Given an atomic nuclei say C-14 or U-233 or anything in-between or outside the range and given the ratio of protons and neutrons in the nuclei, is there a comprehensive equation or set of equations that can model the strong nuclear force and binding energy of the nuclei, to predict the following:
If you take the rest masses of nuclei as input to your model, then you can use the techniques taught in nuclear physics courses to identify the types of allowed decays, and the total energy released in each decay. A good search term for estimating these decay rates is Fermi's golden rule. However, even for the golden rule, you have to have either a theory which predicts the matrix element for the transition, or you have to have data from a set of similar transitions which you can use as input to the special case that you are trying to predict. In order to predict half-lives and transition probabilities, you also have to have some knowledge about the excitation spectrum of the daughter nucleus.
A famous example where the information went the other way was the prediction by Bethe of a particular excited state in carbon, whose presence makes the triple-alpha process to populate stellar cores with carbon and other "metals."
The techniques that I've described above, where you start with nuclear data and make predictions about other nuclear data, are the subject of most introductory textbooks on nuclear physics. You seem to be also asking about the much harder problem of predicting, from scratch, the energies associated with the ground States of various nuclei. That problem has been at the core of theoretical nuclear physics research for decades. It is not simple. Two search terms are the "semi-empirical mass formula" and the "Argonne v18 potential."
