Applications of Buschman–fox H-Function in Nuclear Physics

The paper is devoted to presenting a novel closed-form representation of the resonant thermonuclear functions and the nonrelativistic Voigt function, which are essential tools in nuclear physics. Understanding thermonuclear fusion reaction rates within solar analogs is crucial for understanding stellar evolution and energy production mechanisms. Initially, this paper focuses on evaluating fusion reaction rates, particularly emphasizing resonant reactions, which play pivotal roles in stellar evolution phases. A key challenge lies in solving reaction rate integrals in closed form. The Buschman–Fox H-function of two variables is employed to address this issue. Conventionally, it is assumed that the plasma particles' velocity follows the Maxwell–Boltzmann distribution. However, it is acknowledged that particles may deviate from this assumed equilibrium state in actual scenarios, leading to nonequilibrium situations. The study also aims to address these nonequilibrium situations by utilizing appropriate velocity models from the existing literature. Utilizing the Mellin transform technique, we achieve the closed-form representation of the resonant reaction rate integral. Furthermore, we address the nonrelativistic Voigt profile and, in particular, Voigt function. The Voigt profile, resulting from the convolution of Gaussian and Lorentzian distributions, effectively captures the intricate shapes of spectral lines encountered in spectroscopy. Apart from its significance in spectroscopy, the Voigt function finds application in various areas such as plasma nuclear studies, acoustics, and radiation transfer. Many approximations of the Voigt function can be found in the literature, yet currently, there is no existing closed-form expression. This paper also sets out to fill this gap by deriving the exact closed-form expressions for the Voigt function and its conjugate in terms of Buschman–Fox H-function, employing the Mellin convolution theorem. This paper marks the first instance in the literature where the applications of Buschman Fox's H-function has been documented.