A Mathematica Notebook for Alpha Decay Using an Exponentially Diffuse Boundary Potential

Abstract

Using the exponentially diffuse boundary potential of Green and Lee (1955), we develop a Mathematica notebook to treat alpha decay by using the complex energy approach of Preston (1947), as modified by Pierronne and Marquez (1978). Our approach allows the potential to change slowly from the well depth of the interior of the nucleus to the top of the Coulomb barrier, rather than the sudden step of the simple square well used by Pierronne and Marquez. Recent interest in possible variation in coupling constants such as the strong coupling alpha_s motivates us to develop this algorithm which can allow numerical study of the variation of the decay constant of a nucleus such as U-238 when the depth of the nuclear potential well changes.