Construction of the analytical solution of uranium nuclear radioactive series

• Firstly, this work firstly dialed with (one-step and two-step nuclear decay problems) simple radioactive decay and successive radioactive decay system and successfully solves these systems. • The core part of this work is presenting first analytical solutions of differential equations in the successive radioactive decay of the nucleus. • The homotopy perturbation method (HPM), which is used in this work, is based on the coherence of homotopy in topology, it is a perturbation technique that continuously transform a complicated problem into a simple problem, it is produces a solution series with rapidly convergent terms that are directly calculated. In this paper, the Uranium nuclear radioactive series, an essential radioactive series in nuclear physics, is fully studied and solved analytically, for the first time, using the homotopy perturbation method (HPM). This work begins by considering single-step radioactive decay and then proceeds to study the successive radioactive decay (parent, daughter, and granddaughter nuclei). The primary focus is the general case of the Uranium nuclear radioactive series the numerical nuclear physics data for the Uranium nuclear radioactive series, as well as both simplifications are considered.