Multiple-scattering distributions and angular dependence of the energy loss of slow protons in copper and silver

Abstract

Measurements of angular distributions and of the angular dependence of the energy loss of 4-, 6-, and 9-keV protons transmitted through thin Cu and Ag polycrystalline foils are presented. By means of standard multiple-scattering model calculations it is found that a V (r) ∝ r −2.8 potential leads to significantly better fits of the angular distributions than the standard Thomas Fermi, Lenz-Jensen, or Ziegler-Biersack-Littmark potentials. A theoretical model for the angular dependence of the energy loss based on considering geometric effects on a frictional inelastic energy loss plus an angular-dependent elastic contribution and the effects of foil roughness reproduces the experimental data. This agrees with previous results in Au and Al, therefore extending the applicability of the model to other metallic elements.

Experimental study and computer simulations of the energy loss straggling of slow ions in thin foils: Results for H+ and D+ in C, Si, Cu, Ag and Bi

“…2%, which is a very good figure for the low energy range. The quality of the transmission spectra obtained with this experimental setup has already been reported in previous publications [10,11].…”

“…In the case of C, Cu and Ag we used a procedure based on the fitting of the angular dependence of the energy loss of protons [10,11]. The usefulness of this method has been verified applying it the case of Si where also AFM roughness determinations had been made [4].…”

“…In fact, the main experimental difficulties at low energies arise from the greater influence of target roughness due to the requirement of using very thin targets, leading to disadvantageous roughness to thickness ratios. For this reason, although there are several accurate measurements of stopping powers down to very low energies ($1-2 keV) [2][3][4][5][6][7][8][9][10][11], there are very few experimental determinations of straggling values for energies below 10 keV [12]. Also, as shown by Konac et al [12], there are significant discrepancies in low-energy straggling data reported by different groups, which gradually disappear at larger energies.…”

Energy loss of low-energy ions in transmission and backscattering experiments

“…For direct transmission, α = 0, the influences of these effects will be minimized, their relative importance depending on ψ 1/2 and on the total energy loss [37]. Possible contributions due to foil thickness variations or roughness will not be considered here [38,39].…”

Multiple scattering of low energy ions in matter: Influence of energy loss and interaction potential

“…A complete review with typical applications of this theory is presented by Amsel et al [11]. Many studies in the low-energy regime containing theoretical and experimental angular distributions have been published [12][13][14][15][16][17][18].…”