On the origin of the Bloch correction in stopping

Abstract

Abstract. 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, η = Z 1 e 2 /hv 1 (Z 1 e and v are, respectively, the charge and velocity of the projectile): for any value of η, the quantum effects appear to be significant in the close vicinity of the projectile trajectory (small impact parameters) restricted by the distance ∼λ =h/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.

Convolution approximation for the energy loss, ionization probability and straggling of fast ions

“…Thus, the three-body problem (active electron, effective target and projectile) is reduced to a two-body one namely the scattering of the active electron described by a wavepacket corresponding to the ground-state wavefunction φ 0 ( r) = r|0 by the projectile potential. This problem can be solved either in the projectile reference frame [16] or in the frame where the target atom is initially at rest. In the latter case, Eq.…”

Depth-dose distribution of proton beams using inelastic-collision cross sections of liquid water

“…The reference data base for Stopping power and range tables for protons (PSTAR) is provided by the National Institute of Standard and Technology (NIST) of the US department of Commerce. These values are obtained, for high energies, through Bethe's stopping formula including shell corrections, Barkas and Bloch corrections [16,17] and density effect corrections. The mean excitation energy, I, used in PSTAR is taken from ICRU 37 [18], corresponding to I = 75 eV for liquid water.…”

Nuclear and electronic contributions to Coulomb correction for Moliere screening angle

“…The term "Coulomb correction" in physics of highenergy atomic collisions conventionally designates deviation from the 1st Born approximation for certain observables, for which it depends solely on the Coulomb parameter -the product of nuclear charges of the colliding particles and their reciprocal collision velocity, but not on the screening function. In 1930-1950-ies, corrections of that kind were independently discovered for ionization energy loss [1][2][3][4][5], multiple Coulomb scattering [6,8,9], bremsstrahlung [10][11][12], and electron-positron pair production [13][14][15]. For different processes, different formalisms were applied, such as partial wave expansion [1][2][3], eikonal approximation [5,6,8,9,12,14], Furry-Sommerfeld-Maue wave functions [4,10,13,15], so, the final results were sometimes presented in different forms, as well.…”

“…In 1930-1950-ies, corrections of that kind were independently discovered for ionization energy loss [1][2][3][4][5], multiple Coulomb scattering [6,8,9], bremsstrahlung [10][11][12], and electron-positron pair production [13][14][15]. For different processes, different formalisms were applied, such as partial wave expansion [1][2][3], eikonal approximation [5,6,8,9,12,14], Furry-Sommerfeld-Maue wave functions [4,10,13,15], so, the final results were sometimes presented in different forms, as well.…”