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 th e laboratory frame, the picture can be represented as a spatial distributio n of energy losses to the electron. It has been shown that the local rate o f the energy gain can be presented as a product of the induced electron cur rent and the projectile electric field. The analytical results and numerica l calculations reveal a principal disagreement with the generally recognize d condition for the classical description, eta = Z(1)e(2)/(h) over bar grea ter than or similar to 1 (Z(1)e and v are, respectively, the charge and vel ocity 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 analy sis of collisions with electron wavepackets. The main results of the Bloch theory are reproduced in a simpler way. The clearer basis permits us to eli minate the ambiguity in the interpretation of the origin of the Bloch corre ction, which reflects in fact the evolution of the classical features in th e quantum mechanical picture.