Nuclear stopping power

Equation 9 is an extremely useful description for the differential cross section and has been used extensively in a variety of applications. With the use of Equation 9, the nuclear stopping power becomes ... 

To determine the amount of energy deposited in the surface region. In many instances this is approximated by a quantity proportional to the nuclear stopping power (see Equation 10). 

Fig. 21. Reduced nuclear stopping power, s (e), as a function of e, bottom scale and of E for Ar —Cu, top scale. Based on Thomas-Fermi potential (see Equation 5). (Based on data presented in ref )...

The most interesting feature of the work of Lindhard et al. is the possibility of expressing the electronic and the nuclear stopping power in terms of universal constants, a form independent of the mass and charge of the individual atoms. A universal energy e and a universal range p are defined, and the energy loss is expressed in terms... 

The nuclear stopping power per atom may be computed directly from the impact-parameter integration of the nuclear energy loss. 

Fig. 3. Scaled nuclear stopping power as a function of the projectile energy for protons (short-dashed and thick solid line), antiprotons (long-dashed and dash-dotted lines) and neutral hydrogen incident on hydrogen atoms. Thin solid line ZBL prediction [53] for neutral projectiles. For two of the curves (short-dashed and dashdotted) dynamic target polarization has been accounted for in the calculation.

Fig. 5.2. The universal screening function, Fig. 2.3, can be used to calculate the nuclear stopping power using (5.13). The result is shown in reduced coordinates. Also shown are the nuclear stopping calculations based on the four classical atomic models (Ziegler et al.

At velocities v < VqZ, the energy loss through nuclear elastic collisions becomes important. The so-called nuclear stopping power is given by the following approximate expression" ... 

While the electronic stopping power (de/dp) continuously decreases as the ion speed V decreases, the nuclear stopping power increases as v decreases, goes through a maximum, and then decreases again (Fig. 4.13). 

Fig. 3. Reduced nuclear stopping power vs. reduced energy c calculated for three different interaction potentials (solid lines after Sigmund, 1981), Also shown are the predictions fiem Eq. (23) (open circles).

Nuclear stopping power, Sn for fast ions is similarly obtained as follows ... 

The binding energy is approximately equal to the heat of vaporization of 2-4 eV. The factor aNS is approximately the deposited energy, where a = 0.25 for practical purposes, S is the nuclear stopping power, and dEfdx n = NS ... 

The total stopping power for electrons is the sum of collision and radiative stopping powers, as described in O Chap. 6 in this Volume. These quantities have been tabulated in the ICRU Report 37 for electrons and positrons (ICRU 1989a). The total stopping power for protons, alpha particles (helium ions) and heavy ions is the sum of collision (atomic) and nuclear stopping powers, the latter being important only at low energies. 

Total and nuclear stopping power for protons in aluminum, copper and lead... 

Depending on the energy range of the primary particle, elastic and inelastic collisions take place. Elastic collisions dominate interactions in the kiloelectron volt range. Elastic collisions can be described by the nuclear stopping power, which is defined by the energy loss of the primary particle per path length. 

FIGURE 1 Electronic and nuclear stopping powers versus penetration depth of (a) 100-keV and (b) 100-keV As" ions implanted in polyethylene. Tfie energy loss parameters were calculated by the TRIM (transport of ions in matter) code [13]. 

FIGURE 6 Oxygen depth profile for polyethylene implanted with 5 x 10 B /cm at 100 keV. The nuclear stopping power depth distribution csJculated by means of the TRIM code is shown for comparison. 

The stopping power can be split up into two contributions, as indicated in eq. (8.1). For all but the lowest projectile velocities, it is dominated by processes which lead to ionization or excitation of the target electrons. The resulting term is called the electronic stopping power. At low particle speed, energy is transfened to the target atoms as a whole in elastic collisions. This contribution is often called the nuclear stopping power. 

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