On the origin of the Bloch correction in stopping

The energy loss in the collision of a moving charged projectile with a free electron is described in a rigorous approach. The collision is treated as stationary scattering of an electron in the projectile Coulomb field. In the laboratory frame, the picture can be represented as a spatial distribution of energy losses to the electron. It has been shown that the local rate of the energy gain can be presented as a product of the induced electron current and the projectile electric field. The analytical results and numerical calculations reveal a principal disagreement with the generally recognized condition for the classical description, eta = Z(1)e(2)/(h) over bar greater than or similar to 1 (Z(1)e and v are, respectively, the charge and velocity of the projectile): for any value of eta, the quantum effects appear to be significant in the close Vicinity of the projectile trajectory (small impact parameters) restricted by the distance similar to lambda = (h) over bar/mv. Essentially, the problem has been cleared in the qualitative analysis of collisions with electron wavepackets. The main results of the Bloch theory are reproduced in a simpler way. The clearer basis permits us to eliminate the ambiguity in the interpretation of the origin of the Bloch correction, which reflects in fact the evolution of the classical features in the quantum mechanical picture.