Stopping Power of Multiply Charged Ions
Received Date: Nov 01, 2014 / Accepted Date: Jan 12, 2015 / Published Date: Jan 15, 2015
Keywords: protons; electronic energy; excitation energy
Fast ions, such as protons and alphas, interact with, and deposit energy in, target ions and molecules by converting kinetic energy of the projectile to target electronic energy. Such energy deposition occurs in situations as different as deep space and plasmas and can involve targets as different as atomic ions and rather complicated organic molecules . In most cases, the deposition of electronic energy by a fast ion with velocity v in a target of scatterer particle density n is described by the equation:
Where S(v) is the stopping cross section of the target and, in the Bethe approximation  which assumes the projectile velocity is much larger than the target electron velocities, is given by:
Here Z1 and Z2 are the projectile charge and target electron number, respectively, and I0 is the target mean excitation energy, The mean excitation energy is defined  as the first energy weighted moment of the dipole oscillator strength distribution:
and is the determining factor for the amount of electronic energy deposited in a target by a fast ion. Thus, for electronic energy deposition by a fast ion at a given velocity in a target, the larger the mean excitation energy of target, the less electronic energy will be deposited. It should also be noted that the target may fragment or some projectile energy may be transferred to the target nuclear kinetic energy, but those possibilities are not considered here.
As an example, consider the simple case of protons colliding with an aluminum ion . The table presents the calculated mean excitation energy  and stopping cross section for a proton with an (arbitrary) velocity of 20 a.u. (10 MeV) colliding with various aluminum ions. No values for the stopping cross section are given for Al11+ and Al12+ as the velocity of the 1s electrons in Al is larger than the projectile velocity, and thus the Bethe approximation does not apply. Otherwise, the results are as expected with theincreasing mean excitation energy of more highly charged ions leading to a decrease in stopping cross section.
It is also interesting to note that the largest changes in the mean excitation energy with ion charge, and thus in the stopping cross section as well, come when the outermost electrons, which give the largest contribution to the stopping cross section, come from differing electronic subshells, such as Al2+ → Al3+, Al8+ → Al9+, and Al10+ → Al11+ (Table 1).
|I0 (au)||S(v=20) (au)|
Table 1: Mean Excitation Energies and Stopping Cross Sections for v = 20a.u. Protons colliding with Aluminum Ions.
Similar results are found for many other of the light ions . Although similar studies have not yet been carried out for heavier atomic ions, similar results are to be expected.
If the target is a molecule or molecular ion, things are much more complicated. In principle the same collision of an ion with a polyatomic target leads to the same conversion of projectile kinetic energy to electronic energy and deposition of electronic energy in the target. Although each target atomic ion has a well-defined mean excitation energy, the same is not true for polyatomic targets. For molecules, the mean excitation energy depends on the molecular conformer  and orientation of the target with respect to the projectile . In addition, while an atomic ion can be excited or ionized, a polyatomic target can be excited, ionized, fractionated, reoriented, or some combination of the foregoing.
Due to the complications mentioned here, very little has been done on polyatomic targets. Little has been done here, but much more work needs to be done, both theoretically and experimentally.
Another, as yet to be theoretically studied system is energy deposition by a polyatomic projectile!
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Citation: Sabin JR (2016) Stopping Power of Multiply Charged Ions. J Phys Chem Biophys 6: e132. Doi: 10.4172/2161-0398.1000e132
Copyright: © 2016 Sabin JR. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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