Generalized formulation of stopping-power theory for nucleons in the first Born approximation

A generalized formulation of the Bethe theory of stopping power for nucleons is presented without the usual restriction $\frac{\gamma m}{M}\ll 1$, where m and M are the electron and nucleon rest masses, $\gamma ={(1-{\beta }^2)}^{-\frac{1}{2}}$, and β is the ratio of the speed of the nucleon to that of light. New formulas are derived from the general expression for nucleon current and cast in forms that reduce to the ordinary relativistic formulas for heavy charged particles when $\frac{\gamma m}{M}\ll 1$. They also yield directly the transformed Rosenbluth formula, used previously to calculate stopping power for ultrarelativistic protons and muons. The stopping power of matter for relativistic and ultrarelativistic neutrons is calculated in the following paper.