Energy Loss Calculations

The dominant mechanism for the energy loss in this system is the phenomenon of dielectric energy loss or plasmon loss. For aluminium, the bulk plasmon loss occurs at an energy of 15eV. That is, a photon of energy 15eV will excite an oscillation of the electrons within a large block of aluminium, giving up all its energy in the process. It is also possible to lose energy to the surface plasmon modes. These arise due to rearrangements of the charge on the surface of the objects and they occur at different frequencies to the bulk plasmons. For an isolated sphere, the surface plasmon losses occur at discrete energies given by;
omega sub sphere
= omega sub plasma squareroot(l/(2l+1))
and omega sub plasma is the bulk plasmon energy. Thus for aluminium, the first surface plasmon mode occurs when l=1 and is called the dipole surface plasmon. It occurs at 8.67eV for aluminium.

Other surface plasmons can arrise due to the coupling of spheres, when they are close proximity. However, a theoretical calculation of these coupled surface plasmons is very difficult. Recently, a theoretical calculation was performed on a linear chain of spheres. Previous to that, only a pair of spheres had been succesfully calculated for. In this figure we show the energy loss curves which we calculated using out photonics code OPAL.

Stopping Power
vs. Energy Graph

Note the very broad loss peaks, indictating a whole spectrum of loss modes extending to zero. The major peaks occur below the bulk plasmon energy and the first dipole surface plasmon energy. Furthermore, they cannot be described by the couplings of a pair or chain of spheres. Thus we conclude that the coupled surface plasmons are far more complicated and important to the energy loss than those predicted by simplistic theories.

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