A new method for the approximate calculation of the potential energy of interaction between two atomic nuclei (the case of the Coulomb interaction)
Modeling of the collision process of atomic nuclei requires knowing the potential energy of their interaction. Increasing the accuracy of the description of the system's shape (i. e. the number of the degrees of freedom), as well as taking into account the structure of atomic nuclei can significantly advance the understanding of the processes during their collision. On the other hand, the rising accuracy of the calculation significantly increases the time of its performamce. Thus, taking into account the four shape parameters (the distance between the centers of mass of the nuclei, the deformation parameter of the projectile nucleus and of the target nucleus, as well as the angle between the line connecting the centers of mass of the nuclei and the axis of symmetry of the target nucleus), the potential energy map takes about one day. Adding the parameter, which describes the orientation of the projectile nucleus in the space, increases the time of calculation of the map by ten times. Calculating all the possible relative orientations of colliding nuclei (three Euler angles) require one more parameter, which increases the calculation time by ten times more. Finally, taking into account the diffuseness of the nuclear surface increases the calculation time by a thousand times. As a result, the problem of calculating the potential energy map of atomic nuclei interaction becomes practically impossible. In this paper, the authors propose an approximation method to speed up the process of calculating the interaction energy of colliding atomic nuclei, while the accuracy of the calculation remains high enough. The proposed method can significantly accelerate the process of calculating the interaction energy of colliding atomic nuclei, while the calculation accuracy remains high enough. The method was tested to calculate the potential energy of the Coulomb interaction between two spherical atomic nuclei located at the different distance from each other. The paper compares the accuracy and time of calculations performed using traditional methods, the proposed approximate method and the analytical formula for the Coulomb interaction of two spherically symmetric atomic nuclei. The results show that the application of the developed method is appropriate in calculations that take into account the deformation and mutual orientation of colliding nuclei, as well as, if necessary, take into account the diffuseness of the distribution of nuclear matter (the diffuseness of the nuclear surface).