Density functional calculation of stopping power of an electron gas for slow ions

We describe the first calculation of the stopping power of an electron gas for slow ions using the density-functional formalism. We evaluate the nonlinear self-consistent potential around the ion and from scattering theory determine the energy loss directly. Comparison with the results of linear theory is made.     

电子关联效应对金离子的影响

运用多组态Dirac-Fock(MCDF)方法,考虑不同的电子关联效应,详细地研究了类Li,类Be,类B,类Na,类Mg,类Al,类Cu,类Zn,以及类Ga金离子的特性.结果表明,考虑价电子与原子实的电子相互作用,其结果更加符合实验和其他理论结果. 关键词： 电子关联效应 能级 波长     

Effective stopping charges and stopping power calculations for heavy ions

In this study the model suggested by Sugiyama has been developed and applied for the calculation of the stopping powers for nonrelativistic heavy ions in various target materials. Sugiyama's model has been expanded to low and high energy regions in our work. Analytical expressions are obtained in the modified BB stopping power formula for the effective charge and effective mean excitation energies. In the modified LSS formula, a quasi-molecule criterion has been applied to both the projectiles and the target atoms. Electronic excitation contribution, S _e0, and quasi-molecule contribution, S _ei , to stopping power were found for a wide energy region. It is observed that in intermediate energy region both contributions have maxima. The stopping power due to excitation-ionization in the intermediate and higher energy region is found to be dominant, whereas quasi-molecule contribution is dominant in the lower energy region. The calculated results of stopping power are in good agreement with experimental data for various ions and targets within a few percent in a wide projectile energy range.     

Reciprocity in the electronic stopping of slow ions in matter

The principle of reciprocity, i.e., the invariance of the inelastic excitation in ion-atom collisions against interchange of projectile and target, has been applied to the electronic stopping cross section of low-velocity ions and tested empirically on ion-target combinations supported by a more or less adequate amount of experimental data. Reciprocity is well obeyed (within ~10%) for many systems studied, and deviations exceeding ~20% are exceptional. Systematic deviations such as gas-solid or metal-insulator differences have been looked for but not identified on the present basis. A direct consequence of reciprocity is the equivalence of Z₁ with Z₂ structure for random slowing down. This feature is reasonably well supported empirically for ion-target combinations involving carbon, nitrogen, aluminium and argon. Reciprocity may be utilized as a criterion to reject questionable experimental data. In cases where a certain stopping cross section has not been or cannot be measured, the stopping cross section for the inverted system may be available and serve as a first estimate. It is suggested to build in reciprocity as a fundamental requirement into empirical interpolation schemes directed at the stopping of low-velocity ions. Examination of the SRIM and MSTAR codes reveals cases where reciprocity is obeyed accurately, but deviations of up to a factor of two are common. In case of heavy ions such as gold, electronic stopping cross sections predicted by SRIM are asserted to be almost an order of magnitude too high.     

Channeling stopping power for high energy ions

Making use of the inelastic scattering function introduced by Ohtsuki, the position dependent stopping power is derived for energetic ions in a channeling condition. We can interprete the Lindhard theory, Esbensen-Golovchenko theory, and Burenkov-Komarov-Kumakhov theory for the channeling stopping power in terms of our method. Our results agree very well with experiment.     

Measurement of the stopping power of Au and MgF2 for slow muons

The spectral flux densityn(T) of ^– emerging from a Au or MgF₂ moderator has been measured at low energiesT using time-of-flight. Fromn(T) the stopping powerS(T) of Au was determined for 2 keVT22 keV, and of MgF₂ for 2 keVT12 keV. For Au,S(T) is smaller than calculated values obtained from proton atomic data practically in the wholeT range (Barkas effect); at lowT S(T) approaches the calculated values. For MgF₂,S(T) agrees fairly with the calculated values above 5 keV and then drops below these values. We ascribe this dropping to the large energy gap of the MgF₂ insulator.We wish to thank H. Angerer, H. Plendl, G. Schmidt, and C.A. Schug for help with the data taking, J. Homolka for computational help, H. Hagn, and H. Weiss for technical assistance and P. Maier-Komor and R. Scherrer for manufacturing the windows and targets. The hospitality of PSI and financial support by the German Bundesministerium für Forschung und Technologie are acknowledged.     

Apparent velocity threshold in the electronic stopping of slow hydrogen ions in LiF

The electronic energy loss of hydrogen ions (protons and deuterons) in thin supported films of LiF has been studied in backscattering geometry for specific energies from 700 eV/u to 700 keV/u, using Rutherford backscattering spectroscopy and time-of-flight low-energy ion scattering spectroscopy. For specific energies below 8 keV/u, our data confirm velocity proportionality for the stopping cross section epsilon (like in a metal) down to 3.8 keV/u, as observed previously for protons and antiprotons despite the large band gap (14 eV) of LiF. Below 3.8 keV/u, the present results indicate an apparent velocity threshold at about 0.1 a.u. for the onset of electronic stopping.     

Electronic excitations of slow ions in a free electron gas metal: evidence for charge exchange effects

Electronic energy loss of light ions transmitted through nanometer films of Al has been studied at very low ion velocities. For hydrogen, the electronic stopping power S is found to be perfectly proportional to velocity, as expected for a free electron gas. For He, the same is anticipated, but S shows a transition between two distinct regimes, in both of which S is velocity proportional-however, with remarkably different slopes. This finding can be explained as a consequence of charge exchange in close encounters between He and Al atoms, which represents an additional energy loss channel.     

Comparative study of various stopping power formulations for heavy ions in solids

A comparative study of different energy loss formulations viz. Benton and Henke, Mukherjee and Nayak, Zieglar et al. and Hubert et al. has been done at lower energies (0.5 to 5 MeV/n) with the aim to identify their relative validity in this energy range. Calculated results using these formulations have been compared with experimental results available in literature.     

Experimental study and Monte Carlo simulation of the correlation between electron emission and stopping power for swift proton impact on amorphous carbon target

It is usually well accepted that for swift protons, the induced backward and forward electron emission yield is proportional to the projectile electronic stopping power. This was observed in particular for thin amorphous carbon foils. However, this law was established from a non extensive set of experimental data and somewhat confirmed by rough macroscopic theories. We then developed a standard Monte Carlo simulation to predict the yield dependence on proton energy [0.5–10 MeV] and for a wide range of foil thickness. After evaluating the reliability of this simulation, we showed and explained why the law of proportionality cannot generally hold for forward electron emission. In particular, the ratio between forward yield and stopping power generally depends on foil thickness and proton energy. We performed a new experiment that confirmed our theoretical predictions. Received 9 March 2001     

Velocity dependence in low-velocity electronic stopping power of heavy ions

The velocity dependence in the low-velocity electronic stopping power of heavy ions has been studied for Al and Si ions in Ta in the velocity region 0.4v₀−4v₀ (v₀ is the Bohr velocity). The first experimental information is obtained from the range distribution and Doppler-shift-attenuation data.     

Interplay of charge exchange and projectile excitation in the stopping of swift heavy ions

The electronic energy loss of a dressed ion penetrating through matter is commonly considered as being synonymous with the sum of the excitation energies of the target and the projectile in atomic collisions undergone during the passage. We show that this is not justified in projectile-ionizing collisions and discuss some consequences. Received 23 October 2002 / Received in final form 1st December 2002 Published online 18 February 2003     

Calculation of stopping power for partially stripped ions using an oscillator model

Collision of swift ions with atoms was considered in this paper. The projectile and target atoms were modeled as assemblies of quantum oscillators and it was assumed that both, target and projectile could be excited or ionized, without charge exchange. The model presented here is an extension of the one given by Sigmund and Haagerup [Phys. Rev. A 34, 892 (1986)]. The number of electrons bound to the projectile, as a function of the projectile velocity, was used from Cabrera-Trujillo et al. [Phys. Rev. A 55, 2864 (1997)]. Contributions to energy loss from excitation of the projectile and targets were separately considered. It has been found that projectile excitation contributes up to 20% to the total energy loss in the lower energy region. Comparisons with other authors, including SRIM 2003, are also given and good agreement was found.