<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>Effect in the Stopping Power of Matter for Charged Particles

We consider in a classical formulation the interaction of a particle of charge ${Z}_{1}e$ incident at a given impact parameter with an electron bound isotropically and harmonically to the origin with a frequency $\ensuremath{\omega}$. Using a perturbation expansion that assumes that the displacement of the bound electron is small compared to the impact parameter, and integrating over the impact parameter from some minimum value to infinity, we are led to an expression for the stopping power. The leading term in this expansion is proportional to ${({Z}_{1}{e}^{2})}^{2}$ and is the usual result for this type of model, while the second term gives us the ${({Z}_{1}{e}^{2})}^{3}$ correction. The ${Z}_{1}^{3}$ correction for the Lenz-Jensen statistical model for the atom is presented. The predictions of this theory are in excellent agreement with available experimental data.