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

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){proportional_to}r{sup -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.

[1]  N. Arista,et al.  Energy loss versus exit angle for H+ and He+ ions channeled in Au (100) at very low energies, and observation of a molecular effect for incident H2+ , 2008 .

[2]  H. Winter,et al.  Rainbow scattering under axial surface channeling , 2005 .

[3]  F. Lovey,et al.  Angular dispersion of protons transmitted through thin gold films , 2004 .

[4]  G. Battistig,et al.  Small angle multiple scattering of fast ions, physics, stochastic theory and numerical calculations , 2003 .

[5]  F. Lovey,et al.  Energy loss and angular dispersion of 2–200 keV protons in amorphous silicon , 2002 .

[6]  M. Fama,et al.  Angular dependence of the energy loss of ions in solids: Computer simulations and analysis of models , 2001 .

[7]  M. Fama,et al.  Energy-angle distribution of low-energy hydrogen ions in thin aluminum and gold foils , 2000 .

[8]  G. V. Dedkov.  The interatomic interaction potentials in radiation physics , 1995 .

[9]  Valdés,et al.  Energy-loss effects in multiple-scattering angular distributions of ions in matter. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[10]  Eckardt,et al.  Energy loss of slow protons in solids: Deviation from the proportionality with projectile velocity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[11]  N. Arista,et al.  Electronic energy loss of low velocity H+ beams in Al, Ag, Sb, Au and Bi , 1993 .

[12]  M. Jakas,et al.  Scaling for the angular variation of the energy loss of ions induced by foil inhomogeneities , 1989 .

[13]  R. Shimizu,et al.  Approximation Formula of Cross-section for the Universal Potential Expression Proposed by Ziegler et al. , 1984 .

[14]  P. Sigmund,et al.  Small-angle multiple scattering of ions in the screened Coulomb region: I. Angular distributions , 1974 .

[15]  L. Meyer,et al.  Plural and multiple scattering of low-energy heavy particles in solids , 1971 .

[16]  J. C. Eckardt,et al.  Preparation of Extremely Thin Self‐Supporting Metal Foils , 1971 .

[17]  W. Bothe.  Das allgemeine Fehlergesetz, die Schwankungen der Feldstärke in einem Dielektrikum und die Zerstreuung derα-Strahlen , 1921 .