Rutherford cross section

By inserting a semiconductor x-ray detector into the analysis chamber, one can measure particle induced x-rays. The cross section for particle induced x-ray emission (PIXE) is much greater than that for Rutherford backscattering and PIXE is a fast and convenient method for measuring the identity of atomic species within... 

This is the Rutherford scattering cross section. It is interesting to note that Bom and classical theory also reproduce this cross section. Moreover,... 

In the analogous RBS analysis, da/dil is given precisely and analytically by the Rutherford scattering formula. Unfortunately, the case of ( He, H) scattering is not quite so simple. While the processes are indeed elastic, their cross sections are dominated by nuclear interaction components except at very low energies. (The H(%e, iH)%e cross section approaches the Rutherford value for energies below 0.8 MeV.)... 

The absolute precision of ERS therefore depends on that of da/dfl (Ej, (t>). Unfortunately, some disagreement prevails among measurements of the recoil cross section. One recent determination is shown in Figure 4a for (t> = 30° and 25°. The convergence of these data with the Rutherford cross section near 1 MeV lends support to their validity. The solid lines are least squares fits to the polynomial form used by Tirira et al.. For (t> = 30°, the expression reads ... 

The measured cross section data for are shown in Figure 4b. The dominant resonance at 2.13 MeV offers a powerful enhancement to sensitivity for deuterium detection, exceedii the Rutherford cross section by two orders of magnitude. 

The probability for a ion to scatter in a particular direction is determined by the ion-target interaction, and can be expressed in terms of a cross section For a Coulomb potential, the diflFerential cross section is the well-known Rutherford formula ... 

The scattering cross-section is considerably different from the Rutherford cross-section, because the distance of closest approach, Ri i , is rather large at low energies. Thus, electronic screening of the interaction between the nuclei is important. The screened scattering potential V(r) reads ... 

For quantitative evaluation of ERDA energy spectra considerable deviations of recoil cross-sections from the Rutherford cross-section (Eq. 3.51) must be taken into account. Light projectiles with high energy can penetrate the Coulomb barrier of the recoil atom the nuclear interaction generally leads to a cross-section that is larger than ctr, see Eq. (3.51). For example, the H recoil cross-section for MeV He projec-... 

Deviations from Rutherford cross-sections are also found for heavy projectiles at lower impact energies, when the projectile can bind inner shell electrons which screen the nuclear charge. These deviations are usually small and can easily be taken into account by use of a theoretical correction [3.160]. 

If the force between the beam particle and the target nucleus is assumed to be the Coulomb force, the basic equation for the differential scattering cross-section is given by Rutherford s formula ... 

Equation (2.2) is just the Rutherford cross section for scattering of, strictly speaking, free charges. To apply this to atomic electrons that are not free but can be excited4 with energy En, Bohr surmised the sum rule... 

For knock-on collisions, one uses the Rutherford cross section for free electrons, and the number of free electrons is taken equal to the integral of the oscillator strength up to the energy loss e (dispersion approximation). Thus,... 

With this knowledge and using the Rutherford cross section, the energy deposited in the core by the electrons of the first group is given by... 

In Eq. (4.18), it is implicitly assumed that the ionization is a direct, one-electron process that is, the contribution of superexcited states to ionization is not included. The latter process is indirect and essentially of a two-electron nature. When the energy loss is much larger than the ionization potential, however, ionization is almost a certainty. For high energies of the secondary electron, Eq. (4.18) approaches the Rutherford cross section, or the Mott cross section if the incident particle is an electron. 

There is some disagreement in the literature as to the value of the (4He, H) elastic scattering cross section. Values differing by almost a factor of two have been reported, as reviewed by Paszti et al. (1986). The cross section is strongly non-Rutherford, but ab initio calculations have been reported that agree well with the trend of experimental data and could be used in simulation calculations (Tirira et al., 1990). The cross section for deuterium analysis has a resonance near a 4He+ energy of 2.15 MeV, which allows enhanced sensitivity. Detailed measurements of this cross section have been reported by Besenbacher et al. (1986). In practice, rather than calculate an experiment s calibration from first principles, calibration standards are usually used hydrogen-implanted silicon standard are the norm. 

There have been several brave attempts to evaluate generalized oscillator strengths which involve matrix elements of the type of equation (15). Such computations are quite laborious [62] because of numerous high-lying states involved, and much computation time is employed to confirm the validity of Rutherford s law although that may not be evident. More seriously, such calculations can at best serve a complete evaluation of a stopping cross section in... 

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