Threshold effects in the energy loss of slow protons in metals and insulators

E. A. FIGUEROA, E. D. CANTERO, J. C. ECKARDT, G. H. LANTSCHNER, J.E. VALDÉS, N. R. ARISTA, L.N. SERKOVIC, E.A. SÁNCHEZ, O. GRIZZI

Playa del Cármen, México

Workshop; 27th Brandt-Ritchie Workshop; 2007

It has been commonly accepted for many years, based on experimental evidence and theoretical expectations, that the energy loss of point particles in metals, in the range of low velocities, should be proportional to the ion velocity, whereas, in the case of insulators, significant deviations from this dependence should be expected. Previous experiments in our laboratory [1] showed unexpected deviations from the velocity proportionality in some poly-crystalline metals (Cu, Ag, and Au) in the extreme of low energies, which were explained in terms of band structure effects related to the properties of d electrons in transition or noble metals. More recently, by combining two experimental techniques we have been able to explore with more detail the energy loss of protons in very different type of targets: (a) mono-crystalline Au targets, using channeling techniques, and (b) high band-gap insulator layer (AlF3), using transmission and time of flight (TOF) techniques. One one side, the measurements of the energy loss of protons and deuterons channeled in very thin single-crystal foil of Au provide the most clear evidence of the deviation of the energy loss from the proportionality with ion velocity in a metal, showing a transition between two well defined regimes [2]. This behavior is explained by a theoretical model based on quantum scattering, which takes into account the electronic band structure of Au, separating the contribution of the conduction band (described as a free Fermi gas) from that of the nearly-free d electrons, which are affected by a threshold behavior due to the shift of the density of states with respect to the Fermi level. On the other hand, the measurements of proton energy losses in fresh AlF3, evaporated in situ on self-supported C foils, showed an almost linear increase of the stopping power with the mean projectile velocity, starting from a velocity threshold located at about 0.1 a.u. [3]. These features are also well reproduced by the former quantum scattering model taking into account in this case the excitation of valence electrons and the properties of the electronic bands of the insulators. The model uses the known values of the insulator gap and electron density, and the velocity distribution of the active 2p electrons in the F- anions. The model also reproduces the threshold behavior observed previously on LiF [2]. [1] J.E. Valdés, J.C. Eckardt, G.H. Lantschner, and N.R. Arista, Phys. Rev. A 49, 1083 (1994). [2] E. A. Figueroa, E. D. Cantero, J. C. Eckardt, G. H.Lantschner, J. E. Valdés and N. R. Arista, Physical Review A 75, 010901 /p.1-4 (2007). [3] L.N. Serkovic, E.A. Sánchez, O. Grizzi, J.C. Eckardt, G.H. Lantschner and N.R. Arista, Physical Review A 76, 040901, p.1-4 (2007). [4] M. Draxler, S. P. Chenakin, S. N. Markin, and P. Bauer, Phys. Rev. Lett. 95, 113201 (2005).(a) mono-crystalline Au targets, using channeling techniques, and (b) high band-gap insulator layer (AlF3), using transmission and time of flight (TOF) techniques. One one side, the measurements of the energy loss of protons and deuterons channeled in very thin single-crystal foil of Au provide the most clear evidence of the deviation of the energy loss from the proportionality with ion velocity in a metal, showing a transition between two well defined regimes [2]. This behavior is explained by a theoretical model based on quantum scattering, which takes into account the electronic band structure of Au, separating the contribution of the conduction band (described as a free Fermi gas) from that of the nearly-free d electrons, which are affected by a threshold behavior due to the shift of the density of states with respect to the Fermi level. On the other hand, the measurements of proton energy losses in fresh AlF3, evaporated in situ on self-supported C foils, showed an almost linear increase of the stopping power with the mean projectile velocity, starting from a velocity threshold located at about 0.1 a.u. [3]. These features are also well reproduced by the former quantum scattering model taking into account in this case the excitation of valence electrons and the properties of the electronic bands of the insulators. The model uses the known values of the insulator gap and electron density, and the velocity distribution of the active 2p electrons in the F- anions. The model also reproduces the threshold behavior observed previously on LiF [2]. [1] J.E. Valdés, J.C. Eckardt, G.H. Lantschner, and N.R. Arista, Phys. Rev. A 49, 1083 (1994). [2] E. A. Figueroa, E. D. Cantero, J. C. Eckardt, G. H.Lantschner, J. E. Valdés and N. R. Arista, Physical Review A 75, 010901 /p.1-4 (2007). [3] L.N. Serkovic, E.A. Sánchez, O. Grizzi, J.C. Eckardt, G.H. Lantschner and N.R. Arista, Physical Review A 76, 040901, p.1-4 (2007). [4] M. Draxler, S. P. Chenakin, S. N. Markin, and P. Bauer, Phys. Rev. Lett. 95, 113201 (2005).