Inspecting the Information Quantity in Ion-Hydrogen Electron Capture Process with the Shannon Entropy

Information Shannon entropy is calculated for the electron capture process from hydrogen atoms by multicharged Coulomb projectiles. The principal, orbital, and magnetic quantum numbers (n, l, and m) of the electron in the final state on the projectile are considered as all the possible events taking place, like the faces of a “dice”. The big data set of the theoretical eikonal impulse approximation values published by M.S. Gravielle in this book is used. Comparisons with the simple Brinkman–Kramers approximation are displayed when possible. The Shannon entropy is calculated over the discrete variables considering three different sets of quantum numbers, just on n; on n and l; and on n, l, and m. It is found that the more the quantum numbers, the larger is the entropy, indicating that the “surprise” increases with the incorporation of new variables, or, equivalently, new faces of the “dice”. Mathematical limits for large and small velocities are calculated.