the applicability of this technique to the description of similar reactions that originate in the first three minutes after the birth of the universe.