Calculation of the first four moments of electronic energy loss of protons in aluminium

• Published in: Radiation effects and defects in solids 2001-01, Vol.153 (2), p.103-114
• Main Authors: Biersack, J. P., Blass, A.
• Format: Article
• Language: English
• Subjects: Applied sciences; Atomic and molecular collision processes and interactions; Atomic and molecular physics; Channeling phenomena (blocking, energy loss, etc.); Condensed matter: structure, mechanical and thermal properties; Electronic energy loss; Electronic stopping power; Energy loss and stopping power; Exact sciences and technology; Metals and alloys; Metals. Metallurgy; Physics; Radiation effects on specific materials; Scattering of atoms, molecules and ions; Structure of solids and liquids; crystallography
• ISSN: 1042-0150; 1029-4953
• DOI: 10.1080/10420150108213264

We present a novel scheme for calculating electronic energy losses and their higher moments which allows to fully account for the electronic structure of solids. Typical structures in solid materials are found in metals with their half filled conduction bands, and in insulators which exhibit a completely filled valence band, and above this a forbidden band gap. The conduction electrons in a metal resemble most closely a free electron gas which would fill a Fermi sphere in velocity space (or in momentum space) homogeneously from ν = 0 to ν = νF. The core electrons are separated from the freely available phase space by distinct band gaps. For protons slowing-down in metals, this means that conduction electrons can accept small energy transfers which are inacceptable for core electrons or valence electrons in insulators. This leads to a completely different stopping behavior of metals, particularly at low velocities. In metals we expect that all energy loss moments increase strictly proportional to νn starting at zero velocity, i.e., the energy loss proportional to ν1, the energy loss straggling proportional to ν 2 etc. We perform the stopping calculations first for the metal Al, where the theoretical input is well known, and where most measurements have been performed. The comparison of theory and experiments shows agreement within the experimental straggle.