Proton Stopping Cross-sections

Equations (16) and (17) were then used to calculate the molecular orbital contributions to and - just as Oddershede and Sabin did in their more accurate calculations - a table for the velocity-dependence of core, bond, and lone-pair contributions to Se for protons was constructed [25,42], These results together with equation (10) lead to the calculation of the proton stopping cross section in compound materials with chemical binding effects incorporated. 

Fig. 7. Proton stopping cross section in atomic gaseous targets (a) Oxygen, (b) Argon, (c) Bromine as a function of projectile velocity (atomic units). (—) OLPA-TFD(l/8)W...

Fig. 9. Pressure dependence of the proton stopping cross section in Si as obtained in this work.

The orbital implementation of the KT has established a firm theoretieal basis for the CAB formalism whereby ehemieal binding effects on proton stopping cross sections may be estimated. Furthermore, we have given evidence on the flexibility of this theory to allow for the incorporation of alternative descriptions of orbital and total mean excitation energies - such as the OLPA scheme - which may be adapted for the study of energy-loss problems in matter under different conditions (i.e., gases, solids, and matter under high pressure). 

For gas targets (atomic and molecular) the theory yields quite reasonable predictions of proton stopping cross sections as compared with experiment. Moreover, since chemical binding effects are naturally incorporated in the theory, the construction of tables of the velocity-dependence of CAB contributions to 5 for different compounds allows - once and for all - the estimate of 5 for protons in materials with similar CAB components without resource to Bragg s additivity rule. 

Fig. 14. Comparison of antiproton and proton stopping cross section in atomic hydrogen as a function of the projectile energy. The upper and lower dashed lines are the region of acceptable behavior for the antiproton with the central line being the average fit to the experimental data [64]. The results for protons on hydrogen are identical to Fig. 5.

Prediction of proton stopping cross-sections in metal films[95] and crystals [49, 50]... 

Proton Stopping Cross-sections and Dielectric Functions... 

With colleagues, the first author has used GTOFF (and FILMS) to provide the charge densities and KS bands and orbitals needed as input to both approximate calculations (via the so-called orbital local plasma approximation) and rather precise calculations (via the RPA form of the dielectric function) of the proton stopping cross-sections in metal UTFs [49,50,95,115-117]. Since those calculations rely on GTOFF outputs as inputs to other codes but do not use GTOFF otherwise, in the interest of space we do not review those results here but simply refer the reader to the references just cited. 

Proton Stopping Cross-Sections and Dielectric Functions 216... 

Fig. 8.8. The stopping cross section for coifiding with heUum atoms, as deduced from measurements of the energy ioss per time, is plotted as a funcdon of the projectiie energy and veiocity. It is compared with the proton stopping cross section of Andersen and Segler [3.57]. From Kottmann [8.39],...

Fig. 2. Stopping cross section for protons impinging on oriented H2O as a function of proton velocity. See Fig. 1 for the definition of target orientations.

Fig. 3. Orientationally averaged total stopping cross section St for protons impinging on H2O as a function of proton velocity along with the experimental results of Reynolds et ah (filled circles) [28]. 5 e, and represent the electronic, nuclear, and rovibrational contributions to the stopping, respectively.

Fig. 1. Velocity dependence of the electronic stopping cross section for protons in atomic...

Fig. 2. Velocity dependence of the electronic stopping cross section for protons in propane. (—) prediction by the OLPA-FSGO treatment [42]. ( ) Oddershede and Sabin calculations [29]. (----) best fit curve to experimental data from Refs. [44,45].

Figure 2 Contributions to the total stopping cross section 5t from ionization Ci by and H°, electron capture cec by H, electron loss cel by H°, and excitation o-gx by protons in water. The data are from a compilation by Uehara et al. [14], The ICRU recommendation 5t-ICRU is from Ref 5.

Bond stopping cross sections for protons incident on molecular targets within the OLPA/FSGO implementation of the kinetic theory. ... 

Before proceeding to calculate the stopping cross section, we calculate the fraction of protons,/(H ), and the fraction of neutral hydrogens,/(H), in the beam during the collision according to equation (9). With the calculated values obtained for the electron capture and loss cross sections as shown in Fig. 3, we present in Fig. 4 the fraction of and in the hydrogen beam... 

Fig. 5. Stopping cross section for proton incident on atomic hydrogen as a function of the projectile energy. The lines labeled with END are the results of this work with electronic (e), nuclear (n), and total (nuclear -h electronic = t) contribution. The experiments are [44] O [45] [46] [47] and X [48]. Also, for comparison, we present the results obtained by TRIM-99 [49].

Fig. 9. Stopping cross section per atom for proton projectiles colliding with atomic and molecular hydrogen targets as a function of the acceptance angle 0 for projectiles energies of 0.5, 1.5, 5.0, 10.0, and 25.0 keV. Note the nuclear plus rovibrational contributions when large scattering angles are taken into account.

R. Cabrera-Trujillo, Y. Ohrn, E. Deumens and J.R. Sabin, Stopping cross section in the low to intermediate energy range Study of proton and hydrogen atom collisions with atomic N, O, and F, Phys. Rev. A, 62 (2000) 052714. 

Fig. 4. The electronic stopping cross section vs. incident energy for protons on amorphous carbon Solid line Bethe theory [Eq. (24)] dashed line Lindhard and Seharff (1961) [Eq. (25)] O Kaneko (1993) and A Ziegler et al. (1985).

Fig. 8.1. The stopping cross section, defined as S = -N dEldx, for protons traversing a Ne target is shown here as function of the projectile energy. The points indicate experimental data, while the curve is the semiempirical fit of Andersen and Ziegler [3.57]. This figure was adapted from Besenbacher et al. [8.21] where references to the experimental work can be found.

Compared to EDS, which uses 10-100 keV electrons, PEXE provides orders-of-magnitude improvement in the detection limits for trace elements. This is a consequence of the much reduced background associated with the deceleration of ions (called bremsstrahlun compared to that generated by the stopping of the electrons, and of the similarity of the cross sections for ioiuzing atoms by ions and electrons. Detailed comparison of PIXE with XRF showed that PDCE should be preferred for the analysis of thin samples, surfrce layers, and samples with limited amounts of materials. XRF is better (or bulk analysis and thick specimens because the somewhat shallow penetration of the ions (e.g., tens of pm for protons) limits the analytical volume in PIXE. 

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